1
|
Deng Q, Guo T, Qiu Z, Chen Y. A mathematical model for HIV dynamics with multiple infections: implications for immune escape. J Math Biol 2024; 89:6. [PMID: 38762831 DOI: 10.1007/s00285-024-02104-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2023] [Revised: 12/15/2023] [Accepted: 04/25/2024] [Indexed: 05/20/2024]
Abstract
Multiple infections enable the recombination of different strains, which may contribute to viral diversity. How multiple infections affect the competition dynamics between the two types of strains, the wild and the immune escape mutant, remains poorly understood. This study develops a novel mathematical model that includes the two strains, two modes of viral infection, and multiple infections. For the representative double-infection case, the reproductive numbers are derived and global stabilities of equilibria are obtained via the Lyapunov direct method and theory of limiting systems. Numerical simulations indicate similar viral dynamics regardless of multiplicities of infections though the competition between the two strains would be the fiercest in the case of quadruple infections. Through sensitivity analysis, we evaluate the effect of parameters on the set-point viral loads in the presence and absence of multiple infections. The model with multiple infections predict that there exists a threshold for cytotoxic T lymphocytes (CTLs) to minimize the overall viral load. Weak or strong CTLs immune response can result in high overall viral load. If the strength of CTLs maintains at an intermediate level, the fitness cost of the mutant is likely to have a significant impact on the evolutionary dynamics of mutant viruses. We further investigate how multiple infections alter the viral dynamics during the combination antiretroviral therapy (cART). The results show that viral loads may be underestimated during cART if multiple-infection is not taken into account.
Collapse
Affiliation(s)
- Qi Deng
- School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing, 210094, People's Republic of China
- Department of Mathematics, Wilfrid Laurier University, Waterloo, N2L 3C5, Canada
| | - Ting Guo
- Aliyun School of Big Data, Changzhou University, Changzhou, 213164, People's Republic of China
| | - Zhipeng Qiu
- School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing, 210094, People's Republic of China
| | - Yuming Chen
- Department of Mathematics, Wilfrid Laurier University, Waterloo, N2L 3C5, Canada.
| |
Collapse
|
2
|
Zitzmann C, Ke R, Ribeiro RM, Perelson AS. How robust are estimates of key parameters in standard viral dynamic models? PLoS Comput Biol 2024; 20:e1011437. [PMID: 38626190 PMCID: PMC11051641 DOI: 10.1371/journal.pcbi.1011437] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2023] [Revised: 04/26/2024] [Accepted: 04/01/2024] [Indexed: 04/18/2024] Open
Abstract
Mathematical models of viral infection have been developed, fitted to data, and provide insight into disease pathogenesis for multiple agents that cause chronic infection, including HIV, hepatitis C, and B virus. However, for agents that cause acute infections or during the acute stage of agents that cause chronic infections, viral load data are often collected after symptoms develop, usually around or after the peak viral load. Consequently, we frequently lack data in the initial phase of viral growth, i.e., when pre-symptomatic transmission events occur. Missing data may make estimating the time of infection, the infectious period, and parameters in viral dynamic models, such as the cell infection rate, difficult. However, having extra information, such as the average time to peak viral load, may improve the robustness of the estimation. Here, we evaluated the robustness of estimates of key model parameters when viral load data prior to the viral load peak is missing, when we know the values of some parameters and/or the time from infection to peak viral load. Although estimates of the time of infection are sensitive to the quality and amount of available data, particularly pre-peak, other parameters important in understanding disease pathogenesis, such as the loss rate of infected cells, are less sensitive. Viral infectivity and the viral production rate are key parameters affecting the robustness of data fits. Fixing their values to literature values can help estimate the remaining model parameters when pre-peak data is missing or limited. We find a lack of data in the pre-peak growth phase underestimates the time to peak viral load by several days, leading to a shorter predicted growth phase. On the other hand, knowing the time of infection (e.g., from epidemiological data) and fixing it results in good estimates of dynamical parameters even in the absence of early data. While we provide ways to approximate model parameters in the absence of early viral load data, our results also suggest that these data, when available, are needed to estimate model parameters more precisely.
Collapse
Affiliation(s)
- Carolin Zitzmann
- Theoretical Biology and Biophysics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico
| | - Ruian Ke
- Theoretical Biology and Biophysics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico
| | - Ruy M. Ribeiro
- Theoretical Biology and Biophysics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico
| | - Alan S. Perelson
- Theoretical Biology and Biophysics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico
| |
Collapse
|
3
|
Cassidy T, Stephenson KE, Barouch DH, Perelson AS. Modeling resistance to the broadly neutralizing antibody PGT121 in people living with HIV-1. PLoS Comput Biol 2024; 20:e1011518. [PMID: 38551976 PMCID: PMC11006161 DOI: 10.1371/journal.pcbi.1011518] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2023] [Revised: 04/10/2024] [Accepted: 03/14/2024] [Indexed: 04/11/2024] Open
Abstract
PGT121 is a broadly neutralizing antibody in clinical development for the treatment and prevention of HIV-1 infection via passive administration. PGT121 targets the HIV-1 V3-glycan and demonstrated potent antiviral activity in a phase I clinical trial. Resistance to PGT121 monotherapy rapidly occurred in the majority of participants in this trial with the sampled rebound viruses being entirely resistant to PGT121 mediated neutralization. However, two individuals experienced long-term ART-free viral suppression following antibody infusion and retained sensitivity to PGT121 upon viral rebound. Here, we develop mathematical models of the HIV-1 dynamics during this phase I clinical trial. We utilize these models to understand the dynamics leading to PGT121 resistance and to identify the mechanisms driving the observed long-term viral control. Our modeling highlights the importance of the relative fitness difference between PGT121 sensitive and resistant subpopulations prior to treatment. Specifically, by fitting our models to data, we identify the treatment-induced competitive advantage of previously existing or newly generated resistant population as a primary driver of resistance. Finally, our modeling emphasizes the high neutralization ability of PGT121 in both participants who exhibited long-term viral control.
Collapse
Affiliation(s)
- Tyler Cassidy
- School of Mathematics, University of Leeds, Leeds, United Kingdom
| | - Kathryn E. Stephenson
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, Massachusetts, United States of America
- Division of Infectious Diseases, Beth Israel Deaconess Medical Center, Boston, Massachusetts, United States of America
- Ragon Institute of MGH, MIT and Harvard, Cambridge, Massachusetts, United States of America
| | - Dan H. Barouch
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, Massachusetts, United States of America
- Division of Infectious Diseases, Beth Israel Deaconess Medical Center, Boston, Massachusetts, United States of America
- Ragon Institute of MGH, MIT and Harvard, Cambridge, Massachusetts, United States of America
| | - Alan S. Perelson
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, New Mexico, United States of America
| |
Collapse
|
4
|
Clarke C, Pankavich S. Three-stage modeling of HIV infection and implications for antiretroviral therapy. J Math Biol 2024; 88:34. [PMID: 38418658 DOI: 10.1007/s00285-024-02056-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2023] [Revised: 12/01/2023] [Accepted: 01/28/2024] [Indexed: 03/02/2024]
Abstract
We consider a deterministic model of HIV infection that involves macrophages as a long-term active reservoir to describe all three stages of the disease process: the acute stage, chronic infection, and the transition to AIDS. The proposed model is shown to retain crucial properties, such as the positivity of solutions, regardless of variations in model parameters. A dynamical analysis is performed to identify the local stability properties of the viral clearance steady state. This analysis illustrates how chronically infected macrophages can explain the progression to AIDS and provoke viral explosion, while previous models do not. We further demonstrate that the infected T-cell population, even if not responsible for the majority of new infections that lead to viral explosion, may contribute significantly to the transition amongst the three stages of infection. Moreover, we explore the implications of the model for the administration of antiretroviral therapy (ART) and provide quantitative estimates that emphasize the time sensitive nature of treatment initiation and the level of drug efficacy. Finally, we study the effects of treatment interruption on the disease dynamics predicted by the model and elucidate the influence of both interruption time and duration.
Collapse
Affiliation(s)
- Cameron Clarke
- Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO, 80403, USA
| | - Stephen Pankavich
- Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO, 80403, USA.
| |
Collapse
|
5
|
Lai H, Li R, Li Z, Zhang B, Li C, Song C, Zhao Q, Huang J, Zhu Q, Liang S, Chen H, Li J, Liao L, Shao Y, Xing H, Ruan Y, Lan G, Zhang L, Shen M. Modelling the impact of treatment adherence on the transmission of HIV drug resistance. J Antimicrob Chemother 2023:dkad186. [PMID: 37311203 DOI: 10.1093/jac/dkad186] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2023] [Accepted: 05/30/2023] [Indexed: 06/15/2023] Open
Abstract
INTRODUCTION A lower adherence rate (percentage of individuals taking drugs as prescribed) to ART may increase the risk of emergence and transmission of HIV drug resistance, decrease treatment efficacy, and increase mortality rate. Exploring the impact of ART adherence on the transmission of drug resistance could provide insights in controlling the HIV epidemic. METHODS We proposed a dynamic transmission model incorporating the CD4 cell count-dependent rates of diagnosis, treatment and adherence with transmitted drug resistance (TDR) and acquired drug resistance. This model was calibrated and validated by 2008-2018 HIV/AIDS surveillance data and prevalence of TDR among newly diagnosed treatment-naive individuals from Guangxi, China, respectively. We aimed to identify the impact of adherence on drug resistance and deaths during expanding ART. RESULTS In the base case (ART at 90% adherence and 79% coverage), we projected the cumulative total new infections, new drug-resistant infections, and HIV-related deaths between 2022 and 2050 would be 420 539, 34 751 and 321 671. Increasing coverage to 95% would reduce the above total new infections (deaths) by 18.85% (15.75%). Reducing adherence to below 57.08% (40.84%) would offset these benefits of increasing coverage to 95% in reducing infections (deaths). Every 10% decrease in adherence would need 5.07% (3.62%) increase in coverage to avoid an increase in infections (deaths). Increasing coverage to 95% with 90% (80%) adherence would increase the above drug-resistant infections by 11.66% (32.98%). CONCLUSIONS A decrease in adherence might offset the benefits of ART expansion and exacerbate the transmission of drug resistance. Ensuring treated patients' adherence might be as important as expanding ART to untreated individuals.
Collapse
Affiliation(s)
- Hao Lai
- China-Australia Joint Research Center for Infectious Diseases, School of Public Health, Xi'an Jiaotong University Health Science Center, Xi'an, Shaanxi 710061, P.R. China
| | - Rui Li
- China-Australia Joint Research Center for Infectious Diseases, School of Public Health, Xi'an Jiaotong University Health Science Center, Xi'an, Shaanxi 710061, P.R. China
| | - Zengbin Li
- China-Australia Joint Research Center for Infectious Diseases, School of Public Health, Xi'an Jiaotong University Health Science Center, Xi'an, Shaanxi 710061, P.R. China
| | - Baoming Zhang
- College of Stomatology, Xi'an Jiaotong University, Xi'an, Shaanxi 710004, P.R. China
- Key Laboratory of Shaanxi Province for Craniofacial Precision Medicine Research, College of Stomatology, Xi'an Jiaotong University, Xi'an, Shaanxi 710004, P.R. China
- School of Public Health, Xi'an Jiaotong University Health Science Center, Xi'an, Shaanxi 710061, P.R. China
| | - Chao Li
- School of Public Health, Xi'an Jiaotong University Health Science Center, Xi'an, Shaanxi 710061, P.R. China
| | - Chang Song
- State Key Laboratory of Infectious Disease Prevention and Control (SKLID), National Center for AIDS/STD Control and Prevention (NCAIDS), Chinese Center for Disease Control and Prevention (China CDC), Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases, Beijing 102206, P.R. China
| | - Quanbi Zhao
- State Key Laboratory of Infectious Disease Prevention and Control (SKLID), National Center for AIDS/STD Control and Prevention (NCAIDS), Chinese Center for Disease Control and Prevention (China CDC), Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases, Beijing 102206, P.R. China
| | - Jinghua Huang
- Guangxi Key Laboratory of Major Infectious Disease Prevention Control and Biosafety Emergency Response, Guangxi Center for Disease Control and Prevention, Nanning 530028, P.R. China
| | - Qiuying Zhu
- Guangxi Key Laboratory of Major Infectious Disease Prevention Control and Biosafety Emergency Response, Guangxi Center for Disease Control and Prevention, Nanning 530028, P.R. China
| | - Shujia Liang
- Guangxi Key Laboratory of Major Infectious Disease Prevention Control and Biosafety Emergency Response, Guangxi Center for Disease Control and Prevention, Nanning 530028, P.R. China
| | - Huanhuan Chen
- Guangxi Key Laboratory of Major Infectious Disease Prevention Control and Biosafety Emergency Response, Guangxi Center for Disease Control and Prevention, Nanning 530028, P.R. China
| | - Jianjun Li
- Guangxi Key Laboratory of Major Infectious Disease Prevention Control and Biosafety Emergency Response, Guangxi Center for Disease Control and Prevention, Nanning 530028, P.R. China
| | - Lingjie Liao
- State Key Laboratory of Infectious Disease Prevention and Control (SKLID), National Center for AIDS/STD Control and Prevention (NCAIDS), Chinese Center for Disease Control and Prevention (China CDC), Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases, Beijing 102206, P.R. China
- Guangxi Key Laboratory of Major Infectious Disease Prevention Control and Biosafety Emergency Response, Guangxi Center for Disease Control and Prevention, Nanning 530028, P.R. China
| | - Yiming Shao
- State Key Laboratory of Infectious Disease Prevention and Control (SKLID), National Center for AIDS/STD Control and Prevention (NCAIDS), Chinese Center for Disease Control and Prevention (China CDC), Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases, Beijing 102206, P.R. China
- Guangxi Key Laboratory of Major Infectious Disease Prevention Control and Biosafety Emergency Response, Guangxi Center for Disease Control and Prevention, Nanning 530028, P.R. China
| | - Hui Xing
- State Key Laboratory of Infectious Disease Prevention and Control (SKLID), National Center for AIDS/STD Control and Prevention (NCAIDS), Chinese Center for Disease Control and Prevention (China CDC), Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases, Beijing 102206, P.R. China
- Guangxi Key Laboratory of Major Infectious Disease Prevention Control and Biosafety Emergency Response, Guangxi Center for Disease Control and Prevention, Nanning 530028, P.R. China
| | - Yuhua Ruan
- State Key Laboratory of Infectious Disease Prevention and Control (SKLID), National Center for AIDS/STD Control and Prevention (NCAIDS), Chinese Center for Disease Control and Prevention (China CDC), Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases, Beijing 102206, P.R. China
- Guangxi Key Laboratory of Major Infectious Disease Prevention Control and Biosafety Emergency Response, Guangxi Center for Disease Control and Prevention, Nanning 530028, P.R. China
| | - Guanghua Lan
- Guangxi Key Laboratory of Major Infectious Disease Prevention Control and Biosafety Emergency Response, Guangxi Center for Disease Control and Prevention, Nanning 530028, P.R. China
| | - Lei Zhang
- China-Australia Joint Research Center for Infectious Diseases, School of Public Health, Xi'an Jiaotong University Health Science Center, Xi'an, Shaanxi 710061, P.R. China
- Artificial Intelligence and Modelling in Epidemiology Program, Melbourne Sexual Health Centre, Alfred Health, Melbourne, Australia
- Central Clinical School, Faculty of Medicine, Monash University, Melbourne, Australia
| | - Mingwang Shen
- China-Australia Joint Research Center for Infectious Diseases, School of Public Health, Xi'an Jiaotong University Health Science Center, Xi'an, Shaanxi 710061, P.R. China
- Key Laboratory for Disease Prevention and Control and Health Promotion of Shaanxi Province, School of Public Health, Xi'an Jiaotong University Health Science Center, Xi'an, Shaanxi, P.R. China
| |
Collapse
|
6
|
Tunc H, Sari M, Kotil S. Machine learning aided multiscale modelling of the HIV-1 infection in the presence of NRTI therapy. PeerJ 2023; 11:e15033. [PMID: 37020854 PMCID: PMC10069423 DOI: 10.7717/peerj.15033] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2022] [Accepted: 02/19/2023] [Indexed: 04/03/2023] Open
Abstract
Human Immunodeficiency Virus (HIV) is one of the most common chronic infectious diseases in humans. Extending the expected lifetime of patients depends on the use of optimal antiretroviral therapies. Emergence of the drug-resistant strains can reduce the effectiveness of treatments and lead to Acquired Immunodeficiency Syndrome (AIDS), even with antiretroviral therapy. Investigating the genotype-phenotype relationship is a crucial process for optimizing the therapy protocols of the patients. Here, a mathematical modelling framework is proposed to address the impact of existing mutations, timing of initiation, and adherence levels of nucleotide reverse transcriptase inhibitors (NRTIs) on the evolutionary dynamics of the virus strains. For the first time, the existing Stanford HIV drug resistance data have been combined with a multi-strain within-host ordinary differential equation (ODE) model to track the dynamics of the most common NRTI-resistant strains. Overall, the D4T-3TC, D4T-AZT and TDF-D4T drug combinations have been shown to provide higher success rates in preventing treatment failure and further drug resistance. The results are in line with the genotype-phenotype data and pharmacokinetic parameters of the NRTI inhibitors. Moreover, we show that the undetectable mutant strains at the diagnosis have a significant effect on the success/failure rates of the NRTI treatments. Predictions on undetectable strains through our multi-strain within-host model yielded the possible role of viral evolution on the treatment outcomes. It has been recognized that the improvement of multi-scale models can contribute to the understanding of the evolutionary dynamics, and treatment options, and potentially increase the reliability of genotype-phenotype models.
Collapse
Affiliation(s)
- Huseyin Tunc
- Department of Biostatistics and Medical Informatics, School of Medicine, Bahcesehir University, Istanbul, Turkey
| | - Murat Sari
- Mathematics Engineering, Faculty of Science and Letters, Istanbul Technical University, Istanbul, Turkey
| | - Seyfullah Kotil
- Department of Biophysics, School of Medicine, Bahcesehir University, Istanbul, Turkey
- Department of Molecular Biology and Genetics, Faculty of Arts and Sciences, Bogazici University, Istanbul, Turkey
| |
Collapse
|
7
|
Gao S, Shen M, Wang X, Wang J, Martcheva M, Rong L. A multi-strain model with asymptomatic transmission: Application to COVID-19 in the US. J Theor Biol 2023; 565:111468. [PMID: 36940811 PMCID: PMC10027298 DOI: 10.1016/j.jtbi.2023.111468] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2022] [Revised: 02/08/2023] [Accepted: 03/16/2023] [Indexed: 03/23/2023]
Abstract
COVID-19, induced by the SARS-CoV-2 infection, has caused an unprecedented pandemic in the world. New variants of the virus have emerged and dominated the virus population. In this paper, we develop a multi-strain model with asymptomatic transmission to study how the asymptomatic or pre-symptomatic infection influences the transmission between different strains and control strategies that aim to mitigate the pandemic. Both analytical and numerical results reveal that the competitive exclusion principle still holds for the model with the asymptomatic transmission. By fitting the model to the COVID-19 case and viral variant data in the US, we show that the omicron variants are more transmissible but less fatal than the previously circulating variants. The basic reproduction number for the omicron variants is estimated to be 11.15, larger than that for the previous variants. Using mask mandate as an example of non-pharmaceutical interventions, we show that implementing it before the prevalence peak can significantly lower and postpone the peak. The time of lifting the mask mandate can affect the emergence and frequency of subsequent waves. Lifting before the peak will result in an earlier and much higher subsequent wave. Caution should also be taken to lift the restriction when a large portion of the population remains susceptible. The methods and results obtained her e may be applied to the study of the dynamics of other infectious diseases with asymptomatic transmission using other control measures.
Collapse
Affiliation(s)
- Shasha Gao
- School of Mathematics and Statistics, Jiangxi Normal University, Nanchang, 330000, China; Department of Mathematics, University of Florida, Gainesville, FL 32611, United States of America
| | - Mingwang Shen
- China-Australia Joint Research Centre for Infectious Diseases, School of Public Health, Xi'an Jiaotong University Health Science Center, Xi'an, Shaanxi, China
| | - Xueying Wang
- Department of Mathematics and Statistics, Washington State University, Pullman, WA 99163, United States of America
| | - Jin Wang
- Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States of America
| | - Maia Martcheva
- Department of Mathematics, University of Florida, Gainesville, FL 32611, United States of America
| | - Libin Rong
- Department of Mathematics, University of Florida, Gainesville, FL 32611, United States of America.
| |
Collapse
|
8
|
Towards a new combination therapy with vectored immunoprophylaxis for HIV: Modeling "shock and kill" strategy. Math Biosci 2023; 355:108954. [PMID: 36525996 DOI: 10.1016/j.mbs.2022.108954] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2022] [Revised: 09/23/2022] [Accepted: 12/06/2022] [Indexed: 12/15/2022]
Abstract
Latently infected cells are considered as a major barrier to curing Human Immunodeficiency Virus (HIV) infection. Reactivation of latently infected cells followed by killing the actively infected cells may be a potential strategy ("shock and kill") to purge the latent reservoir. Based on vectored immunoprophylaxis (VIP) experiment that can elicit bNAbs, in this paper a mathematical model is formulated to explore the efficacy of "shock and kill" strategy with VIP. We derive the basic reproduction number R0 of the model and show that R0 completely determines the dynamics of the model: if R0<1, the disease-free equilibrium is globally asymptotically stable; if R0>1, the system is uniformly persistent. Numerical simulations suggest that the "shock and kill" strategy with VIP can effectively control HIV infection while this strategy cannot eradicate the reservoir without VIP although it can alleviate the HIV infection. To model the administration of drugs and vaccine more realistically, pharmacokinetics and pulse vaccination are incorporated into the model of ordinary differential equations. The resultants are described by impulsive differential equations. The thresholds are obtained for the frequency and strength of the vaccination to eliminate the viruses. Furthermore, the most appropriate times are numerically investigated for starting a short-term latency-reversing agents (LRAs) treatment relative to ART considering the toxicity of LRAs. The results show that LRAs treatment at the beginning of ART might be a better option. These results have important implications for the design of HIV cure-related clinical trials.
Collapse
|
9
|
Alshorman A, Al-Hosainat N, Jackson T. Analysis of HIV latent infection model with multiple infection stages and different drug classes. JOURNAL OF BIOLOGICAL DYNAMICS 2022; 16:713-732. [PMID: 36264087 DOI: 10.1080/17513758.2022.2113828] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2021] [Accepted: 08/09/2022] [Indexed: 06/16/2023]
Abstract
Latently infected CD4+ T cells represent one of the major obstacles to HIV eradication even after receiving prolonged highly active anti-retroviral therapy (HAART). Long-term use of HAART causes the emergence of drug-resistant virus which is then involved in HIV transmission. In this paper, we develop mathematical HIV models with staged disease progression by incorporating entry inhibitor and latently infected cells. We find that entry inhibitor has the same effect as protease inhibitor on the model dynamics and therefore would benefit HIV patients who developed resistance to many of current anti-HIV medications. Numerical simulations illustrate the theoretical results and show that the virus and latently infected cells reach an infected steady state in the absence of treatment and are eliminated under treatment whereas the model including homeostatic proliferation of latently infected cells maintains the virus at low level during suppressive treatment. Therefore, complete cure of HIV needs complete eradication of latent reservoirs.
Collapse
Affiliation(s)
- Areej Alshorman
- Department of Mathematics, University of Michigan, Ann Arbor, MI, USA
| | | | - Trachette Jackson
- Department of Mathematics, University of Michigan, Ann Arbor, MI, USA
| |
Collapse
|
10
|
LaMont C, Otwinowski J, Vanshylla K, Gruell H, Klein F, Nourmohammad A. Design of an optimal combination therapy with broadly neutralizing antibodies to suppress HIV-1. eLife 2022; 11:76004. [PMID: 35852143 PMCID: PMC9467514 DOI: 10.7554/elife.76004] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2021] [Accepted: 07/04/2022] [Indexed: 11/13/2022] Open
Abstract
Infusion of broadly neutralizing antibodies (bNAbs) has shown promise as an alternative to anti-retroviral therapy against HIV. A key challenge is to suppress viral escape, which is more effectively achieved with a combination of bNAbs. Here, we propose a computational approach to predict the efficacy of a bNAb therapy based on the population genetics of HIV escape, which we parametrize using high-throughput HIV sequence data from bNAb-naive patients. By quantifying the mutational target size and the fitness cost of HIV-1 escape from bNAbs, we predict the distribution of rebound times in three clinical trials. We show that a cocktail of three bNAbs is necessary to effectively suppress viral escape, and predict the optimal composition of such bNAb cocktail. Our results offer a rational therapy design for HIV, and show how genetic data can be used to predict treatment outcomes and design new approaches to pathogenic control.
Collapse
Affiliation(s)
- Colin LaMont
- Max Planck Institute for Dynamics and Self-Organization
| | | | | | | | | | | |
Collapse
|
11
|
Poonia A, Chakrabarty SP. Two strains and drug adherence: An HIV model in the paradigm of community transmission. NONLINEAR DYNAMICS 2022; 108:2767-2792. [PMID: 35310019 PMCID: PMC8916704 DOI: 10.1007/s11071-022-07323-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/11/2021] [Accepted: 01/31/2022] [Indexed: 06/14/2023]
Abstract
A two-strain model, comprising of drug-sensitive and drug-resistant strains, is proposed for the dynamics of Human Immunodeficiency Virus (HIV) spread in a community. A treatment model is introduced by taking drug adherence into account. The treatment-free model is analyzed for the effect of treatment availability and drug adherence on disease dynamics. The analysis revealed that for the treatment-free model, at least one strain faces competitive exclusion, and co-existence of both strains is not possible. On the contrary, both strains may co-exist in presence of treatment. The analysis carried out was both local, as well as global. A comprehensive bifurcation analysis showed periodic behaviour and all solutions approached a stable limit cycle for a wide range of parametric values. Overall, we concluded that the treatment availability and drug adherence play a significant role in determining the dynamics of HIV spread. Numerical simulations are performed to validate the analytical results using MATLAB.
Collapse
Affiliation(s)
- Ashish Poonia
- Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, India
| | | |
Collapse
|
12
|
Olabode D, Rong L, Wang X. Stochastic investigation of HIV infection and the emergence of drug resistance. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:1174-1194. [PMID: 35135199 DOI: 10.3934/mbe.2022054] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Drug-resistant HIV-1 has caused a growing concern in clinic and public health. Although combination antiretroviral therapy can contribute massively to the suppression of viral loads in patients with HIV-1, it cannot lead to viral eradication. Continuing viral replication during sub-optimal therapy (due to poor adherence or other reasons) may lead to the accumulation of drug resistance mutations, resulting in an increased risk of disease progression. Many studies also suggest that events occurring during the early stage of HIV-1 infection (i.e., the first few hours to days following HIV exposure) may determine whether the infection can be successfully established. However, the numbers of infected cells and viruses during the early stage are extremely low and stochasticity may play a critical role in dictating the fate of infection. In this paper, we use stochastic models to investigate viral infection and the emergence of drug resistance of HIV-1. The stochastic model is formulated by a continuous-time Markov chain (CTMC), which is derived based on an ordinary differential equation model proposed by Kitayimbwa et al. that includes both forward and backward mutations. An analytic estimate of the probability of the clearance of HIV infection of the CTMC model near the infection-free equilibrium is obtained by a multitype branching process approximation. The analytical predictions are validated by numerical simulations. Unlike the deterministic dynamics where the basic reproduction number R0 serves as a sharp threshold parameter (i.e., the disease dies out if R0<1 and persists if R0>1), the stochastic models indicate that there is always a positive probability for HIV infection to be eradicated in patients. In the presence of antiretroviral therapy, our results show that the chance of clearance of the infection tends to increase although drug resistance is likely to emerge.
Collapse
Affiliation(s)
- Damilola Olabode
- Department of Mathematics and Statistics, Washington State University, Pullman, WA 99164, USA
| | - Libin Rong
- Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
| | - Xueying Wang
- Department of Mathematics and Statistics, Washington State University, Pullman, WA 99164, USA
| |
Collapse
|
13
|
Modelling Mutation in Equine Infectious Anemia Virus Infection Suggests a Path to Viral Clearance with Repeated Vaccination. Viruses 2021; 13:v13122450. [PMID: 34960718 PMCID: PMC8706554 DOI: 10.3390/v13122450] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2021] [Revised: 12/01/2021] [Accepted: 12/02/2021] [Indexed: 11/20/2022] Open
Abstract
Equine infectious anemia virus (EIAV) is a lentivirus similar to HIV that infects horses. Clinical and experimental studies demonstrating immune control of EIAV infection hold promise for efforts to produce an HIV vaccine. Antibody infusions have been shown to block both wild-type and mutant virus infection, but the mutant sometimes escapes. Using these data, we develop a mathematical model that describes the interactions between antibodies and both wild-type and mutant virus populations, in the context of continual virus mutation. The aim of this work is to determine whether repeated vaccinations through antibody infusions can reduce both the wild-type and mutant strains of the virus below one viral particle, and if so, to examine the vaccination period and number of infusions that ensure eradication. The antibody infusions are modelled using impulsive differential equations, a technique that offers insight into repeated vaccination by approximating the time-to-peak by an instantaneous change. We use impulsive theory to determine the maximal vaccination intervals that would be required to reduce the wild-type and mutant virus levels below one particle per horse. We show that seven boosts of the antibody vaccine are sufficient to eradicate both the wild-type and the mutant strains. In the case of a mutant virus infection that is given infusions of antibodies targeting wild-type virus (i.e., simulation of a heterologous infection), seven infusions were likewise sufficient to eradicate infection, based upon the data set. However, if the period between infusions was sufficiently increased, both the wild-type and mutant virus would eventually persist in the form of a periodic orbit. These results suggest a route forward to design antibody-based vaccine strategies to control viruses subject to mutant escape.
Collapse
|
14
|
Stephenson KE, Julg B, Tan CS, Zash R, Walsh SR, Rolle CP, Monczor AN, Lupo S, Gelderblom HC, Ansel JL, Kanjilal DG, Maxfield LF, Nkolola J, Borducchi EN, Abbink P, Liu J, Peter L, Chandrashekar A, Nityanandam R, Lin Z, Setaro A, Sapiente J, Chen Z, Sunner L, Cassidy T, Bennett C, Sato A, Mayer B, Perelson AS, deCamp A, Priddy FH, Wagh K, Giorgi EE, Yates NL, Arduino RC, DeJesus E, Tomaras GD, Seaman MS, Korber B, Barouch DH. Safety, pharmacokinetics and antiviral activity of PGT121, a broadly neutralizing monoclonal antibody against HIV-1: a randomized, placebo-controlled, phase 1 clinical trial. Nat Med 2021; 27:1718-1724. [PMID: 34621054 PMCID: PMC8516645 DOI: 10.1038/s41591-021-01509-0] [Citation(s) in RCA: 35] [Impact Index Per Article: 11.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2021] [Accepted: 08/16/2021] [Indexed: 02/08/2023]
Abstract
Human immunodeficiency virus (HIV)-1-specific broadly neutralizing monoclonal antibodies are currently under development to treat and prevent HIV-1 infection. We performed a single-center, randomized, double-blind, dose-escalation, placebo-controlled trial of a single administration of the HIV-1 V3-glycan-specific antibody PGT121 at 3, 10 and 30 mg kg-1 in HIV-uninfected adults and HIV-infected adults on antiretroviral therapy (ART), as well as a multicenter, open-label trial of one infusion of PGT121 at 30 mg kg-1 in viremic HIV-infected adults not on ART (no. NCT02960581). The primary endpoints were safety and tolerability, pharmacokinetics (PK) and antiviral activity in viremic HIV-infected adults not on ART. The secondary endpoints were changes in anti-PGT121 antibody titers and CD4+ T-cell count, and development of HIV-1 sequence variations associated with PGT121 resistance. Among 48 participants enrolled, no treatment-related serious adverse events, potential immune-mediated diseases or Grade 3 or higher adverse events were reported. The most common reactions among PGT121 recipients were intravenous/injection site tenderness, pain and headache. Absolute and relative CD4+ T-cell counts did not change following PGT121 infusion in HIV-infected participants. Neutralizing anti-drug antibodies were not elicited. PGT121 reduced plasma HIV RNA levels by a median of 1.77 log in viremic participants, with a viral load nadir at a median of 8.5 days. Two individuals with low baseline viral loads experienced ART-free viral suppression for ≥168 days following antibody infusion, and rebound viruses in these individuals demonstrated full or partial PGT121 sensitivity. The trial met the prespecified endpoints. These data suggest that further investigation of the potential of antibody-based therapeutic strategies for long-term suppression of HIV is warranted, including in individuals off ART and with low viral load.
Collapse
Affiliation(s)
- Kathryn E Stephenson
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA
- Division of Infectious Diseases, Beth Israel Deaconess Medical Center, Boston, MA, USA
- Ragon Institute of MGH, MIT and Harvard, Cambridge, MA, USA
| | - Boris Julg
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA
- Ragon Institute of MGH, MIT and Harvard, Cambridge, MA, USA
- Infectious Disease Division, Massachusetts General Hospital, Boston, MA, USA
| | - C Sabrina Tan
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA
- Division of Infectious Diseases, Beth Israel Deaconess Medical Center, Boston, MA, USA
| | - Rebecca Zash
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA
- Division of Infectious Diseases, Beth Israel Deaconess Medical Center, Boston, MA, USA
| | - Stephen R Walsh
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA
| | | | - Ana N Monczor
- McGovern Medical School at The University of Texas Health Science Center, Houston, TX, USA
| | - Sofia Lupo
- McGovern Medical School at The University of Texas Health Science Center, Houston, TX, USA
| | | | - Jessica L Ansel
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA
| | - Diane G Kanjilal
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA
| | - Lori F Maxfield
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA
| | - Joseph Nkolola
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA
| | - Erica N Borducchi
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA
| | - Peter Abbink
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA
| | - Jinyan Liu
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA
| | - Lauren Peter
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA
| | - Abishek Chandrashekar
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA
| | - Ramya Nityanandam
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA
| | - Zijin Lin
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA
| | - Alessandra Setaro
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA
| | - Joseph Sapiente
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA
| | - Zhilin Chen
- Ragon Institute of MGH, MIT and Harvard, Cambridge, MA, USA
| | - Lisa Sunner
- International AIDS Vaccine Initiative, New York, NY, USA
| | - Tyler Cassidy
- Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - Chelsey Bennett
- Statistical Center for HIV/AIDS Research and Prevention, Fred Hutchinson Cancer Research Center, Seattle, WA, USA
| | - Alicia Sato
- Statistical Center for HIV/AIDS Research and Prevention, Fred Hutchinson Cancer Research Center, Seattle, WA, USA
| | - Bryan Mayer
- Statistical Center for HIV/AIDS Research and Prevention, Fred Hutchinson Cancer Research Center, Seattle, WA, USA
| | - Alan S Perelson
- Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - Allan deCamp
- Statistical Center for HIV/AIDS Research and Prevention, Fred Hutchinson Cancer Research Center, Seattle, WA, USA
| | | | - Kshitij Wagh
- Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - Elena E Giorgi
- Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - Nicole L Yates
- Duke Human Vaccine Institute, Duke University, Durham, NC, USA
- Departments of Surgery, Immunology and Molecular Genetics and Microbiology, Duke University, Durham, NC, USA
| | - Roberto C Arduino
- McGovern Medical School at The University of Texas Health Science Center, Houston, TX, USA
| | | | - Georgia D Tomaras
- Duke Human Vaccine Institute, Duke University, Durham, NC, USA
- Departments of Surgery, Immunology and Molecular Genetics and Microbiology, Duke University, Durham, NC, USA
| | - Michael S Seaman
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA
| | - Bette Korber
- Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, NM, USA
- New Mexico Consortium, Los Alamos, NM, USA
| | - Dan H Barouch
- Center for Virology and Vaccine Research, Beth Israel Deaconess Medical Center, Boston, MA, USA.
- Division of Infectious Diseases, Beth Israel Deaconess Medical Center, Boston, MA, USA.
- Ragon Institute of MGH, MIT and Harvard, Cambridge, MA, USA.
| |
Collapse
|
15
|
Feder AF, Harper KN, Brumme CJ, Pennings PS. Understanding patterns of HIV multi-drug resistance through models of temporal and spatial drug heterogeneity. eLife 2021; 10:e69032. [PMID: 34473060 PMCID: PMC8412921 DOI: 10.7554/elife.69032] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2021] [Accepted: 08/03/2021] [Indexed: 01/09/2023] Open
Abstract
Triple-drug therapies have transformed HIV from a fatal condition to a chronic one. These therapies should prevent HIV drug resistance evolution, because one or more drugs suppress any partially resistant viruses. In practice, such therapies drastically reduced, but did not eliminate, resistance evolution. In this article, we reanalyze published data from an evolutionary perspective and demonstrate several intriguing patterns about HIV resistance evolution - resistance evolves (1) even after years on successful therapy, (2) sequentially, often via one mutation at a time and (3) in a partially predictable order. We describe how these observations might emerge under two models of HIV drugs varying in space or time. Despite decades of work in this area, much opportunity remains to create models with realistic parameters for three drugs, and to match model outcomes to resistance rates and genetic patterns from individuals on triple-drug therapy. Further, lessons from HIV may inform other systems.
Collapse
Affiliation(s)
- Alison F Feder
- Department of Integrative Biology, University of California, BerkeleyBerkeleyUnited States
- Department of Genome Sciences, University of WashingtonSeattleUnited States
| | - Kristin N Harper
- Harper Health and Science Communications, LLCSeattleUnited States
| | - Chanson J Brumme
- British Columbia Centre for Excellence in HIV/AIDSVancouverCanada
- Department of Medicine, University of British ColumbiaVancouverCanada
| | - Pleuni S Pennings
- Department of Biology, San Francisco State UniversitySan FranciscoUnited States
| |
Collapse
|
16
|
A diffusive virus model with a fixed intracellular delay and combined drug treatments. J Math Biol 2021; 83:19. [PMID: 34324062 DOI: 10.1007/s00285-021-01646-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2020] [Revised: 04/26/2021] [Accepted: 07/18/2021] [Indexed: 10/20/2022]
Abstract
The method of administration of an effective drug treatment to eradicate viruses within a host is an important issue in studying viral dynamics. Overuse of a drug can lead to deleterious side effects, and overestimating the efficacy of a drug can result in failure to treat infection. In this study, we proposed a reaction-diffusion within-host virus model which incorporated information regarding spatial heterogeneity, drug treatment, and the intracellular delay to produce productively infected cells and viruses. We also calculated the basic reproduction number [Formula: see text] under the assumptions of spatial heterogeneity. We have shown that the infection-free periodic solution is globally asymptotically stable when [Formula: see text], whereas when [Formula: see text] there is an infected periodic solution and the infection is uniformly persistent. By conducting numerical simulations, we also revealed the effects of various parameters on the value of [Formula: see text]. First, we showed that the dependence of [Formula: see text] on the intracellular delay could be monotone or non-monotone, depending on the death rate of infected cells in the immature stage. Second, we found that the mobility of infected cells or virions could facilitate the virus clearance. Third, we found that the spatial fragmentation of the virus environment enhanced viral infection. Finally, we showed that the combination of spatial heterogeneity and different sets of diffusion rates resulted in complicated viral dynamic outcomes.
Collapse
|
17
|
Kamkwalala AR, Wang K, O’Halloran J, Williams DW, Dastgheyb R, Fitzgerald KC, Spence AB, Maki PM, Gustafson DR, Milam J, Sharma A, Weber KM, Adimora AA, Ofotokun I, Sheth AN, Lahiri CD, Fischl MA, Konkle-Parker D, Xu Y, Rubin LH. Starting or Switching to an Integrase Inhibitor-Based Regimen Affects PTSD Symptoms in Women with HIV. AIDS Behav 2021; 25:225-236. [PMID: 32638219 PMCID: PMC7948485 DOI: 10.1007/s10461-020-02967-2] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
As the use of Integrase inhibitor (INSTI)-class antiretroviral medications becomes more common to maintain long-term viral suppression, early reports suggest the potential for CNS side-effects when starting or switching to an INSTI-based regimen. In a population already at higher risk for developing mood and anxiety disorders, these drugs may have significant effects on PTSD scale symptom scores, particularly in women with HIV (WWH). A total of 551 participants were included after completing ≥ 1 WIHS study visits before and after starting/switching to an INSTI-based ART regimen. Of these, 14% were ART naïve, the remainder switched from primarily a protease inhibitor (PI) or non-nucleoside reverse transcriptase inhibitor (NNRTI)-based regimen. Using multivariable linear mixed effects models, we compared PTSD Civilian Checklist subscale scores before and after a "start/switch" to dolutegravir (DTG), raltegravir (RAL), or elvitegravir (EVG). Start/switch to EVG improved re-experiencing subscale symptoms (P's < 0.05). Switching to EVG improved symptoms of avoidance (P = 0.01). Starting RAL improved arousal subscale symptoms (P = 0.03); however, switching to RAL worsened re-experiencing subscale symptoms (P < 0.005). Starting DTG worsened avoidance subscale symptoms (P = 0.03), whereas switching to DTG did not change subscale or overall PTSD symptoms (P's > 0.08). In WWH, an EVG-based ART regimen is associated with improved PTSD symptoms, in both treatment naïve patients and those switching from other ART. While a RAL-based regimen was associated with better PTSD symptoms than in treatment naïve patients, switching onto a RAL-based regimen was associated with worse PTSD symptoms. DTG-based regimens either did not affect, or worsened symptoms, in both naïve and switch patients. Further studies are needed to determine mechanisms underlying differential effects of EVG, RAL and DTG on stress symptoms in WWH.
Collapse
Affiliation(s)
- Asante R. Kamkwalala
- Department of Neurology, Johns Hopkins University School of Medicine, Baltimore, MD
| | - Kunbo Wang
- Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD
| | - Jane O’Halloran
- Department of Medicine, Washington University School of Medicine in St. Louis, St. Louis, MO
| | - Dionna W. Williams
- Department of Molecular and Comparative Pathobiology, Johns Hopkins University School of Medicine, Baltimore, MD,Division of Clinical Pharmacology, Johns Hopkins University School of Medicine, Baltimore, MD
| | - Raha Dastgheyb
- Department of Neurology, Johns Hopkins University School of Medicine, Baltimore, MD
| | | | - Amanda B. Spence
- Department of Medicine, Division of Infectious Disease and Travel Medicine, Georgetown University, Washington, DC
| | - Pauline M. Maki
- Departments of Psychiatry, Psychology and OB/GYN, University of Illinois at Chicago, Chicago, IL
| | - Deborah R. Gustafson
- Department of Neurology, State University of New York Downstate Health Sciences University, Brooklyn, NY
| | - Joel Milam
- Institute for Health Promotion & Disease Prevention Research, University of Southern California, Los Angeles, California
| | | | - Kathleen M. Weber
- CORE Center, Cook County Health and Hektoen Institute of Medicine, Chicago, IL
| | - Adaora A. Adimora
- Division of Infectious Diseases, Department of Medicine, University of North Carolina at Chapel Hill, Chapel Hill, NC
| | - Igho Ofotokun
- Department of Medicine, Division of Infectious Diseases, Emory University, Atlanta, GA
| | - Anandi N. Sheth
- Department of Medicine, Division of Infectious Diseases, Emory University, Atlanta, GA
| | - Cecile D. Lahiri
- Department of Medicine, Division of Infectious Diseases, Emory University, Atlanta, GA
| | | | - Deborah Konkle-Parker
- Division of Infectious Diseases, University of Mississippi Medical Center, Jackson, Mississippi
| | - Yanxun Xu
- Department of Medicine, Washington University School of Medicine in St. Louis, St. Louis, MO,Division of Biostatistics and Bioinformatics at The Sidney Kimmel Comprehensive Cancer Center, Johns Hopkins University School of Medicine, Baltimore, MD
| | - Leah H. Rubin
- Department of Neurology, Johns Hopkins University School of Medicine, Baltimore, MD,Department of Epidemiology, Johns Hopkins University Bloomberg School of Public Health, Baltimore, MD,Department of Psychiatry, Johns Hopkins University School of Medicine, Baltimore, MD
| |
Collapse
|
18
|
Alfonso S, Jenner AL, Craig M. Translational approaches to treating dynamical diseases through in silico clinical trials. CHAOS (WOODBURY, N.Y.) 2020; 30:123128. [PMID: 33380031 DOI: 10.1063/5.0019556] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2020] [Accepted: 11/20/2020] [Indexed: 06/12/2023]
Abstract
The primary goal of drug developers is to establish efficient and effective therapeutic protocols. Multifactorial pathologies, including dynamical diseases and complex disorders, can be difficult to treat, given the high degree of inter- and intra-patient variability and nonlinear physiological relationships. Quantitative approaches combining mechanistic disease modeling and computational strategies are increasingly leveraged to rationalize pre-clinical and clinical studies and to establish effective treatment strategies. The development of clinical trials has led to new computational methods that allow for large clinical data sets to be combined with pharmacokinetic and pharmacodynamic models of diseases. Here, we discuss recent progress using in silico clinical trials to explore treatments for a variety of complex diseases, ultimately demonstrating the immense utility of quantitative methods in drug development and medicine.
Collapse
Affiliation(s)
- Sofia Alfonso
- Department of Physiology, McGill University, Montreal, Quebec H3A 0G4, Canada
| | - Adrianne L Jenner
- Department of Mathematics and Statistics, Université de Montréal, Montreal, Quebec H3C 3J7, Canada
| | - Morgan Craig
- Department of Physiology, McGill University, Montreal, Quebec H3A 0G4, Canada
| |
Collapse
|
19
|
Li B, Jiao F. A delayed HIV-1 model with cell-to-cell spread and virus waning. JOURNAL OF BIOLOGICAL DYNAMICS 2020; 14:802-825. [PMID: 33084532 DOI: 10.1080/17513758.2020.1836272] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2020] [Accepted: 09/29/2020] [Indexed: 06/11/2023]
Abstract
In this paper, we propose and analyse a delayed HIV-1 model with both viral and cellular transmissions and virus waning. We obtain the threshold dynamics of the proposed model, characterized by the basic reproduction number R0 . If R0<1 , the infection-free steady state is globally asymptotically stable; whereas if R0>1 , the system is uniformly persistent. When the delays are positive, we show that the intracellular delays in both viral and cellular infections may lead to stability switches of the infected steady state. Both analytical and numerical results indicate that if the effect of cell-to-cell transmission is ignored, then the risk of HIV-1 infection will be underestimated. Moreover, the viral load of model without virus waning is higher than the one of model with virus waning. These results highlight the important role of two ways of viral transmission and virus waning on HIV-1 infection.
Collapse
Affiliation(s)
- Bing Li
- School of Mathematical Science, Harbin Normal University, Harbin, People's Republic of China
| | - Feng Jiao
- Center for Applied Mathematics, Guangzhou University, Guangzhou, People's Republic of China
| |
Collapse
|
20
|
Chen SS, Cheng CY, Rong L. Within-Host Viral Dynamics in a Multi-compartmental Environment. Bull Math Biol 2019; 81:4271-4308. [DOI: 10.1007/s11538-019-00658-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2019] [Accepted: 08/09/2019] [Indexed: 11/29/2022]
|
21
|
Modeling HIV Dynamics Under Combination Therapy with Inducers and Antibodies. Bull Math Biol 2019; 81:2625-2648. [PMID: 31161559 DOI: 10.1007/s11538-019-00621-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2018] [Accepted: 05/27/2019] [Indexed: 12/12/2022]
Abstract
A mathematical model is proposed to simulate the "shock-kill" strategy where broadly neutralizing antibodies (bNAbs) are injected with a combination of HIV latency activators to reduce persistent HIV reservoirs. The basic reproductive ratio of virus is computed to extrapolate how the combinational therapy of inducers and antibodies affects the persistence of HIV infection. Numerical simulations demonstrate that a proper combination of inducers and bNAbs can drive the basic reproductive ratio below unity. Interestingly, it is found that a longer dosage interval leads to the higher HIV survival opportunity and a smaller dosage interval is preferred, which is fundamental to design an optimal therapeutic scheme. Further simulations reveal the conditions under which the joint therapy of inducer and antibodies induces a large extension of viral rebound time, which highlights the mechanism of delayed viral rebound from the experiment (Halper-Stromberg et al. in Cell 158:989-999, 2014). Optimal time for cessation of treatment is also analyzed to aid practical applications.
Collapse
|
22
|
Beauchemin CAA, Kim YI, Yu Q, Ciaramella G, DeVincenzo JP. Uncovering critical properties of the human respiratory syncytial virus by combining in vitro assays and in silico analyses. PLoS One 2019; 14:e0214708. [PMID: 30986239 PMCID: PMC6464176 DOI: 10.1371/journal.pone.0214708] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2018] [Accepted: 03/19/2019] [Indexed: 12/12/2022] Open
Abstract
Many aspects of the respiratory syncytial virus (RSV) are still poorly understood. Yet these knowledge gaps have had and could continue to have adverse, unintended consequences for the efficacy and safety of antivirals and vaccines developed against RSV. Mathematical modelling was used to test and evaluate hypotheses about the rate of loss of RSV infectivity and the mechanisms and kinetics of RSV infection spread in SIAT cells in vitro. While the rate of loss of RSV integrity, as measured via qRT-PCR, is well-described by an exponential decay, the latter mechanism failed to describe the rate at which RSV A Long loses infectivity over time in vitro based on the data presented herein. This is unusual given that other viruses (HIV, HCV, influenza) have been shown to lose their infectivity exponentially in vitro, and indeed an exponential rate of loss of infectivity is always assumed in mathematical modelling and experimental analyses. The infectivity profile of RSV in HEp-2 and SIAT cells remained consistent over the course of an RSV infection, over time and a large range of infectivity. However, SIAT cells were found to be ∼ 100× less sensitive to RSV infection than HEp-2 cells. In particular, we found that RSV spreads inefficiently in SIAT cells, in a manner we show is consistent with the establishment of infection resistance in uninfected cells. SIAT cells are a good in vitro model in which to study RSV in vivo dissemination, yielding similar infection timescales. However, the higher sensitivity of HEp-2 cells to RSV together with its RSV infectivity profile being similar to that of SIAT cells, makes HEp-2 cells more suitable for quantifying RSV infectivity over the course of in vitro RSV infections in SIAT cells. Our findings highlight the importance and urgency of resolving the mechanisms at play in the dissemination of RSV infections in vitro, and the processes by which this infectivity is lost.
Collapse
Affiliation(s)
- Catherine A. A. Beauchemin
- Department of Physics, Ryerson University, Toronto, Ontario, Canada
- Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) Research Program at RIKEN, Wako, Saitama, Japan
- * E-mail:
| | - Young-In Kim
- Department of Pediatrics, University of Tennessee Health Science Center, Memphis, Tennessee, United States of America
- Children’s Foundation Research Institute at Le Bonheur Children’s Hospital, Memphis, Tennessee, United States of America
| | - Qin Yu
- AstraZeneca Pharmaceuticals, Waltham, Massachusetts, United States of America
| | - Giuseppe Ciaramella
- AstraZeneca Pharmaceuticals, Waltham, Massachusetts, United States of America
| | - John P. DeVincenzo
- Department of Pediatrics, University of Tennessee Health Science Center, Memphis, Tennessee, United States of America
- Children’s Foundation Research Institute at Le Bonheur Children’s Hospital, Memphis, Tennessee, United States of America
- Department of Microbiology, Immunology and Biochemistry, University of Tennessee Health Science Center, Memphis, Tennessee, United States of America
| |
Collapse
|
23
|
Shen M, Xiao Y, Rong L, Meyers LA. Conflict and accord of optimal treatment strategies for HIV infection within and between hosts. Math Biosci 2019; 309:107-117. [PMID: 30684516 PMCID: PMC10826718 DOI: 10.1016/j.mbs.2019.01.007] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/14/2018] [Revised: 01/23/2019] [Accepted: 01/23/2019] [Indexed: 11/21/2022]
Abstract
Most of previous studies investigated the optimal control of HIV infection at either within-host or between-host level. However, the optimal treatment strategy for the individual may not be optimal for the population and vice versa. To determine when the two-level optimal controls are in accord or conflict, we develop a multi-scale model using various functions that link the viral load within host and the transmission rate between hosts, calibrated by cohort data. We obtain the within-host optimal treatment scheme that minimizes the viral load and maximizes the count of healthy cells at the individual level, and the coupled optimal scheme that minimizes the basic reproduction number at the population level. Mathematical analysis shows that whether the two-level optimal controls coincide depends on the sign of the product of their switching functions. Numerical results suggest that they are in accord for a high maximal drug efficacy but may conflict for a low drug efficacy. Using the multi-scale model, we also identify a threshold of the treatment effectiveness that determines how early treatment initiation can affect the disease dynamics among population. These results may help develop a synergistic treatment protocol beneficial to both HIV-infected individuals and the whole population.
Collapse
Affiliation(s)
- Mingwang Shen
- Department of Applied Mathematics, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, PR China; Department of Epidemiology and Biostatistics, School of Public Health, Xi'an Jiaotong University Health Science Center, Xi'an, Shaanxi, 710061, PR China
| | - Yanni Xiao
- Department of Applied Mathematics, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, PR China.
| | - Libin Rong
- Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
| | - Lauren Ancel Meyers
- Department of Integrative Biology, The University of Texas at Austin, Austin, Texas 78712, USA; The Santa Fe Institute, Santa Fe, New Mexico 87501, USA
| |
Collapse
|
24
|
Pinto CMA, Carvalho ARM, Tavares JN. Time-varying pharmacodynamics in a simple non-integer HIV infection model. Math Biosci 2018; 307:1-12. [PMID: 30399368 DOI: 10.1016/j.mbs.2018.11.001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2018] [Revised: 09/10/2018] [Accepted: 11/02/2018] [Indexed: 01/19/2023]
Abstract
In this paper we study the effect of time-varying drug exposure in the dynamics of a fractional order model for the human immunodeficiency virus infection. We compute the reproduction number of the model and verify the stability of the disease-free equilibrium. The model is simulated for parameters directly modelling the pharmacodynamics of HIV, namely the slope of the dose-response curve, the drug's half-life, and the dosing interval. The later affect in a significant way the infection patterns. The order of the fractional derivative is also a key player of the model, adding more information, which could be useful for a deeper understanding of the pharmacodynamics of HIV, necessary for more accurate therapeutic regimens.
Collapse
Affiliation(s)
- Carla M A Pinto
- School of Engineering, Polytechnic of Porto, Rua Dr António Bernardino de Almeida, 431, Porto 4249-015, Portugal.
| | - Ana R M Carvalho
- Faculty of Sciences, University of Porto, Rua do Campo Alegre s/n, Porto 4440-452, Portugal
| | - João N Tavares
- Faculty of Sciences, University of Porto, Rua do Campo Alegre s/n, Porto 4440-452, Portugal
| |
Collapse
|
25
|
Zitzmann C, Kaderali L. Mathematical Analysis of Viral Replication Dynamics and Antiviral Treatment Strategies: From Basic Models to Age-Based Multi-Scale Modeling. Front Microbiol 2018; 9:1546. [PMID: 30050523 PMCID: PMC6050366 DOI: 10.3389/fmicb.2018.01546] [Citation(s) in RCA: 41] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2018] [Accepted: 06/21/2018] [Indexed: 12/14/2022] Open
Abstract
Viral infectious diseases are a global health concern, as is evident by recent outbreaks of the middle east respiratory syndrome, Ebola virus disease, and re-emerging zika, dengue, and chikungunya fevers. Viral epidemics are a socio-economic burden that causes short- and long-term costs for disease diagnosis and treatment as well as a loss in productivity by absenteeism. These outbreaks and their socio-economic costs underline the necessity for a precise analysis of virus-host interactions, which would help to understand disease mechanisms and to develop therapeutic interventions. The combination of quantitative measurements and dynamic mathematical modeling has increased our understanding of the within-host infection dynamics and has led to important insights into viral pathogenesis, transmission, and disease progression. Furthermore, virus-host models helped to identify drug targets, to predict the treatment duration to achieve cure, and to reduce treatment costs. In this article, we review important achievements made by mathematical modeling of viral kinetics on the extracellular, intracellular, and multi-scale level for Human Immunodeficiency Virus, Hepatitis C Virus, Influenza A Virus, Ebola Virus, Dengue Virus, and Zika Virus. Herein, we focus on basic mathematical models on the population scale (so-called target cell-limited models), detailed models regarding the most important steps in the viral life cycle, and the combination of both. For this purpose, we review how mathematical modeling of viral dynamics helped to understand the virus-host interactions and disease progression or clearance. Additionally, we review different types and effects of therapeutic strategies and how mathematical modeling has been used to predict new treatment regimens.
Collapse
Affiliation(s)
- Carolin Zitzmann
- Institute of Bioinformatics and Center for Functional Genomics of Microbes, University Medicine Greifswald, Greifswald, Germany
| | - Lars Kaderali
- Institute of Bioinformatics and Center for Functional Genomics of Microbes, University Medicine Greifswald, Greifswald, Germany
| |
Collapse
|
26
|
Dorratoltaj N, Nikin-Beers R, Ciupe SM, Eubank SG, Abbas KM. Multi-scale immunoepidemiological modeling of within-host and between-host HIV dynamics: systematic review of mathematical models. PeerJ 2017; 5:e3877. [PMID: 28970973 PMCID: PMC5623312 DOI: 10.7717/peerj.3877] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2017] [Accepted: 09/11/2017] [Indexed: 12/17/2022] Open
Abstract
OBJECTIVE The objective of this study is to conduct a systematic review of multi-scale HIV immunoepidemiological models to improve our understanding of the synergistic impact between the HIV viral-immune dynamics at the individual level and HIV transmission dynamics at the population level. BACKGROUND While within-host and between-host models of HIV dynamics have been well studied at a single scale, connecting the immunological and epidemiological scales through multi-scale models is an emerging method to infer the synergistic dynamics of HIV at the individual and population levels. METHODS We reviewed nine articles using the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) framework that focused on the synergistic dynamics of HIV immunoepidemiological models at the individual and population levels. RESULTS HIV immunoepidemiological models simulate viral immune dynamics at the within-host scale and the epidemiological transmission dynamics at the between-host scale. They account for longitudinal changes in the immune viral dynamics of HIV+ individuals, and their corresponding impact on the transmission dynamics in the population. They are useful to analyze the dynamics of HIV super-infection, co-infection, drug resistance, evolution, and treatment in HIV+ individuals, and their impact on the epidemic pathways in the population. We illustrate the coupling mechanisms of the within-host and between-host scales, their mathematical implementation, and the clinical and public health problems that are appropriate for analysis using HIV immunoepidemiological models. CONCLUSION HIV immunoepidemiological models connect the within-host immune dynamics at the individual level and the epidemiological transmission dynamics at the population level. While multi-scale models add complexity over a single-scale model, they account for the time varying immune viral response of HIV+ individuals, and the corresponding impact on the time-varying risk of transmission of HIV+ individuals to other susceptibles in the population.
Collapse
Affiliation(s)
| | - Ryan Nikin-Beers
- Department of Mathematics, Virginia Tech, Blacksburg, United States of America
| | - Stanca M. Ciupe
- Department of Mathematics, Virginia Tech, Blacksburg, United States of America
| | - Stephen G. Eubank
- Biocomplexity Institute, Virginia Tech, Blacksburg, United States of America
| | - Kaja M. Abbas
- Department of Population Health Sciences, Virginia Tech, Blacksburg, United States of America
| |
Collapse
|
27
|
Wang X, Tang S, Song X, Rong L. Mathematical analysis of an HIV latent infection model including both virus-to-cell infection and cell-to-cell transmission. JOURNAL OF BIOLOGICAL DYNAMICS 2017; 11:455-483. [PMID: 27730851 DOI: 10.1080/17513758.2016.1242784] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
HIV can infect cells via virus-to-cell infection or cell-to-cell viral transmission. These two infection modes may occur in a synergistic way and facilitate viral spread within an infected individual. In this paper, we developed an HIV latent infection model including both modes of transmission and time delays between viral entry and integration or viral production. We analysed the model by defining the basic reproductive number, showing the existence, positivity and boundedness of the solution, and proving the local and global stability of the infection-free and infected steady states. Numerical simulations have been performed to illustrate the theoretical results and evaluate the effects of time delays and fractions of infection leading to latency on the virus dynamics. The estimates of the relative contributions to the HIV latent reservoir and the virus population from the two modes of transmission have also been provided.
Collapse
Affiliation(s)
- Xia Wang
- a College of Mathematics and Information Science , Xinyang Normal University , Xinyang , People's Republic of China
| | - Sanyi Tang
- b College of Mathematics and Information Science , Shaanxi Normal University , Xi'an , People's Republic of China
| | - Xinyu Song
- a College of Mathematics and Information Science , Xinyang Normal University , Xinyang , People's Republic of China
| | - Libin Rong
- c Department of Mathematics and Statistics , Oakland University , Rochester , MI , USA
| |
Collapse
|
28
|
Pinky L, Dobrovolny HM. The impact of cell regeneration on the dynamics of viral coinfection. CHAOS (WOODBURY, N.Y.) 2017; 27:063109. [PMID: 28679223 DOI: 10.1063/1.4985276] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Many mathematical models of respiratory viral infections do not include regeneration of cells within the respiratory tract, arguing that the infection is resolved before there is significant cellular regeneration. However, recent studies have found that ∼40% of patients hospitalized with influenza-like illness are infected with at least two different viruses, which could potentially lead to longer-lasting infections. In these longer infections, cell regeneration might affect the infection dynamics, in particular, allowing for the possibility of chronic coinfections. Several mathematical models have been used to describe cell regeneration in infection models, though the effect of model choice on the predicted time course of viral coinfections is not clear. We investigate four mathematical models incorporating different mechanisms of cell regeneration during respiratory viral coinfection to determine the effect of cell regeneration on infection dynamics. We perform linear stability analysis for each of the models and find the steady states analytically. The analysis suggests that chronic illness is possible but only with one viral species; chronic coexistence of two different viral species is not possible with the regeneration models considered here.
Collapse
Affiliation(s)
- Lubna Pinky
- Department of Physics and Astronomy, Texas Christian University, Fort Worth, Texas 76109, USA
| | - Hana M Dobrovolny
- Department of Physics and Astronomy, Texas Christian University, Fort Worth, Texas 76109, USA
| |
Collapse
|
29
|
Kouche M, Boulfoul B, Ainseba B. Mathematical analysis of an HIV infection model including quiescent cells and periodic antiviral therapy. INT J BIOMATH 2017. [DOI: 10.1142/s1793524517500656] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, we revisit the model by Guedj et al. [J. Guedj, R. Thibaut and D. Commenges, Maximum likelihood estimation in dynamical models of HIV, Biometrics 63 (2007) 198–206; J. Guedj, R. Thibaut and D. Commenges, Practical identifiability of HIV dynamics models, Bull. Math. Biol. 69 (2007) 2493–2513] which describes the effect of treatment with reverse transcriptase (RT) inhibitors and incorporates the class of quiescent cells. We prove that there is a threshold value [Formula: see text] of drug efficiency [Formula: see text] such that if [Formula: see text], the basic reproduction number [Formula: see text] and the infection is cleared and if [Formula: see text], the infectious equilibrium is globally asymptotically stable. When the drug efficiency function [Formula: see text] is periodic and of the bang–bang type we establish a threshold, in terms of spectral radius of some matrix, between the clearance and the persistence of the disease. As stated in related works [L. Rong, Z. Feng and A. Perelson, Emergence of HIV-1 drug resistance during antiretroviral treatment, Bull. Math. Biol. 69 (2007) 2027–2060; P. De Leenheer, Within-host virus models with periodic antiviral therapy, Bull. Math. Biol. 71 (2009) 189–210.], we prove that the increase of the drug efficiency or the active duration of drug must clear the infection more quickly. We illustrate our results by some numerical simulations.
Collapse
Affiliation(s)
- Mahiéddine Kouche
- Département de Mathématiques, Université Badji-Mokhtar-Annaba, BP 12, Annaba 23000, Algeria
| | - Bilal Boulfoul
- Faculté de Technologie, Université du 20 Aout 1955-Skikda, Route d’El-hadaiek, B.P. 26 Skikda, Algeria
| | - Bedr’Eddine Ainseba
- Institut de Mathématiques de Bordeaux, UMR CNRS 52 51, Case 36, Université Victor Segalen Bordeaux 2, 3 Ter Place de la Victoire, F33076 Bordeaux Cedex, France
| |
Collapse
|
30
|
Alshorman A, Samarasinghe C, Lu W, Rong L. An HIV model with age-structured latently infected cells. JOURNAL OF BIOLOGICAL DYNAMICS 2017; 11:192-215. [PMID: 27338168 DOI: 10.1080/17513758.2016.1198835] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
HIV latency remains a major obstacle to viral elimination. The activation rate of latently infected cells may depend on the age of latent infection. In this paper, we develop a model of HIV infection including age-structured latently infected cells. We mathematically analyse the model and use numerical simulations with different activation functions to show that the model can explain the persistence of low-level viremia and the latent reservoir stability in patients on therapy. Sensitivity tests suggest that the model is robust to the changes of most parameters but is sensitive to the relative magnitude of the net generation rate and the long-term activation rate of latently infected cells. To reduce the sensitivity, we extend the model to include homeostatic proliferation of latently infected cells. The new model is robust in reproducing the long-term dynamics of the virus and latently infected cells observed in patients receiving prolonged combination therapy.
Collapse
Affiliation(s)
- Areej Alshorman
- a Department of Mathematics and Statistics , Oakland University , Rochester , MI , USA
| | - Chathuri Samarasinghe
- a Department of Mathematics and Statistics , Oakland University , Rochester , MI , USA
| | - Wenlian Lu
- b School of Mathematical Science , Fudan University , Shanghai , People's Republic of China
| | - Libin Rong
- a Department of Mathematics and Statistics , Oakland University , Rochester , MI , USA
| |
Collapse
|
31
|
Alshorman A, Wang X, Joseph Meyer M, Rong L. Analysis of HIV models with two time delays. JOURNAL OF BIOLOGICAL DYNAMICS 2017; 11:40-64. [PMID: 26889761 DOI: 10.1080/17513758.2016.1148202] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Time delays can affect the dynamics of HIV infection predicted by mathematical models. In this paper, we studied two mathematical models each with two time delays. In the first model with HIV latency, one delay is the time between viral entry into a cell and the establishment of HIV latency, and the other delay is the time between cell infection and viral production. We defined the basic reproductive number and showed the local and global stability of the steady states. Numerical simulations were performed to evaluate the influence of time delays on the dynamics. In the second model with HIV immune response, one delay is the time between cell infection and viral production, and the other delay is the time needed for the adaptive immune response to emerge to control viral replication. With two positive delays, we obtained the stability crossing curves for the model, which were shown to be a series of open-ended curves.
Collapse
Affiliation(s)
- Areej Alshorman
- a Department of Mathematics and Statistics , Oakland University , Rochester , MI , USA
| | - Xia Wang
- b College of Mathematics and Information Science , Xinyang Normal University , Xinyang , People's Republic of China
| | - M Joseph Meyer
- a Department of Mathematics and Statistics , Oakland University , Rochester , MI , USA
| | - Libin Rong
- a Department of Mathematics and Statistics , Oakland University , Rochester , MI , USA
| |
Collapse
|
32
|
Huang Y, Zhang C, Wu J, Lou J. Modelling the HIV persistence through the network of lymphocyte recirculation in vivo. Infect Dis Model 2017; 2:90-99. [PMID: 29928731 PMCID: PMC5963313 DOI: 10.1016/j.idm.2017.02.003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2016] [Revised: 02/22/2017] [Accepted: 02/23/2017] [Indexed: 12/29/2022] Open
Abstract
Human Immunodeficiency Virus (HIV) is able to persist in cellular and/or anatomical viral reservoirs, despite the effective inhibition of virus replication by the antiretroviral therapy (ART). Here we develop a mathematical model to gain some insights of HIV persistence relevant to the lymphocyte recirculation network of immune system and the central nervous system (CNS). Our simulations and analyses illustrate the role of the CNS as a virus reservoir to prevent antiretroviral drugs from penetrating the blood-brain (or blood-testis) barrier, and we examine the long-term impact of this reservoir on the transmissibility of an infected individual. We observe numerically that level of HIV in peripheral blood may not accurately reflect the true mechanisms occurring within other organs.
Collapse
Affiliation(s)
- Ying Huang
- Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444, PR China
| | - Chen Zhang
- 2525 West End Ave. Suite725, Nashville, TN, 37215, Vanderbilt Institute for Global Health at Vanderbilt Medical Center, USA
| | - Jianhong Wu
- MITACS Centre for Disease Modeling, York University, Toronto, Ontario, M3J 1P3, Canada
| | - Jie Lou
- Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444, PR China
| |
Collapse
|
33
|
Sutimin, Chirove F, Soewono E, Nuraini N, Suromo LB. A model incorporating combined RTIs and PIs therapy during early HIV-1 infection. Math Biosci 2017; 285:102-111. [PMID: 28108293 DOI: 10.1016/j.mbs.2017.01.004] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2014] [Revised: 05/26/2015] [Accepted: 01/13/2017] [Indexed: 01/20/2023]
Abstract
We develop a within host mathematical model of HIV-1 infection describing the effects of combined RTIs and PIs treatments on early HIV-1 infection when treatment is captured using periodic functions of pharmacokinetics type. We use an alternative of the basic reproduction number to analyze endemicity level of HIV-1 infection. Various treatment scenarios incorporating perfect and imperfect drug adherence in drug administration are explored. Our results show that pharmacokinetics treatment is a more realistic way of administering the treatment. Apart from confirming that PIs drugs are more effective than RTIs drugs and that combined RTIs and PIs therapy is more effective than monotherapy of RTIs or PIs, our results show that imperfect drug adherence leads to the increase of viral in the absence of mutation even though the drug is good.
Collapse
Affiliation(s)
- Sutimin
- Department of Mathematics, Institut Teknologi Bandung, Bandung 40132, Indonesia; Department of Mathematics, Diponegoro University, Semarang 50275, Indonesia.
| | - F Chirove
- School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4041, South Africa
| | - E Soewono
- Department of Mathematics, Institut Teknologi Bandung, Bandung 40132, Indonesia
| | - N Nuraini
- Department of Mathematics, Institut Teknologi Bandung, Bandung 40132, Indonesia
| | - L B Suromo
- Faculty of Medicine, Diponegoro University, Semarang 50275, Indonesia
| |
Collapse
|
34
|
WANG XIYING, LIU XINZHI, XU WEI, XIE WEICHAU, LIU WANPING. THE DYNAMICS OF HIV MODELS WITH SWITCHING PARAMETERS AND PULSE CONTROL. J BIOL SYST 2017. [DOI: 10.1142/s0218339016500200] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
This paper studies some human immunodeficiency virus (HIV) models with switching parameters and pulse control. The classical virus dynamics model is first modified by incorporating switching parameters which are assumed to be time-varying. Some threshold conditions are derived to guarantee the virus elimination by utilizing a Razumikhin-type approach. The results show that the proper switching conditions chosen can increase the counts of CD4+T-cells while reducing viral load. Pulse control strategies are then applied to the above model. More precisely, the treatment strategy and the vaccination strategy are applied to infected cells and uninfected cells, respectively. Each control strategy is analyzed to gauge its success in achieving viral suppression. Numerical simulations are performed to complement the analytical results and motivate future directions.
Collapse
Affiliation(s)
- XIYING WANG
- Department of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, Henan 466001, P. R. China
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario Canada, N2L 3G1, Canada
| | - XINZHI LIU
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario Canada, N2L 3G1, Canada
| | - WEI XU
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, P. R. China
| | - WEI-CHAU XIE
- Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Ontario Canada, N2L 3G1, Canada
| | - WANPING LIU
- College of Computer Science and Engineering, Chongqing University of Technology, Chongqing 400054, P. R. China
| |
Collapse
|
35
|
Abstract
Antiviral drug resistance is a matter of great clinical importance that, historically, has been investigated mostly from a virological perspective. Although the proximate mechanisms of resistance can be readily uncovered using these methods, larger evolutionary trends often remain elusive. Recent interest by population geneticists in studies of antiviral resistance has spurred new metrics for evaluating mutation and recombination rates, demographic histories of transmission and compartmentalization, and selective forces incurred during viral adaptation to antiviral drug treatment. We present up-to-date summaries on antiviral resistance for a range of drugs and viral types, and review recent advances for studying their evolutionary histories. We conclude that information imparted by demographic and selective histories, as revealed through population genomic inference, is integral to assessing the evolution of antiviral resistance as it pertains to human health.
Collapse
Affiliation(s)
- Kristen K Irwin
- School of Life Sciences, École Polytechnique Fédéral de Lausanne (EPFL), Lausanne, Switzerland.,Swiss Institute of Bioinformatics (SIB), Lausanne, Switzerland
| | - Nicholas Renzette
- Department of Microbiology and Physiological Systems, University of Massachusetts Medical School, Worcester, Massachusetts, USA
| | - Timothy F Kowalik
- Department of Microbiology and Physiological Systems, University of Massachusetts Medical School, Worcester, Massachusetts, USA
| | - Jeffrey D Jensen
- School of Life Sciences, École Polytechnique Fédéral de Lausanne (EPFL), Lausanne, Switzerland.,Swiss Institute of Bioinformatics (SIB), Lausanne, Switzerland
| |
Collapse
|
36
|
Kumberger P, Frey F, Schwarz US, Graw F. Multiscale modeling of virus replication and spread. FEBS Lett 2016; 590:1972-86. [PMID: 26878104 DOI: 10.1002/1873-3468.12095] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2015] [Revised: 01/21/2016] [Accepted: 02/07/2016] [Indexed: 01/16/2023]
Abstract
Replication and spread of human viruses is based on the simultaneous exploitation of many different host functions, bridging multiple scales in space and time. Mathematical modeling is essential to obtain a systems-level understanding of how human viruses manage to proceed through their life cycles. Here, we review corresponding advances for viral systems of large medical relevance, such as human immunodeficiency virus-1 (HIV-1) and hepatitis C virus (HCV). We will outline how the combination of mathematical models and experimental data has advanced our quantitative knowledge about various processes of these pathogens, and how novel quantitative approaches promise to fill remaining gaps.
Collapse
Affiliation(s)
- Peter Kumberger
- BioQuant-Center, Heidelberg University, Germany.,Center for Modeling and Simulation in the Biosciences (BIOMS), Heidelberg University, Germany
| | - Felix Frey
- BioQuant-Center, Heidelberg University, Germany.,Institute for Theoretical Physics, Heidelberg University, Germany
| | - Ulrich S Schwarz
- BioQuant-Center, Heidelberg University, Germany.,Institute for Theoretical Physics, Heidelberg University, Germany
| | - Frederik Graw
- BioQuant-Center, Heidelberg University, Germany.,Center for Modeling and Simulation in the Biosciences (BIOMS), Heidelberg University, Germany
| |
Collapse
|
37
|
Sun X, Xiao Y, Tang S, Peng Z, Wu J, Wang N. Early HAART Initiation May Not Reduce Actual Reproduction Number and Prevalence of MSM Infection: Perspectives from Coupled within- and between-Host Modelling Studies of Chinese MSM Populations. PLoS One 2016; 11:e0150513. [PMID: 26930406 PMCID: PMC4773120 DOI: 10.1371/journal.pone.0150513] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2015] [Accepted: 02/15/2016] [Indexed: 12/22/2022] Open
Abstract
Having a thorough understanding of the infectivity of HIV, time of initiating treatment and emergence of drug resistant virus variants is crucial in mitigating HIV infection. There are many challenges to evaluating the long-term effect of the Highly Active Antiretroviral Therapy (HAART) on disease transmission at the population level. We proposed an individual based model by coupling within-host dynamics and between-host dynamics and conduct stochastic simulation in the group of men who have sex with men (MSM). The mean actual reproduction number is estimated to be 3.6320 (95% confidence interval: [3.46, 3.80]) for MSM group without treatment. Stochastic simulations show that given relatively high (low) level of drug efficacy after emergence of drug resistant variants, early initiation of treatment leads to a less (greater) actual reproduction number, lower (higher) prevalence and less (more) incidences, compared to late initiation of treatment. This implies early initiation of HAART may not always lower the actual reproduction number and prevalence of infection, depending on the level of treatment efficacy after emergence of drug resistant virus variants, frequency of high-risk behaviors and etc. This finding strongly suggests early initiation of HAART should be implemented with great care especially in the settings where the effective drugs are limited. Coupling within-host dynamics with between-host dynamics can provide critical information about impact of HAART on disease transmission and thus help to assist treatment strategy design and HIV/AIDS prevention and control.
Collapse
Affiliation(s)
- Xiaodan Sun
- Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an, Shaanxi, China
| | - Yanni Xiao
- Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an, Shaanxi, China
| | - Sanyi Tang
- College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi, China
| | - Zhihang Peng
- School of Public Health, Nanjing Medical University, Nanjing, Jiangsu, China
| | - Jianhong Wu
- Laboratory for Industrial and Applied Mathematics, Centre for Disease Modelling, York Institute for Health Research, York University, Toronto, ON, Canada
| | - Ning Wang
- National Center for AIDS/STD Prevention and Control, Chinese Center for Disease Control and Prevention, Beijing, China
| |
Collapse
|
38
|
Wang X, Song X, Tang S, Rong L. Dynamics of an HIV Model with Multiple Infection Stages and Treatment with Different Drug Classes. Bull Math Biol 2016; 78:322-49. [PMID: 26842389 DOI: 10.1007/s11538-016-0145-5] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2015] [Accepted: 01/20/2016] [Indexed: 02/06/2023]
Abstract
Highly active antiretroviral therapy can effectively control HIV replication in infected individuals. Some clinical and modeling studies suggested that viral decay dynamics may depend on the inhibited stages of the viral replication cycle. In this paper, we develop a general mathematical model incorporating multiple infection stages and various drug classes that can interfere with specific stages of the viral life cycle. We derive the basic reproductive number and obtain the global stability results of steady states. Using several simple cases of the general model, we study the effect of various drug classes on the dynamics of HIV decay. When drugs are assumed to be 100% effective, drugs acting later in the viral life cycle lead to a faster or more rapid decay in viremia. This is consistent with some patient and experimental data, and also agrees with previous modeling results. When drugs are not 100% effective, the viral decay dynamics are more complicated. Without a second population of long-lived infected cells, the viral load decline can have two phases if drugs act at an intermediate stage of the viral replication cycle. The slopes of viral load decline depend on the drug effectiveness, the death rate of infected cells at different stages, and the transition rate of infected cells from one to the next stage. With a second population of long-lived infected cells, the viral load decline can have three distinct phases, consistent with the observation in patients receiving antiretroviral therapy containing the integrase inhibitor raltegravir. We also fit modeling prediction to patient data under efavirenz (a nonnucleoside reverse-transcriptase inhibitor) and raltegravir treatment. The first-phase viral load decline under raltegravir therapy is longer than that under efavirenz, resulting in a lower viral load at initiation of the second-phase decline in patients taking raltegravir. This explains why patients taking a raltegravir-based therapy were faster to achieve viral suppression than those taking an efavirenz-based therapy. Taken together, this work provides a quantitative and systematic comparison of the effect of different drug classes on HIV decay dynamics and can explain the viral load decline in HIV patients treated with raltegravir-containing regimens.
Collapse
Affiliation(s)
- Xia Wang
- School of Mathematics and Information Sciences, Shaanxi Normal University, Xi'an, 710062, China
- College of Mathematics and Information Science, Xinyang Normal University, Xinyang, 464000, China
| | - Xinyu Song
- College of Mathematics and Information Science, Xinyang Normal University, Xinyang, 464000, China
| | - Sanyi Tang
- School of Mathematics and Information Sciences, Shaanxi Normal University, Xi'an, 710062, China
| | - Libin Rong
- Department of Mathematics and Statistics, and Center for Biomedical Research, Oakland University, Rochester, MI, 48309, USA.
| |
Collapse
|
39
|
Li B, Chen Y, Lu X, Liu S. A delayed HIV-1 model with virus waning term. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2016; 13:135-157. [PMID: 26776264 DOI: 10.3934/mbe.2016.13.135] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
In this paper, we propose and analyze a delayed HIV-1 model with CTL immune response and virus waning. The two discrete delays stand for the time for infected cells to produce viruses after viral entry and for the time for CD8+ T cell immune response to emerge to control viral replication. We obtain the positiveness and boundedness of solutions and find the basic reproduction number R0. If R0 < 1, then the infection-free steady state is globally asymptotically stable and the infection is cleared from the T-cell population; whereas if R0 > 1, then the system is uniformly persistent and the viral concentration maintains at some constant level. The global dynamics when R0 > 1 is complicated. We establish the local stability of the infected steady state and show that Hopf bifurcation can occur. Both analytical and numerical results indicate that if, in the initial infection stage, the effect of delays on HIV-1 infection is ignored, then the risk of HIV-1 infection (if persists) will be underestimated. Moreover, the viral load differs from that without virus waning. These results highlight the important role of delays and virus waning on HIV-1 infection.
Collapse
Affiliation(s)
- Bing Li
- Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Technology, 3041#, 2 Yi-Kuang street, Harbin, 150080, China.
| | | | | | | |
Collapse
|
40
|
Tang B, Xiao Y, Cheke RA, Wang N. Piecewise virus-immune dynamic model with HIV-1 RNA-guided therapy. J Theor Biol 2015; 377:36-46. [PMID: 25908208 DOI: 10.1016/j.jtbi.2015.03.040] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2014] [Revised: 02/03/2015] [Accepted: 03/24/2015] [Indexed: 12/22/2022]
Abstract
Clinical studies have used CD4 T cell counts to evaluate the safety or risk of plasma HIV-1 RNA-guided structured treatment interruptions (STIs), aimed at maintaining CD4 T cell counts above a safe level and plasma HIV-1 RNA below a certain level. However, quantifying and evaluating the impact of STIs on the control of HIV replication and on activation of the immune response remains challenging. Here we extend the virus-immune dynamic system by including a piecewise smooth function to describe the elimination of HIV viral loads and the activation of effector cells under plasma HIV-1 RNA-guided therapy, in order to quantitatively explore the STI strategies. We theoretically investigate the global dynamics of the proposed Filippov system. Our main results indicate that HIV viral loads could either go to infinity or be maintained below a certain level or stabilize at a previously given level, depending on the threshold level and initial HIV virus loads and effector cell counts. This suggests that proper combinations of threshold and initial HIV virus loads and effector cell counts, based on threshold policy, can successfully preclude exceptionally high growth of HIV virus and, in particular, maximize the controllable region.
Collapse
Affiliation(s)
- Biao Tang
- School of Mathematics and Statistics, Xi׳an Jiaotong University, Xi׳an, 710049, PR China
| | - Yanni Xiao
- School of Mathematics and Statistics, Xi׳an Jiaotong University, Xi׳an, 710049, PR China.
| | - Robert A Cheke
- Natural Resources Institute, University of Greenwich at Medway, Chatham Maritime, Chatham, Kent ME4 4TB, UK
| | - Ning Wang
- National Center for AIDS/STD Prevention and Control, Chinese Center for Disease Control and Prevention, 27 Nanwei Rd, Beijing 100050, PR China
| |
Collapse
|
41
|
Feng Z, Cen X, Zhao Y, Velasco-Hernandez JX. Coupled within-host and between-host dynamics and evolution of virulence. Math Biosci 2015; 270:204-12. [PMID: 25749184 DOI: 10.1016/j.mbs.2015.02.012] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2014] [Revised: 02/23/2015] [Accepted: 02/25/2015] [Indexed: 11/27/2022]
Abstract
Mathematical models coupling within- and between-host dynamics can be helpful for deriving trade-off functions between disease transmission and virulence at the population level. Such functions have been used to study the evolution of virulence and to explore the possibility of a conflict between natural selection at individual and population levels for directly transmitted diseases (Gilchrist and Coombs, 2006). In this paper, a new coupled model for environmentally-driven diseases is analyzed to study similar biological questions. It extends the model in Cen et al. (2014) and Feng et al. (2013) by including the disease-induced host mortality. It is shown that the extended model exhibits similar dynamical behaviors including the possible occurrence of a backward bifurcation. It is also shown that the within-host pathogen load and the disease prevalence at the positive stable equilibrium are increasing functions of the within- and between-host reproduction numbers (Rw0 and Rb0), respectively. Optimal parasite strategies will maximize these reproduction numbers at the two levels, and a conflict may exist between the two levels. Our results highlight the role of inter-dependence of variables and parameters in the fast and slow systems for persistence of infections and evolution of pathogens in an environmentally-driven disease. Our results also demonstrate the importance of incorporating explicit links of the within- and between-host dynamics into the computation of threshold conditions for disease control.
Collapse
Affiliation(s)
- Zhilan Feng
- Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA.
| | - Xiuli Cen
- Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, P.R. China.
| | - Yulin Zhao
- Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, P.R. China.
| | | |
Collapse
|
42
|
HIV treatment as prevention: contradictory perspectives from dynamic mathematical models. ScientificWorldJournal 2014; 2014:760734. [PMID: 25580461 PMCID: PMC4279253 DOI: 10.1155/2014/760734] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2014] [Accepted: 11/26/2014] [Indexed: 12/20/2022] Open
Abstract
The preventative effects of antiretroviral therapy for people with HIV have been debated since they were first raised. Models commenced studying the preventive effects of treatment in the 1990s, prior to initial public reports. However, the outcomes of the preventive effects of antiretroviral use were not consistent. Some outcomes of dynamic models were based on unfeasible assumptions, such as no consideration of drug resistance, behavior disinhibition, or economic inputs in poor countries, and unrealistic input variables, for example, overstated initiation time, adherence, coverage, and efficacy of treatment. This paper reviewed dynamic mathematical models to ascertain the complex effects of ART on HIV transmission. This review discusses more conservative inputs and outcomes relative to antiretroviral use in HIV infections in dynamic mathematical models. ART alone cannot eliminate HIV transmission.
Collapse
|
43
|
Bertacchi D, Zucca F, Foresti S, Mangioni D, Gori A. Combination versus sequential monotherapy in chronic HBV infection: a mathematical approach. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2014; 32:383-403. [PMID: 25398978 DOI: 10.1093/imammb/dqu022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2013] [Accepted: 10/12/2014] [Indexed: 11/12/2022]
Abstract
Sequential monotherapy is the most widely used therapeutic approach in the treatment of hepatitis B virus (HBV) chronic infection. Unfortunately, under therapy, in some patients the hepatitis virus mutates and gives rise to variants which are drug resistant. We wonder whether those patients would have benefited from the choice of combination therapy instead of sequential monotherapy. To study the action of these two therapeutic approaches and to explain the emergence of drug resistance, we propose a stochastic model for the infection within a patient who is treated with two drugs, either sequentially or contemporaneously, and who, under the first kind of therapy develops a strain of the virus which is resistant to both drugs. Our stochastic model has a deterministic approximation which is a slight modification of a classic three-strain model. We discuss why stochastic simulations are more suitable than the study of the deterministic approximation, when modelling the rise of mutations (this is mainly due to the amplitude of the stochastic fluctuations). We run stochastic simulations with suitable parameters and compare the time when, under the two therapeutic approaches, the resistant strain first reaches detectability in the serum viral load. Our results show that the best choice is to start an early combination therapy, which allows one to stay drug resistance free for a longer time and in many cases leads to viral eradication.
Collapse
Affiliation(s)
- Daniela Bertacchi
- Università di Milano-Bicocca Dipartimento di Matematica e Applicazioni, Via Cozzi 53, 20125 Milano, Italy
| | - Fabio Zucca
- Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
| | - Sergio Foresti
- Division of Infectious Diseases Department of Internal Medicine, 'San Gerardo' Hospital, Università di Milano-Bicocca, 20900 Monza, Italy
| | - Davide Mangioni
- Division of Infectious Diseases Department of Internal Medicine, 'San Gerardo' Hospital, Università di Milano-Bicocca, 20900 Monza, Italy
| | - Andrea Gori
- Division of Infectious Diseases Department of Internal Medicine, 'San Gerardo' Hospital, Università di Milano-Bicocca, 20900 Monza, Italy
| |
Collapse
|
44
|
Gopalakrishnan S, Montazeri H, Menz S, Beerenwinkel N, Huisinga W. Estimating HIV-1 fitness characteristics from cross-sectional genotype data. PLoS Comput Biol 2014; 10:e1003886. [PMID: 25375675 PMCID: PMC4222584 DOI: 10.1371/journal.pcbi.1003886] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2014] [Accepted: 08/26/2014] [Indexed: 12/31/2022] Open
Abstract
Despite the success of highly active antiretroviral therapy (HAART) in the management of human immunodeficiency virus (HIV)-1 infection, virological failure due to drug resistance development remains a major challenge. Resistant mutants display reduced drug susceptibilities, but in the absence of drug, they generally have a lower fitness than the wild type, owing to a mutation-incurred cost. The interaction between these fitness costs and drug resistance dictates the appearance of mutants and influences viral suppression and therapeutic success. Assessing in vivo viral fitness is a challenging task and yet one that has significant clinical relevance. Here, we present a new computational modelling approach for estimating viral fitness that relies on common sparse cross-sectional clinical data by combining statistical approaches to learn drug-specific mutational pathways and resistance factors with viral dynamics models to represent the host-virus interaction and actions of drug mechanistically. We estimate in vivo fitness characteristics of mutant genotypes for two antiretroviral drugs, the reverse transcriptase inhibitor zidovudine (ZDV) and the protease inhibitor indinavir (IDV). Well-known features of HIV-1 fitness landscapes are recovered, both in the absence and presence of drugs. We quantify the complex interplay between fitness costs and resistance by computing selective advantages for different mutants. Our approach extends naturally to multiple drugs and we illustrate this by simulating a dual therapy with ZDV and IDV to assess therapy failure. The combined statistical and dynamical modelling approach may help in dissecting the effects of fitness costs and resistance with the ultimate aim of assisting the choice of salvage therapies after treatment failure. Mutations conferring drug resistance represent major threats to the therapeutic success of highly active antiretroviral therapy (HAART) against human immunodeficiency virus (HIV)-1 infection. Viral mutants differ in their fitness and assessing viral fitness is a challenging task. In this article, we estimate drug-specific mutational pathways by learning from clinical data using statistical techniques and incorporate these into mathematical models of in vivo viral infection dynamics. This approach enables us to estimate mutant fitness characteristics. We illustrate our method by predicting fitness characteristics of mutant genotypes for two different antiretroviral therapies with the drugs zidovudine and indinavir. We recover several established features of mutant fitnesses and quantify fitness characteristics both in the absence and presence of drugs. Our model extends naturally to multiple drugs and we illustrate this by simulating a dual therapy with ZDV and IDV to assess therapy failure. Additionally, our modelling approach relies only on cross-sectional clinical data. We believe that such an approach is a highly valuable tool in assisting the choice of salvage therapies after treatment failure.
Collapse
Affiliation(s)
- Sathej Gopalakrishnan
- Institute of Biochemistry and Biology, University of Potsdam, Potsdam, Germany
- Graduate Research Training Program PharMetrX: Pharmacometrics & Computational Disease Modelling, Free University of Berlin and University of Potsdam, Berlin/Potsdam, Germany
| | - Hesam Montazeri
- Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland
- SIB Swiss Institute of Bioinformatics, Basel, Switzerland
| | - Stephan Menz
- Institute of Mathematics, University of Potsdam, Potsdam, Germany
| | - Niko Beerenwinkel
- Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland
- SIB Swiss Institute of Bioinformatics, Basel, Switzerland
- * E-mail: (NB); (WH)
| | - Wilhelm Huisinga
- Institute of Biochemistry and Biology, University of Potsdam, Potsdam, Germany
- Institute of Mathematics, University of Potsdam, Potsdam, Germany
- * E-mail: (NB); (WH)
| |
Collapse
|
45
|
Emerging disease dynamics in a model coupling within-host and between-host systems. J Theor Biol 2014; 361:141-51. [PMID: 25093825 DOI: 10.1016/j.jtbi.2014.07.030] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2014] [Revised: 07/01/2014] [Accepted: 07/10/2014] [Indexed: 11/23/2022]
Abstract
Epidemiological models and immunological models have been studied largely independently. However, the two processes (between- and within-host interactions) occur jointly and models that couple the two processes may generate new biological insights. Particularly, the threshold conditions for disease control may be dramatically different when compared with those generated from the epidemiological or immunological models separately. An example is considered in this paper for an environmentally driven infectious disease such as Toxoplasma gondii. The model explicitly couples the within-host and between-host dynamics. The within-host sub-system is linked to a contaminated environment E via an additional term g(E) to account for the increase in the parasite load V within a host due to the continuous ingestion of parasites from the contaminated environment. The parasite load V can also affect the rate of environmental contamination, which directly contributes to the infection rate of hosts for the between-host sub-system. When the two sub-systems are considered in isolation, the dynamics are standard and simple. That is, either the infection-free equilibrium is stable or a unique positive equilibrium is stable depending on the relevant reproduction number being less or greater than 1. However, when the two sub-systems are explicitly coupled, the full system exhibits more complex dynamics including backward bifurcations; that is, multiple positive equilibria exist with one of which being stable even if the reproduction number is less than 1. The biological implications of such bifurcations are illustrated using an example concerning the spread and control of toxoplasmosis.
Collapse
|
46
|
Pappas G, Yujiang J, Seiler N, Malcarney MB, Horton K, Shaikh I, Freehill G, Alexander C, Akhter MN, Hidalgo J. Perspectives on the role of patient-centered medical homes in HIV Care. Am J Public Health 2014; 104:e49-53. [PMID: 24832431 PMCID: PMC4056203 DOI: 10.2105/ajph.2014.302022] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 03/26/2014] [Indexed: 01/22/2023]
Abstract
To strengthen the quality of HIV care and achieve improved clinical outcomes, payers, providers, and policymakers should encourage the use of patient-centered medical homes (PCMHs), building on the Ryan White CARE Act Program established in the 1990s. The rationale for a PCMH with HIV-specific expertise is rooted in clinical complexity, HIV's social context, and ongoing gaps in HIV care. Existing Ryan White HIV/AIDS Program clinicians are prime candidates to serve HIV PCMHs, and HIV-experienced community-based organizations can play an important role. Increasingly, state Medicaid programs are adopting a PCMH care model to improve access and quality to care. Stakeholders should consider several important areas for future action and research with regard to development of the HIV PCMH.
Collapse
Affiliation(s)
- Gregory Pappas
- At the time of initial writing and research, Gregory Pappas, Jia Yujiang, Irshad Shaikh, Gunther Freehill, and Mohammad N. Akhter were with the District of Columbia Department of Health, Washington, DC. Naomi Seiler, Mary-Beth Malcarney, Katherine Horton, and Julia Hidalgo were with the Milken Institute School of Public Health, George Washington University, Washington, DC. Carla Alexander was with Institute of Human Virology, University of Maryland School of Medicine, Baltimore
| | | | | | | | | | | | | | | | | | | |
Collapse
|
47
|
Arafa AAM, Rida SZ, Khalil M. A fractional-order model of HIV infection: Numerical solution and comparisons with data of patients. INT J BIOMATH 2014. [DOI: 10.1142/s1793524514500363] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, a fractional-order model which describes the human immunodeficiency type-1 virus (HIV-1) infection is presented. Numerical solutions are obtained using a generalized Euler method (GEM) to handle the fractional derivatives. The fractional derivatives are described in the Caputo sense. We show that the model established in this paper possesses non-negative solutions. Comparisons between the results of the fractional-order model, the results of the integer model and the measured real data obtained from 10 patients during primary HIV-1 infection are presented. These comparisons show that the results of the fractional-order model give predictions to the plasma virus load of the patients better than those of the integer model.
Collapse
Affiliation(s)
- A. A. M. Arafa
- Department of Mathematics and Computer Science, Faculty of Sciences, Port Said University, Port Said, Egypt
| | - S. Z. Rida
- Department of Mathematics, Faculty of Sciences, South Valley University, Qena, Egypt
| | - M. Khalil
- Department of Mathematics, Faculty of Engineering, October University for Modern Sciences and Arts (MSA University), 6th Oct. City, Giza, Egypt
| |
Collapse
|
48
|
LOU JIE, ZHANG HONGMEI, ZHAO QUANBI, LIAO LINGJIE, HAN LITAO. THE STUDY OF HIV INFECTION IN CHINESE ANTIRETROVIRAL THERAPY PATIENTS. J BIOL SYST 2014. [DOI: 10.1142/s0218339014500041] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Analysis of changes in viral load after initiation of treatment with potent antiretroviral agents has provided substantial insights into the dynamics of human immunodeficiency virus type 1. We built a simple mathematics model to study the effect of latent-infected resting memory CD4+ T cells during the HIV infection and highly active anti-retroviral therapy (HAART). Through analysis of eight patients who received HAART in China, we have an insight into the mechanisms of resting memory CD4+ T cells in HIV infection. Simulations show that new infections still exist in the eight patients even under the HAART. Also, because of the long half-life of resting infected memory CD4+ T cells, removal of HIV from patient could take considerably longer time or be unattainable.
Collapse
Affiliation(s)
- JIE LOU
- Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China
| | - HONGMEI ZHANG
- Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China
| | - QUANBI ZHAO
- Department of Research on Virology and Immunology, National Center for AIDS/STD Control and Prevention, Beijing 100050, P. R. China
| | - LINGJIE LIAO
- Department of Research on Virology and Immunology, National Center for AIDS/STD Control and Prevention, Beijing 100050, P. R. China
| | - LITAO HAN
- School of Information, Renmin University of China, Beijing 100872, P. R. China
| |
Collapse
|
49
|
Wang X, Liu S, Rong L. Permanence and extinction of a non-autonomous HIV-1
model with time delays. ACTA ACUST UNITED AC 2014. [DOI: 10.3934/dcdsb.2014.19.1783] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
|
50
|
Jiang C, Wang W. Complete classification of global dynamics of a virus model with
immune responses. ACTA ACUST UNITED AC 2014. [DOI: 10.3934/dcdsb.2014.19.1087] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
|