1
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Xu S. Modelling Role of Protective and Nonprotective HLA Allele Inducing Different HIV Infection Outcomes. Bull Math Biol 2024; 86:107. [PMID: 39003370 PMCID: PMC11246342 DOI: 10.1007/s11538-024-01334-9] [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: 01/24/2024] [Accepted: 06/25/2024] [Indexed: 07/15/2024]
Abstract
Human immunodeficiency virus (HIV) infects CD4+ cells and causes progressive immune function failure, and CD8+ cells lyse infected CD4+ cell via recognising peptide presented by human leukocyte antigens (HLA). Variations in HLA allele lead to observed different HIV infection outcomes. Within-host HIV dynamics involves virus replication within infected cells and lysing of infected cells by CD8+ cells, but how variations in HLA alleles determine different infection outcomes was far from clear. Here, we used mathematical modelling and parameter inference with a new analysis of published virus inhibition assay data to estimate CD8+ cell lysing efficiency, and found that lysing efficiency fall in the gap between low bound (0.1-0.2 day-1 (Elemans et al. in PLoS Comput Biol 8(2):e1002381, 2012)) and upper boundary (6.5-8.4 day-1 (Wick et al. in J Virol 79(21):13579-13586, 2005)). Our outcomes indicate that both lysing efficiency and viral inoculum size jointly determine observed different infection outcomes. Low lysing rate associated with non-protective HLA alleles leads to monostable viral kinetic to high viral titre and oscillatory viral kinetics. High lysing rate associated with protective HLA alleles leads monostable viral kinetic to low viral titre and bistable viral kinetics; at a specific interval of CD8+ cell counts, small viral inoculum sizes are inhibited but not large viral inoculum sizes remain infectious. Further, with CD8+ cell recruitment, HIV kinetics always exhibit oscillatory kinetics, but lysing rate is negatively correlated with range of CD8+ cell count. Our finding highlights role of HLA allele determining different infection outcomes, thereby providing a potential mechanistic explanation for observed good and bad HIV infection outcomes induced by protective HLA allele.
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Affiliation(s)
- Shilian Xu
- Department of Environment and Genetics, School of Agriculture, Biomedicine and Environment, La Trobe University, Bundoora, VIC, 3086, Australia.
- Department of Mathematical and Physical Sciences, La Trobe University, Bundoora, VIC, 3086, Australia.
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2
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Liyanage YR, Heitzman-Breen N, Tuncer N, Ciupe SM. Identifiability investigation of within-host models of acute virus infection. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.05.09.593464. [PMID: 38766177 PMCID: PMC11100786 DOI: 10.1101/2024.05.09.593464] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2024]
Abstract
Uncertainty in parameter estimates from fitting within-host models to empirical data limits the model's ability to uncover mechanisms of infection, disease progression, and to guide pharmaceutical interventions. Understanding the effect of model structure and data availability on model predictions is important for informing model development and experimental design. To address sources of uncertainty in parameter estimation, we use four mathematical models of influenza A infection with increased degrees of biological realism. We test the ability of each model to reveal its parameters in the presence of unlimited data by performing structural identifiability analyses. We then refine the results by predicting practical identifiability of parameters under daily influenza A virus titers alone or together with daily adaptive immune cell data. Using these approaches, we present insight into the sources of uncertainty in parameter estimation and provide guidelines for the types of model assumptions, optimal experimental design, and biological information needed for improved predictions.
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Affiliation(s)
- Yuganthi R Liyanage
- Department of Mathematics and Statistics, Florida Atlantic University, Boca Raton, FL, USA
| | - Nora Heitzman-Breen
- Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA
| | - Necibe Tuncer
- Department of Mathematics and Statistics, Florida Atlantic University, Boca Raton, FL, USA
| | - Stanca M Ciupe
- Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA
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3
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Ciupe SM, Conway JM. Incorporating Intracellular Processes in Virus Dynamics Models. Microorganisms 2024; 12:900. [PMID: 38792730 PMCID: PMC11124127 DOI: 10.3390/microorganisms12050900] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2024] [Revised: 04/25/2024] [Accepted: 04/26/2024] [Indexed: 05/26/2024] Open
Abstract
In-host models have been essential for understanding the dynamics of virus infection inside an infected individual. When used together with biological data, they provide insight into viral life cycle, intracellular and cellular virus-host interactions, and the role, efficacy, and mode of action of therapeutics. In this review, we present the standard model of virus dynamics and highlight situations where added model complexity accounting for intracellular processes is needed. We present several examples from acute and chronic viral infections where such inclusion in explicit and implicit manner has led to improvement in parameter estimates, unification of conclusions, guidance for targeted therapeutics, and crossover among model systems. We also discuss trade-offs between model realism and predictive power and highlight the need of increased data collection at finer scale of resolution to better validate complex models.
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Affiliation(s)
- Stanca M. Ciupe
- Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24060, USA
| | - Jessica M. Conway
- Department of Mathematics and Center for Infectious Disease Dynamics, Penn State University, State College, PA 16802, USA
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4
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Ciupe SM, Dahari H, Ploss A. Mathematical Models of Early Hepatitis B Virus Dynamics in Humanized Mice. Bull Math Biol 2024; 86:53. [PMID: 38594319 PMCID: PMC11003933 DOI: 10.1007/s11538-024-01284-2] [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: 10/25/2023] [Accepted: 03/15/2024] [Indexed: 04/11/2024]
Abstract
Analyzing the impact of the adaptive immune response during acute hepatitis B virus (HBV) infection is essential for understanding disease progression and control. Here we developed mathematical models of HBV infection which either lack terms for adaptive immune responses, or assume adaptive immune responses in the form of cytolytic immune killing, non-cytolytic immune cure, or non-cytolytic-mediated block of viral production. We validated the model that does not include immune responses against temporal serum hepatitis B DNA (sHBV) and temporal serum hepatitis B surface-antigen (HBsAg) experimental data from mice engrafted with human hepatocytes (HEP). Moreover, we validated the immune models against sHBV and HBsAg experimental data from mice engrafted with HEP and human immune system (HEP/HIS). As expected, the model that does not include adaptive immune responses matches the observed high sHBV and HBsAg concentrations in all HEP mice. By contrast, while all immune response models predict reduction in sHBV and HBsAg concentrations in HEP/HIS mice, the Akaike Information Criterion cannot discriminate between non-cytolytic cure (resulting in a class of cells refractory to reinfection) and antiviral block functions (of up to 99 % viral production 1-3 weeks following peak viral load). We can, however, reject cytolytic killing, as it can only match the sHBV and HBsAg data when we predict unrealistic levels of hepatocyte loss.
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Affiliation(s)
- Stanca M Ciupe
- Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA.
| | - Harel Dahari
- Division of Hepatology, Department of Medicine, Loyola University, Chicago, IL, USA
| | - Alexander Ploss
- Department of Molecular Biology, Princeton University, Princeton, NJ, USA
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5
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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.
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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
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6
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Liu HY, Li X, Wang ZG, Liu SL. Virus-mimicking nanosystems: from design to biomedical applications. Chem Soc Rev 2023; 52:8481-8499. [PMID: 37929845 DOI: 10.1039/d3cs00138e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2023]
Abstract
Nanomedicine, as an interdisciplinary discipline involving the development and application of nanoscale materials and technologies, is rapidly developing under the impetus of bionanotechnology and has attracted a great deal of attention from researchers. Especially, with the global outbreak of COVID-19, the in-depth investigation of the infection mechanism of the viruses has made the study of virus-mimicking nanosystems (VMNs) a popular research topic. In this review, we initiate with a brief historical perspective on the emergence and development of VMNs for providing a comprehensive view of the field. Next, we present emerging design principles and functionalization strategies for fabricating VMNs in light of viral infection mechanisms. Then, we describe recent advances in VMNs in biology, with a major emphasis on representative examples. Finally, we summarize the opportunities and challenges that exist in this field, hoping to provide new insights and inspiration to develop VMNs for disease diagnosis and treatment and to attract the interest of more researchers from different fields.
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Affiliation(s)
- Hao-Yang Liu
- State Key Laboratory of Medicinal Chemical Biology, Frontiers Science Centre for New Organic Matter, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Research Centre for Analytical Sciences, College of Chemistry, School of Medicine and Frontiers Science Center for Cell Responses, Nankai University, Tianjin 300071, P. R. China.
| | - Xiao Li
- State Key Laboratory of Medicinal Chemical Biology, Frontiers Science Centre for New Organic Matter, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Research Centre for Analytical Sciences, College of Chemistry, School of Medicine and Frontiers Science Center for Cell Responses, Nankai University, Tianjin 300071, P. R. China.
| | - Zhi-Gang Wang
- State Key Laboratory of Medicinal Chemical Biology, Frontiers Science Centre for New Organic Matter, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Research Centre for Analytical Sciences, College of Chemistry, School of Medicine and Frontiers Science Center for Cell Responses, Nankai University, Tianjin 300071, P. R. China.
| | - Shu-Lin Liu
- State Key Laboratory of Medicinal Chemical Biology, Frontiers Science Centre for New Organic Matter, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Research Centre for Analytical Sciences, College of Chemistry, School of Medicine and Frontiers Science Center for Cell Responses, Nankai University, Tianjin 300071, P. R. China.
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, P. R. China
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7
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Hailegiorgis A, Ishida Y, Collier N, Imamura M, Shi Z, Reinharz V, Tsuge M, Barash D, Hiraga N, Yokomichi H, Tateno C, Ozik J, Uprichard SL, Chayama K, Dahari H. Modeling suggests that virion production cycles within individual cells is key to understanding acute hepatitis B virus infection kinetics. PLoS Comput Biol 2023; 19:e1011309. [PMID: 37535676 PMCID: PMC10426918 DOI: 10.1371/journal.pcbi.1011309] [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: 11/02/2022] [Revised: 08/15/2023] [Accepted: 06/26/2023] [Indexed: 08/05/2023] Open
Abstract
Hepatitis B virus (HBV) infection kinetics in immunodeficient mice reconstituted with humanized livers from inoculation to steady state is highly dynamic despite the absence of an adaptive immune response. To recapitulate the multiphasic viral kinetic patterns, we developed an agent-based model that includes intracellular virion production cycles reflecting the cyclic nature of each individual virus lifecycle. The model fits the data well predicting an increase in production cycles initially starting with a long production cycle of 1 virion per 20 hours that gradually reaches 1 virion per hour after approximately 3-4 days before virion production increases dramatically to reach to a steady state rate of 4 virions per hour per cell. Together, modeling suggests that it is the cyclic nature of the virus lifecycle combined with an initial slow but increasing rate of HBV production from each cell that plays a role in generating the observed multiphasic HBV kinetic patterns in humanized mice.
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Affiliation(s)
- Atesmachew Hailegiorgis
- The Program for Experimental & Theoretical Modeling, Division of Hepatology, Department of Medicine, Stritch School of Medicine, Loyola University Chicago, Maywood, Illinois, United States of America
| | - Yuji Ishida
- PhoenixBio Co., Ltd., Hiroshima, Japan
- Research Center for Hepatology and Gastroenterology, Graduate School of Biomedical and Health Sciences, Hiroshima University, Hiroshima, Japan
| | - Nicholson Collier
- Consortium for Advanced Science and Engineering, University of Chicago, Chicago, Illinois, United States of America
- Decision and Infrastructure Sciences, Argonne National Laboratory, Argonne, Illinois, United States of America
| | - Michio Imamura
- Research Center for Hepatology and Gastroenterology, Graduate School of Biomedical and Health Sciences, Hiroshima University, Hiroshima, Japan
| | - Zhenzhen Shi
- The Program for Experimental & Theoretical Modeling, Division of Hepatology, Department of Medicine, Stritch School of Medicine, Loyola University Chicago, Maywood, Illinois, United States of America
| | - Vladimir Reinharz
- Department of Computer Science, Université du Québec à Montréal, Montreal, Canada
| | - Masataka Tsuge
- The Program for Experimental & Theoretical Modeling, Division of Hepatology, Department of Medicine, Stritch School of Medicine, Loyola University Chicago, Maywood, Illinois, United States of America
- Research Center for Hepatology and Gastroenterology, Graduate School of Biomedical and Health Sciences, Hiroshima University, Hiroshima, Japan
- Department of Gastroenterology, Graduate School of Biomedical & Health Sciences, Hiroshima University, Hiroshima, Japan
| | - Danny Barash
- Department of Computer Science, Ben-Gurion University, Beer-Sheva, Israel
| | - Nobuhiko Hiraga
- Research Center for Hepatology and Gastroenterology, Graduate School of Biomedical and Health Sciences, Hiroshima University, Hiroshima, Japan
| | | | - Chise Tateno
- PhoenixBio Co., Ltd., Hiroshima, Japan
- Research Center for Hepatology and Gastroenterology, Graduate School of Biomedical and Health Sciences, Hiroshima University, Hiroshima, Japan
| | - Jonathan Ozik
- Consortium for Advanced Science and Engineering, University of Chicago, Chicago, Illinois, United States of America
- Decision and Infrastructure Sciences, Argonne National Laboratory, Argonne, Illinois, United States of America
| | - Susan L. Uprichard
- The Program for Experimental & Theoretical Modeling, Division of Hepatology, Department of Medicine, Stritch School of Medicine, Loyola University Chicago, Maywood, Illinois, United States of America
- The Infectious Disease and Immunology Research Institute, Stritch School of Medicine, Loyola University Chicago, Maywood, Illinois, United States of America
| | - Kazuaki Chayama
- Research Center for Hepatology and Gastroenterology, Graduate School of Biomedical and Health Sciences, Hiroshima University, Hiroshima, Japan
- RIKEN Center for Integrative Medical Sciences, Yokohama, Japan
- Collaborative Research Laboratory of Medical Innovation, Graduate School of Biomedical and Health Sciences, Hiroshima University, Hiroshima, Japan
- Hiroshima Institute of Life Sciences, Hiroshima, Japan
| | - Harel Dahari
- The Program for Experimental & Theoretical Modeling, Division of Hepatology, Department of Medicine, Stritch School of Medicine, Loyola University Chicago, Maywood, Illinois, United States of America
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8
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Yosyingyong P, Viriyapong R. Global dynamics of multiple delays within-host model for a hepatitis B virus infection of hepatocytes with immune response and drug therapy. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:7349-7386. [PMID: 37161155 DOI: 10.3934/mbe.2023319] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
In this paper, a mathematical model describing the hepatitis B virus (HBV) infection of hepatocytes with the intracellular HBV-DNA containing capsids, cytotoxic T-lymphocyte (CTL), antibodies including drug therapy (blocking new infection and inhibiting viral production) with two-time delays is studied. It incorporates the delay in the productively infected hepatocytes and the delay in an antigenic stimulation generating CTL. We verify the positivity and boundedness of solutions and determine the basic reproduction number. The local and global stability of three equilibrium points (infection-free, immune-free, and immune-activated) are investigated. Finally, the numerical simulations are established to show the role of these therapies in reducing viral replication and HBV infection. Our results show that the treatment by blocking new infection gives more significant results than the treatment by inhibiting viral production for infected hepatocytes. Further, both delays affect the number of infections and duration i.e. the longer the delay, the more severe the HBV infection.
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Affiliation(s)
- Pensiri Yosyingyong
- Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand
| | - Ratchada Viriyapong
- Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand
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9
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El Messaoudi S, Lemenuel-Diot A, Gonçalves A, Guedj J. A Semi-mechanistic Model to Characterize the Long-Term Dynamics of Hepatitis B Virus Markers During Treatment With Lamivudine and Pegylated Interferon. Clin Pharmacol Ther 2023; 113:390-400. [PMID: 36408671 DOI: 10.1002/cpt.2798] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2022] [Accepted: 11/07/2022] [Indexed: 11/22/2022]
Abstract
Antiviral treatments against hepatitis B virus (HBV) suppress viral replication but do not eradicate the virus, and need therefore to be taken lifelong to avoid relapse. Mathematical models can be useful to support the development of curative anti-HBV agents; however, they mostly focus on short-term HBV DNA data and neglect the complex host-pathogen interaction. This work aimed to characterize the effect of treatment with lamivudine and/or pegylated interferon (Peg-IFN) in 1,300 patients (hepatitis B envelope antigen (HBeAg)-positive and HBeAg-negative) treated for 1 year. A mathematical model was developed incorporating two populations of infected cells, namely I 1 , with a high transcriptional activity, that progressively evolve into I 2 , at a rate δ tr , representing cells with integrated HBV DNA that have a lower transcriptional activity. Parameters of the model were estimated in patients treated with lamivudine or Peg-IFN alone (N = 894), and the model was then validated in patients treated with lamivudine plus Peg-IFN (N = 436) to predict the virological response after a year of combination treatment. Lamivudine had a larger effect in blocking viral production than Peg-IFN (99.4-99.9% vs. 91.8-95.1%); however, Peg-IFN had a significant immunomodulatory effect, leading to an enhancement of the loss rates of I 1 (×1.7 in HBeAg-positive patients), I 2 (> ×7 irrespective of HBeAg status), and δ tr (×4.6 and ×2.0 in HBeAg-positive and HBeAg-negative patients, respectively). Using this model, we were able to describe the synergy of the different effects occurring during treatment with combination and predicted an effect of 99.99% on blocking viral production. This framework can therefore support the optimization of combination therapy with new anti-HBV agents.
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Affiliation(s)
- Selma El Messaoudi
- Université Paris Cité, Institut National de la Santé et de la Recherche Médicale, Infection, Antimicrobials, Modelling, Evolution, Paris, France
| | - Annabelle Lemenuel-Diot
- Pharmaceutical Sciences, Roche Pharmaceutical Research and Early Development, Roche Innovation Center, Basel, Switzerland
| | - Antonio Gonçalves
- Université Paris Cité, Institut National de la Santé et de la Recherche Médicale, Infection, Antimicrobials, Modelling, Evolution, Paris, France
| | - Jérémie Guedj
- Université Paris Cité, Institut National de la Santé et de la Recherche Médicale, Infection, Antimicrobials, Modelling, Evolution, Paris, France
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10
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Qurashi MA, Rashid S, Jarad F. A computational study of a stochastic fractal-fractional hepatitis B virus infection incorporating delayed immune reactions via the exponential decay. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:12950-12980. [PMID: 36654030 DOI: 10.3934/mbe.2022605] [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] [Indexed: 06/17/2023]
Abstract
Recently, researchers have become interested in modelling, monitoring, and treatment of hepatitis B virus infection. Understanding the various connections between pathogens, immune systems, and general liver function is crucial. In this study, we propose a higher-order stochastically modified delay differential model for the evolution of hepatitis B virus transmission involving defensive cells. Taking into account environmental stimuli and ambiguities, we presented numerical solutions of the fractal-fractional hepatitis B virus model based on the exponential decay kernel that reviewed the hepatitis B virus immune system involving cytotoxic T lymphocyte immunological mechanisms. Furthermore, qualitative aspects of the system are analyzed such as the existence-uniqueness of the non-negative solution, where the infection endures stochastically as a result of the solution evolving within the predetermined system's equilibrium state. In certain settings, infection-free can be determined, where the illness settles down tremendously with unit probability. To predict the viability of the fractal-fractional derivative outcomes, a novel numerical approach is used, resulting in several remarkable modelling results, including a change in fractional-order δ with constant fractal-dimension ϖ, δ with changing ϖ, and δ with changing both δ and ϖ. White noise concentration has a significant impact on how bacterial infections are treated.
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Affiliation(s)
- Maysaa Al Qurashi
- Department of Mathematics, King Saud University, P. O. Box 22452, Riyadh 11495, Saudi Arabia
- Department of Mathematics, Saudi Electronic University, Riyadh, Saudi Arabia
| | - Saima Rashid
- Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
| | - Fahd Jarad
- Department of Physics, Government College University, Faisalabad 38000, Pakistan
- Department of Mathmatics, Cankaya University, Ankara, Turkey
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
- Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
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11
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Karaman B. The global stability investigation of the mathematical design of a fractional-order HBV infection. JOURNAL OF APPLIED MATHEMATICS & COMPUTING 2022; 68:4759-4775. [PMID: 35378779 PMCID: PMC8968785 DOI: 10.1007/s12190-022-01721-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/07/2022] [Revised: 02/16/2022] [Accepted: 02/21/2022] [Indexed: 06/14/2023]
Abstract
This work presents approximate solutions of a fractional-order design for hepatitis B virus infection. The numerical solution of the system is given by using an implicit fractional linear multi-step method of the second order. Here, Caputo fractional derivative is considered for fractional derivative. Basic theoretical properties are discussed. We prove the global stability analysis of the fractional-order model. Numerical simulations are demonstrated to display our theoretical results. This current study is to reveal that the order of the fractional derivative β does not affect the regular state's stability concerning both theoretical and numerical results. Besides, if the fractional-order β increases, the solutions converge more rapidly to the regular states. Finally, we note that this study can provide beneficial outcomes for understanding and estimating the dissipation of distinct epidemics.
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Affiliation(s)
- Bahar Karaman
- Department of Mathematics, Eskişehir Technical University, 26470 Eskisehir, Turkey
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12
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An age-structured model of hepatitis B viral infection highlights the potential of different therapeutic strategies. Sci Rep 2022; 12:1252. [PMID: 35075156 PMCID: PMC8786976 DOI: 10.1038/s41598-021-04022-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2021] [Accepted: 12/10/2021] [Indexed: 12/19/2022] Open
Abstract
Hepatitis B virus (HBV) is a global health threat, and its elimination by 2030 has been prioritised by the World Health Organisation. Here we present an age-structured model for the immune response to an HBV infection, which takes into account contributions from both cell-mediated and humoral immunity. The model has been validated using published patient data recorded during acute infection. It has been adapted to the scenarios of chronic infection, clearance of infection, and flare-ups via variation of the immune response parameters. The impacts of immune response exhaustion and non-infectious subviral particles on the immune response dynamics are analysed. A comparison of different treatment options in the context of this model reveals that drugs targeting aspects of the viral life cycle are more effective than exhaustion therapy, a form of therapy mitigating immune response exhaustion. Our results suggest that antiviral treatment is best started when viral load is declining rather than in a flare-up. The model suggests that a fast antibody production rate always leads to viral clearance, highlighting the promise of antibody therapies currently in clinical trials.
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13
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Oludoun O, Adebimpe O, Ndako J, Abiodun OE, Gbadamosi B, Aladeitan BB. Global stability analysis of hepatitis B virus dynamics. F1000Res 2022; 10:429. [PMID: 35528951 PMCID: PMC9043681 DOI: 10.12688/f1000research.52785.2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Accepted: 01/19/2022] [Indexed: 11/20/2022] Open
Abstract
This paper considers the impact of an acute individual's spontaneous clearance, recovery of a chronic individual with full immunity, and risk factor reduction on a hepatitis B virus (HBV) model. The existence and the positivity solution of the model are established. The model threshold quantity is defined and sensitivity analysis is analyzed to demonstrate the effect of various parameters on the spread of the virus. The global stability analysis of the equilibrium is shown using Lyapunov and comparison theorem methods. Finally, computational simulation is presented to validate the analytical solution. The results show that treatment, spontaneous clearance and reduction of the risk factor are highly successful in transmitting and regulating HBV transmission. The effective measure of these parameters as substantiated by our simulations, providing an excellent control method of the transmissible infection of HBV.
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Affiliation(s)
- Olajumoke Oludoun
- Department of Physical Sciences, Landmark University, Omu-Aran, Kwara State, Nigeria
| | - Olukayode Adebimpe
- Department of Physical Sciences, Landmark University, Omu-Aran, Kwara State, Nigeria
| | - James Ndako
- Department of Microbiology, Landmark University, Omu-Aran, Kwara State, Nigeria
| | - Oluwakemi E. Abiodun
- Department of Physical Sciences, Landmark University, Omu-Aran, Kwara State, Nigeria
| | - Babatunde Gbadamosi
- Department of Computer Sciences, Landmark University, Omu-Aran, Kwara State, Nigeria
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14
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Heitzman-Breen N, Golden J, Vazquez A, Kuchinsky SC, Duggal NK, Ciupe SM. Modeling the dynamics of Usutu virus infection in birds. J Theor Biol 2021; 531:110896. [PMID: 34506809 DOI: 10.1016/j.jtbi.2021.110896] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2021] [Revised: 08/30/2021] [Accepted: 09/02/2021] [Indexed: 02/08/2023]
Abstract
Usutu virus is an emerging zoonotic flavivirus causing high avian mortality rates and occasional severe neurological disorders in humans. Several virus strains are co-circulating and the differences in their characteristics and avian pathogenesis levels are still unknown. In this study, we use within-host mathematical models to characterize the mechanisms responsible for virus expansion and clearance in juvenile chickens challenged with four Usutu virus strains. We find heterogeneity between the virus strains, with the time between cell infection and viral production varying between 16 h and 23 h, the infected cell lifespan varying between 48 min and 9.5 h, and the basic reproductive number R0 varying between 12.05 and 19.49. The strains with high basic reproductive number have short infected cell lifespan, indicative of immune responses. The virus strains with low basic reproductive number have lower viral peaks and longer lasting viremia, due to lower infection rates and high infected cell lifespan. We discuss how the host and virus heterogeneities may differently impact the public health threat presented by these virus strains.
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Affiliation(s)
- Nora Heitzman-Breen
- Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA
| | - Jacob Golden
- Department of Biological Sciences, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA
| | - Ana Vazquez
- National Centre for Microbiology, Instituto de Salud Carlos III (ISCIII), Epidemiology and Public Health Network of Biomedical Research Centre (CIBERESP), Madrid, Spain
| | - Sarah C Kuchinsky
- Department of Biomedical Sciences and Pathobiology, Virginia-Maryland College of Veterinary Medicine, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA
| | - Nisha K Duggal
- Department of Biomedical Sciences and Pathobiology, Virginia-Maryland College of Veterinary Medicine, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA
| | - Stanca M Ciupe
- Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA.
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15
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A quantitative systems pharmacology model for acute viral hepatitis B. Comput Struct Biotechnol J 2021; 19:4997-5007. [PMID: 34589180 PMCID: PMC8449028 DOI: 10.1016/j.csbj.2021.08.052] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2021] [Revised: 08/31/2021] [Accepted: 08/31/2021] [Indexed: 12/25/2022] Open
Abstract
Mechanistic model characterizing acute immune response and HBV system interactions. Key role of the cellular and regulatory response triggering hepatitis B chronicity. Modelling framework to easily incorporate and explore additional biological mechanisms.
Hepatitis B liver infection is caused by hepatitis B virus (HBV) and represents a major global disease problem when it becomes chronic, as is the case for 80–90% of vertical or early life infections. However, in the vast majority (>95%) of adult exposures, the infected individuals are capable of mounting an effective immune response leading to infection resolution. A good understanding of HBV dynamics and the interaction between the virus and immune system during acute infection represents an essential step to characterize and understand the key biological processes involved in disease resolution, which may help to identify potential interventions to prevent chronic hepatitis B. In this work, a quantitative systems pharmacology model for acute hepatitis B characterizing viral dynamics and the main components of the innate, adaptive, and tolerant immune response has been successfully developed. To do so, information from multiple sources and across different organization levels has been integrated in a common mechanistic framework. The final model adequately describes the chronology and plausibility of an HBV-triggered immune response, as well as clinical data from acute patients reported in the literature. Given the holistic nature of the framework, the model can be used to illustrate the relevance of the different immune pathways and biological processes to ultimate response, observing the negligible contribution of the innate response and the key contribution of the cellular response on viral clearance. More specifically, moderate reductions of the proliferation of activated cytotoxic CD8+ lymphocytes or increased immunoregulatory effects can drive the system towards chronicity.
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Key Words
- AHB, acute hepatitis B
- ALT, alanine aminotransferase
- CHB, chronic hepatitis B
- CTL*, activated CTL
- CTL, antigen-specific cytotoxic T lymphocytes
- CTLm, memory CTL
- DC*, activated dendritic cells
- DC, dendritic cells
- HB, Hepatitis B
- HBV, hepatitis B virus, HBV DNA, circulating DNA levels of HBV
- HBsAg, hepatitis B surface antigen
- Hep, hepatocytes
- Hepatitis B
- Heptot, total hepatocytes
- IFN, interferon
- Immune system dynamics
- LN, lymph node
- LPC, long-lived plasma cells
- LV, liver
- MDSC, myeloid-derived suppressor cells
- Mechanistic modeling
- NK*, activated NK
- NK, natural killer cells
- ODE, ordinary differential equations
- PB, plasmablasts
- PC, plasma cells
- PL, plasma
- QSP, quantitative systems pharmacology
- Quantitative systems pharmacology
- SPC, short-lived plasma cells
- TRAIL, tumor necrosis factor–related apoptosis-inducing ligand
- Th0, naïve T cells
- Treg, regulatory T cells
- Viral dynamics
- anti-HBc, specific antibodies against core hepatitis B antigen
- anti-HBs, specific antibodies against surface hepatitis B antigen
- dHep, debris hepatocytes
- iHep, infected hepatocytes
- pDC, plasmacytoid DC
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16
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Fatehi F, Bingham RJ, Dykeman EC, Stockley PG, Twarock R. Comparing antiviral strategies against COVID-19 via multiscale within-host modelling. ROYAL SOCIETY OPEN SCIENCE 2021; 8:210082. [PMID: 34430042 PMCID: PMC8355669 DOI: 10.1098/rsos.210082] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2021] [Accepted: 07/23/2021] [Indexed: 05/06/2023]
Abstract
Within-host models of COVID-19 infection dynamics enable the merits of different forms of antiviral therapy to be assessed in individual patients. A stochastic agent-based model of COVID-19 intracellular dynamics is introduced here, that incorporates essential steps of the viral life cycle targeted by treatment options. Integration of model predictions with an intercellular ODE model of within-host infection dynamics, fitted to patient data, generates a generic profile of disease progression in patients that have recovered in the absence of treatment. This is contrasted with the profiles obtained after variation of model parameters pertinent to the immune response, such as effector cell and antibody proliferation rates, mimicking disease progression in immunocompromised patients. These profiles are then compared with disease progression in the presence of antiviral and convalescent plasma therapy against COVID-19 infections. The model reveals that using both therapies in combination can be very effective in reducing the length of infection, but these synergistic effects decline with a delayed treatment start. Conversely, early treatment with either therapy alone can actually increase the duration of infection, with infectious virions still present after the decline of other markers of infection. This suggests that usage of these treatments should remain carefully controlled in a clinical environment.
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Affiliation(s)
- F. Fatehi
- Department of Mathematics, University of York, York YO10 5DD, UK
- York Cross-disciplinary Centre for Systems Analysis, University of York, York YO10 5DD, UK
| | - R. J. Bingham
- Department of Mathematics, University of York, York YO10 5DD, UK
- York Cross-disciplinary Centre for Systems Analysis, University of York, York YO10 5DD, UK
- Department of Biology, University of York, York YO10 5DD, UK
| | - E. C. Dykeman
- Department of Mathematics, University of York, York YO10 5DD, UK
- York Cross-disciplinary Centre for Systems Analysis, University of York, York YO10 5DD, UK
| | - P. G. Stockley
- Astbury Centre for Structural Molecular Biology, Faculty of Biological Sciences, University of Leeds, Leeds LS2 9JT, UK
| | - R. Twarock
- Department of Mathematics, University of York, York YO10 5DD, UK
- York Cross-disciplinary Centre for Systems Analysis, University of York, York YO10 5DD, UK
- Department of Biology, University of York, York YO10 5DD, UK
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17
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Rihan FA, Alsakaji HJ. Analysis of a stochastic HBV infection model with delayed immune response. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:5194-5220. [PMID: 34517484 DOI: 10.3934/mbe.2021264] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Considering the environmental factors and uncertainties, we propose, in this paper, a higher-order stochastically perturbed delay differential model for the dynamics of hepatitis B virus (HBV) infection with immune system. Existence and uniqueness of an ergodic stationary distribution of positive solution to the system are investigated, where the solution fluctuates around the endemic equilibrium of the deterministic model and leads to the stochastic persistence of the disease. Under some conditions, infection-free can be obtained in which the disease dies out exponentially with probability one. Some numerical simulations, by using Milstein's scheme, are carried out to show the effectiveness of the obtained results. The intensity of white noise plays an important role in the treatment of infectious diseases.
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Affiliation(s)
- Fathalla A Rihan
- Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al-Ain 15551, UAE
| | - Hebatallah J Alsakaji
- Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al-Ain 15551, UAE
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18
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Ciupe SM, Boribong BP, Kadelka S, Jones CN. Bistable Mathematical Model of Neutrophil Migratory Patterns After LPS-Induced Epigenetic Reprogramming. Front Genet 2021; 12:633963. [PMID: 33708241 PMCID: PMC7940759 DOI: 10.3389/fgene.2021.633963] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2020] [Accepted: 01/27/2021] [Indexed: 11/17/2022] Open
Abstract
The highly controlled migration of neutrophils toward the site of an infection can be altered when they are trained with lipopolysaccharides (LPS), with high dose LPS enhancing neutrophil migratory pattern toward the bacterial derived source signal and super-low dose LPS inducing either migration toward an intermediary signal or dysregulation and oscillatory movement. Empirical studies that use microfluidic chemotaxis-chip devices with two opposing chemoattractants showed differential neutrophil migration after challenge with different LPS doses. The epigenetic alterations responsible for changes in neutrophil migratory behavior are unknown. We developed two mathematical models that evaluate the mechanistic interactions responsible for neutrophil migratory decision-making when exposed to competing chemoattractants and challenged with LPS. The first model, which considers the interactions between the receptor densities of two competing chemoattractants, their kinases, and LPS, displayed bistability between high and low ratios of primary to intermediary chemoattractant receptor densities. In particular, at equilibrium, we observe equal receptor densities for low LPS (< 15ng/mL); and dominance of receptors for the primary chemoattractant for high LPS (> 15ng/mL). The second model, which included additional interactions with an extracellular signal-regulated kinase in both phosphorylated and non-phosphorylated forms, has an additional dynamic outcome, oscillatory dynamics for both receptors, as seen in the data. In particular, it found equal receptor densities in the absence of oscillation for super-low and high LPS challenge (< 0.4 and 1.1 376 ng/mL). Predicting the mechanisms and the type of external LPS challenge responsible for neutrophils migration toward pro-inflammatory chemoattractants, migration toward pro-tolerant chemoattractants, or oscillatory movement is necessary knowledge in designing interventions against immune diseases, such as sepsis.
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Affiliation(s)
- Stanca M. Ciupe
- Department of Mathematics, Virginia Tech, Blacksburg, VA, United States
| | - Brittany P. Boribong
- Division of Pediatric Pulmonology, Massachusetts General Hospital, Boston, MA, United States
| | - Sarah Kadelka
- Department of Environmental Systems Science, ETH Zurich, Zurich, Switzerland
| | - Caroline N. Jones
- Department of Bioengineering, University of Texas, Dallas, TX, United States
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19
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Kadelka S, Dahari H, Ciupe SM. Understanding the antiviral effects of RNAi-based therapy in HBeAg-positive chronic hepatitis B infection. Sci Rep 2021; 11:200. [PMID: 33420293 PMCID: PMC7794570 DOI: 10.1038/s41598-020-80594-6] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2020] [Accepted: 12/21/2020] [Indexed: 01/29/2023] Open
Abstract
The RNA interference (RNAi) drug ARC-520 was shown to be effective in reducing serum hepatitis B virus (HBV) DNA, hepatitis B e antigen (HBeAg) and hepatitis B surface antigen (HBsAg) in HBeAg-positive patients treated with a single dose of ARC-520 and daily nucleosidic analogue (entecavir). To provide insights into HBV dynamics under ARC-520 treatment and its efficacy in blocking HBV DNA, HBsAg, and HBeAg production we developed a multi-compartmental pharmacokinetic-pharamacodynamic model and calibrated it with frequent measured HBV kinetic data. We showed that the time-dependent single dose ARC-520 efficacies in blocking HBsAg and HBeAg are more than 96% effective around day 1, and slowly wane to 50% in 1-4 months. The combined single dose ARC-520 and entecavir effect on HBV DNA was constant over time, with efficacy of more than 99.8%. The observed continuous HBV DNA decline is entecavir mediated, the strong but transient HBsAg and HBeAg decays are ARC-520 mediated. The modeling framework may help assess ongoing RNAi drug development for hepatitis B virus infection.
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Affiliation(s)
- Sarah Kadelka
- Department of Mathematics, Virginia Tech, Blacksburg, VA, 24060, USA
| | - Harel Dahari
- Program for Experimental and Theoretical Modeling, Stritch School of Medicine, Loyola University Chicago, Maywood, IL, 60153, USA
| | - Stanca M Ciupe
- Department of Mathematics, Virginia Tech, Blacksburg, VA, 24060, USA.
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20
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Aniji M, Kavitha N, Balamuralitharan S. Approximate solutions for HBV infection with stability analysis using LHAM during antiviral therapy. BOUNDARY VALUE PROBLEMS 2020; 2020:80. [PMID: 33719357 PMCID: PMC7223922 DOI: 10.1186/s13661-020-01373-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/05/2020] [Accepted: 04/02/2020] [Indexed: 06/12/2023]
Abstract
Hepatitis B virus (HBV) is a life-threatening virus that causes very serious liver-related diseases from the family of Hepadnaviridae having very rare qualities resembling retroviruses. In this paper, we analyze the effect of antiviral therapy through mathematical modeling by using Liao's homotopy analysis method (LHAM) that defines the connection between the target liver cells and the HBV. We also examine the basic nonlinear differential equation by LHAM to get a semi-analytical solution. This can be a very straight and direct method which provides the appropriate solution. Moreover, the local and global stability analysis of disease-free and endemic equilibrium is done using Lyapunov function. Mathematica 12 software is used to find out the solutions and graphical representations. We also discuss the numerical simulations up to sixth-order approximation and error analysis using the same software.
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Affiliation(s)
- M. Aniji
- Department of Mathematics, University College of Engineering, Rajamadam, Pattukkottai, Tamilnadu, India
| | - N. Kavitha
- Department of Mathematics, University College of Engineering, Rajamadam, Pattukkottai, Tamilnadu, India
| | - S. Balamuralitharan
- Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Tamilnadu, India
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21
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Shi R, Lu T, Wang C. Dynamic analysis of a fractional-order delayed model for hepatitis B virus with CTL immune response. Virus Res 2019; 277:197841. [PMID: 31887328 DOI: 10.1016/j.virusres.2019.197841] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2019] [Accepted: 12/13/2019] [Indexed: 01/07/2023]
Abstract
In this paper, a fractional-order delayed model with Holling II functional response and CTL immune response is constructed to describe the transmission of hepatitis B virus. Firstly, the existence and uniqueness of positive solutions are proved. Secondly, the basic reproduction number and the sufficient conditions for the existence of three equilibriums are obtained. Thirdly, the stability of three equilibriums are investigated. In addition, some sufficient conditions for the occurrence of Hopf bifurcation near the endemic equilibrium are demonstrated by using time delay as the bifurcation parameter. After that, some numerical simulations are performed to verify the theoretical prediction. At last, a brief discussion is presented to end this paper.
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Affiliation(s)
- Ruiqing Shi
- School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China.
| | - Ting Lu
- School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China.
| | - Cuihong Wang
- School of Mathematics and Computer Science, Shanxi Normal University, Linfen 041004, China.
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22
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Wasik S, Jaroszewski M, Nowaczyk M, Szostak N, Prejzendanc T, Blazewicz J. VirDB: Crowdsourced Database for Evaluation of Dynamical Viral Infection Models. Curr Bioinform 2019. [DOI: 10.2174/1574893614666190308155904] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Background:Open science is an emerging movement underlining the importance of transparent, high quality research where results can be verified and reused by others. However, one of the biggest problems in replicating experiments is the lack of access to the data used by the authors. This problem also occurs during mathematical modeling of a viral infections. It is a process that can provide valuable insights into viral activity or into a drug’s mechanism of action when conducted correctly.Objective:We present the VirDB database (virdb.cs.put.poznan.pl), which has two primary objectives. First, it is a tool that enables collecting data on viral infections that could be used to develop new dynamic models of infections using the FAIR data sharing principles. Second, it allows storing references to descriptions of viral infection models, together with their evaluation results.Methods:To facilitate the fast population of database and the ease of exchange of scientific data, we decided to use crowdsourcing for collecting data. Such approach has already been proved to be very successful in projects such as Wikipedia.Conclusion:VirDB builds on the concepts and recommendations of Open Science and shares data using the FAIR principles. Thanks to this storing data required for designing and evaluating models of viral infections which can be freely available on the Internet.
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Affiliation(s)
- Szymon Wasik
- Institute of Computing Science, Poznan University of Technology, Poznan, Poland
| | - Marcin Jaroszewski
- Institute of Computing Science, Poznan University of Technology, Poznan, Poland
| | - Mateusz Nowaczyk
- Institute of Computing Science, Poznan University of Technology, Poznan, Poland
| | - Natalia Szostak
- Institute of Computing Science, Poznan University of Technology, Poznan, Poland
| | - Tomasz Prejzendanc
- Institute of Computing Science, Poznan University of Technology, Poznan, Poland
| | - Jacek Blazewicz
- Institute of Computing Science, Poznan University of Technology, Poznan, Poland
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23
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Manda EC, Chirove F. Acute hepatitis B virus infection model within the host incorporating immune cells and cytokine responses. Theory Biosci 2019; 139:153-169. [PMID: 31650408 DOI: 10.1007/s12064-019-00305-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2018] [Accepted: 10/01/2019] [Indexed: 02/06/2023]
Abstract
We formulate and analyze a within-host hepatitis B viral mathematical model for hepatitis B in the acute phase of infection. The model incorporates hepatocytes, hepatitis B virus, immune system cells and cytokine dynamics using a system of ordinary differential equations. We use the model to demonstrate the trends of the hepatitis B infection qualitatively without the effects of immune cells and cytokines. Using these trends, we tested the effects of incorporating the immune cells only and immune cells with cytokine responses at low and high inhibitions on the hepatitis B virus infection. Our results showed that it is impossible to have the immune cells work independently from cytokines when there is an acute hepatitis B virus infection. Therefore, our results suggest that incorporating immune cells and cytokine dynamics in the acute hepatitis B virus infection stage delays infection in the hepatocytes and excluding such dynamics speeds up infection during this phase. Results from this study are useful in developing strategies for control of hepatocellular carcinoma which is caused by hepatitis B virus infection.
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Affiliation(s)
| | - Faraimunashe Chirove
- University of KwaZulu-Natal, Pietermaritzburg, South Africa.,University of Johannesburg, Johannesburg, South Africa
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24
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Abstract
Hepatitis B virus infection is the cause of liver diseases such as cirrhosis and liver cancer. Understanding the host-virus mechanisms that mediate virus pathogenesis can help design better preventive measures for disease control. Mathematical models have been used alongside experimental data to provide insight into the role of immune responses during the acute and chronic hepatitis B infections as well as virus dynamics following administration of combined drug therapy. In this paper, we review several modeling studies on virus-host interactions during acute infection, the virus-host characteristics responsible for transition to chronic disease, and the efficacy and optimal control measures of drug therapy. We conclude by presenting our opinion on the future directions of the field.
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Affiliation(s)
- Stanca M Ciupe
- Department of Mathematics, Virginia Tech, Blacksburg, VA, USA
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25
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Li M, Zu J. The review of differential equation models of HBV infection dynamics. J Virol Methods 2019; 266:103-113. [PMID: 30716348 DOI: 10.1016/j.jviromet.2019.01.014] [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: 08/06/2018] [Revised: 12/30/2018] [Accepted: 01/24/2019] [Indexed: 12/21/2022]
Abstract
Understanding the infection and pathogenesis mechanism of hepatitis B virus (HBV) is very important for the prevention and treatment of hepatitis B. Mathematical models contribute to illuminate the dynamic process of HBV replication in vivo. Therefore, in this paper we review the viral dynamics in HBV infection, which may help us further understand the dynamic mechanism of HBV infection and efficacy of antiviral treatment. Firstly, we introduce a family of deterministic models by considering different biological mechanisms, such as, antiviral therapy, CTL immune response, multi-types of infected hepatocytes, time delay and spatial diffusion. Particularly, we briefly describe the stochastic models of HBV infection. Secondly, we introduce the commonly used parameter estimation methods for HBV viral dynamic models and briefly discuss how to use these methods to estimate unknown parameters (such as drug efficacy) through two specific examples. We also discuss the idea and method of model identification and use a specific example to illustrate its application. Finally, we propose three new research programs, namely, considering HBV drug-resistant strain, coupling within-host and between-host dynamics in HBV infection and linking population dynamics with evolutionary dynamics of HBV diversity.
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Affiliation(s)
- Miaolei Li
- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, PR China
| | - Jian Zu
- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, PR China.
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26
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Danane J, Allali K. Mathematical Analysis and Treatment for a Delayed Hepatitis B Viral Infection Model with the Adaptive Immune Response and DNA-Containing Capsids. High Throughput 2018; 7:E35. [PMID: 30463194 PMCID: PMC6306857 DOI: 10.3390/ht7040035] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2018] [Revised: 11/08/2018] [Accepted: 11/13/2018] [Indexed: 01/09/2023] Open
Abstract
We model the transmission of the hepatitis B virus (HBV) by six differential equations that represent the reactions between HBV with DNA-containing capsids, the hepatocytes, the antibodies and the cytotoxic T-lymphocyte (CTL) cells. The intracellular delay and treatment are integrated into the model. The existence of the optimal control pair is supported and the characterization of this pair is given by the Pontryagin's minimum principle. Note that one of them describes the effectiveness of medical treatment in restraining viral production, while the second stands for the success of drug treatment in blocking new infections. Using the finite difference approximation, the optimality system is derived and solved numerically. Finally, the numerical simulations are illustrated in order to determine the role of optimal treatment in preventing viral replication.
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Affiliation(s)
- Jaouad Danane
- Laboratory of Mathematics and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, P.O. Box 146, 20650 Mohammedia, Morocco.
| | - Karam Allali
- Laboratory of Mathematics and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, P.O. Box 146, 20650 Mohammedia, Morocco.
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27
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Ishida Y, Chung TL, Imamura M, Hiraga N, Sen S, Yokomichi H, Tateno C, Canini L, Perelson AS, Uprichard SL, Dahari H, Chayama K. Acute hepatitis B virus infection in humanized chimeric mice has multiphasic viral kinetics. Hepatology 2018; 68:473-484. [PMID: 29572897 PMCID: PMC6097938 DOI: 10.1002/hep.29891] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/04/2017] [Revised: 02/23/2018] [Accepted: 02/26/2018] [Indexed: 01/09/2023]
Abstract
UNLABELLED Chimeric urokinase type plasminogen activator (uPA)/severely severe combined immunodeficiency (SCID) mice reconstituted with humanized livers are useful for studying hepatitis B virus (HBV) infection in the absence of an adaptive immune response. However, the detailed characterization of HBV infection kinetics necessary to enable in-depth mechanistic studies in this in vivo HBV infection model is lacking. To characterize HBV kinetics post-inoculation (p.i.) to steady state, 42 mice were inoculated with HBV. Serum HBV DNA was frequently measured from 1 minute to 63 days p.i. Total intrahepatic HBV DNA, HBV covalently closed circular DNA (cccDNA), and HBV RNA was measured in a subset of mice at 2, 4, 6, 10, and 13 weeks p.i. HBV half-life (t1/2 ) was estimated using a linear mixed-effects model. During the first 6 hours p.i., serum HBV declined in repopulated uPA/SCID mice with a t1/2 = 62 minutes (95% confidence interval [CI] = 59-67). Thereafter, viral decline slowed followed by a 2-day lower plateau. Subsequent viral amplification was multiphasic with an initial mean doubling time of t2 = 8 ± 3 hours followed by an interim plateau before prolonged amplification (t2 = 2 ± 0.5 days) to a final HBV steady state of 9.3 ± 0.3 log copies (cps)/mL. Serum HBV and intrahepatic HBV DNA were positively correlated (R2 = 0.98). CONCLUSION HBV infection in uPA/SCID chimeric mice is highly dynamic despite the absence of an adaptive immune response. Serum HBV t1/2 in humanized uPA/SCID mice was estimated to be ∼1 hour regardless of inoculum size. The HBV acute infection kinetics presented here is an important step in characterizing this experimental model system so that it can be effectively used to elucidate the dynamics of the HBV life cycle and thus possibly reveal effective antiviral drug targets. (Hepatology 2018).
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Affiliation(s)
- Yuji Ishida
- PhoenixBio Co., Ltd., Hiroshima, Japan,Liver Research Project Center, Hiroshima University, Hiroshima, Japan
| | - Tje Lin Chung
- The Program for Experimental & Theoretical Modeling, Division of Hepatology, Department of Medicine, Loyola University Medical Center, Maywood, IL, USA,Institute of Biostatistics and Mathematical Modeling, Department of Medicine, Goethe University, Frankfurt, Germany
| | - Michio Imamura
- Liver Research Project Center, Hiroshima University, Hiroshima, Japan
| | - Nobuhiko Hiraga
- Liver Research Project Center, Hiroshima University, Hiroshima, Japan
| | - Suranjana Sen
- The Program for Experimental & Theoretical Modeling, Division of Hepatology, Department of Medicine, Loyola University Medical Center, Maywood, IL, USA
| | | | - Chise Tateno
- PhoenixBio Co., Ltd., Hiroshima, Japan,Liver Research Project Center, Hiroshima University, Hiroshima, Japan
| | - Laetitia Canini
- The Program for Experimental & Theoretical Modeling, Division of Hepatology, Department of Medicine, Loyola University Medical Center, Maywood, IL, USA,Centre for Immunity, Infection and Evolution, University of Edinburgh, Edinburgh, United Kingdom
| | - Alan S. Perelson
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - Susan L. Uprichard
- The Program for Experimental & Theoretical Modeling, Division of Hepatology, Department of Medicine, Loyola University Medical Center, Maywood, IL, USA
| | - Harel Dahari
- The Program for Experimental & Theoretical Modeling, Division of Hepatology, Department of Medicine, Loyola University Medical Center, Maywood, IL, USA
| | - Kazuaki Chayama
- Liver Research Project Center, Hiroshima University, Hiroshima, Japan
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Goyal A, Chauhan R. The dynamics of integration, viral suppression and cell-cell transmission in the development of occult Hepatitis B virus infection. J Theor Biol 2018; 455:269-280. [PMID: 29969598 DOI: 10.1016/j.jtbi.2018.06.020] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2018] [Revised: 06/20/2018] [Accepted: 06/25/2018] [Indexed: 12/15/2022]
Abstract
BACKGROUND Out of several phases of HBV infection, the least understood phase is occult hepatitis B virus infection. The paucity of data due to non-availability of biological tissues and the prerequisite of ultra-sensitive assays for the detection of occult hepatitis B virus infection prompted us to utilize mathematical modeling in determining mechanisms that lead to occult hepatitis B virus infection and characteristics of HBV infection during occult hepatitis B virus infection. METHODS We proposed two mathematical models (M1 and M2), considering two different phenomenon for episomal maintenance and accumulation of covalently closed circular DNA (cccDNA) in infected hepatocytes: (i) M1 - recirculation of the relaxed circular DNA/double-stranded linear DNA from cytoplasm to the nucleus, and (ii) M2 - reinfection of infected hepatocytes with virions. We further incorporated the dynamics of integrated Hepatitis B virus DNA (iHBV) to investigate its role in the development of occult hepatitis B virus infection. RESULTS The analysis showed that the main mechanism for the spread of infection during occult hepatitis B virus infection is cell-to-cell transmission and not cell-free virus transmission. A significant viral suppression (of at least 99% from its peak production values) was essential but not sufficient in the development of occult hepatitis B virus infection under M1; however under M2, the viral suppression was neither sufficient nor essential as the inhibition of the production of HBsAg without viral suppression can also explain the development of occult hepatitis B virus infection. Our analysis also revealed that occult hepatitis B virus infection seropositive cases are more likely to progress into liver cirrhosis compared to occult hepatitis B virus infection seronegative cases. The iHBV was found to be mostly silent (by either being absent or non-productive for HBsAg) during occult hepatitis B virus infection. CONCLUSION The viral suppression is neither essential nor sufficient to explain the development of occult hepatitis B virus infection on its own. Not only the viral suppression but the inhibition -of the production and the export of HBsAg from cccDNA and iHBV also plays an important role in the development of occult hepatitis B virus infection. This is the first study, which incorporates the dynamics of iHBV and shows that HBV primarily spreads via cell-cell transmission during occult hepatitis B virus infection.
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Affiliation(s)
- Ashish Goyal
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
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29
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Nampala H, Luboobi LS, Mugisha JYT, Obua C, Jablonska-Sabuka M. Modelling hepatotoxicity and antiretroviral therapeutic effect in HIV/HBV coinfection. Math Biosci 2018; 302:67-79. [PMID: 29800563 DOI: 10.1016/j.mbs.2018.05.012] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2017] [Revised: 05/16/2018] [Accepted: 05/21/2018] [Indexed: 01/08/2023]
Abstract
Enzyme alanine aminotransferase (ALT) elevation which reflects hepatocellular injury is a current challenge in people infected with human immunodeficiency virus (HIV) on antiretroviral therapy (ART). One of the factors that enhance the risk of hepatotoxicity is underlying diseases such as hepatitis caused by hepatitis B virus (HBV). HIV/HBV coinfected patients stand a greater risk of hepatotoxicity because all ART are toxic and liver cells (hepatocytes) that are responsible for metabolising the toxic ART, support all stages of HIV and HBV viral production. Mathematical models coupled with numerical simulations are used in this study with the aim of investigating the optimal combination of ART in HIV/HBV coinfection. Emtricitabine, tenofovir and efavirenz is the optimal combination that maximises the therapeutic effect of therapy and minimises the toxic response to medication in HIV/HBV coinfection.
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Affiliation(s)
- Hasifa Nampala
- Department of Mathematics, Kyambogo University, P.O Box 1, Kampala, Uganda.
| | | | - Joseph Y T Mugisha
- Department of Mathematics, Makerere University, P.O Box 7062, Kampala, Uganda
| | - Celestino Obua
- Department of Pharmacology and Therapeutics, Makerere University, Kampala, P.O Box 7062, Uganda
| | - Matylda Jablonska-Sabuka
- Department of Computational Engineering and Physics, Lappeenranta University of Technology, Finland
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30
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Friedman A, Siewe N. Chronic hepatitis B virus and liver fibrosis: A mathematical model. PLoS One 2018; 13:e0195037. [PMID: 29634771 PMCID: PMC5892900 DOI: 10.1371/journal.pone.0195037] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2017] [Accepted: 03/15/2018] [Indexed: 12/14/2022] Open
Abstract
Hepatitis B virus (HBV) infection is a liver disorder that can result in cirrhosis, liver failure and hepatocellular carcinoma. HBV infection remains a major global health problem, as it affects more 350 million people chronically and kills roughly 600,000 people annually. Drugs currently used against HBV include IFN-α that decreases viremia, inflammation and the growth of liver fibrosis, and adefovir that decreases the viral load. Each of these drugs can have severe side-effects. In the present paper, we consider the treatment of chronic HBV by a combination of IFN-α and adefovir, and raise the following question: What should be the optimal ratio between IFN-α and adefovir in order to achieve the best 'efficacy' under constraints on the total amount of the drugs; here the efficacy is measured by the reduction of the levels of inflammation and of fibrosis? We develop a mathematical model of HBV pathogenesis by a system of partial differential equations (PDEs) and use the model to simulate a 'synergy map' which addresses the above question.
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Affiliation(s)
- Avner Friedman
- Mathematical Biosciences Institute & Department of Mathematics, The Ohio State University, Columbus, Ohio, United States of America
| | - Nourridine Siewe
- National Institute for Mathematical and Biological Synthesis, University of Tennessee, Knoxville, Tennessee, United States of America
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31
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Fatehi Chenar F, Kyrychko YN, Blyuss KB. Mathematical model of immune response to hepatitis B. J Theor Biol 2018; 447:98-110. [PMID: 29574141 DOI: 10.1016/j.jtbi.2018.03.025] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2017] [Revised: 03/02/2018] [Accepted: 03/16/2018] [Indexed: 12/17/2022]
Abstract
A new detailed mathematical model for dynamics of immune response to hepatitis B is proposed, which takes into account contributions from innate and adaptive immune responses, as well as cytokines. Stability analysis of different steady states is performed to identify parameter regions where the model exhibits clearance of infection, maintenance of a chronic infection, or periodic oscillations. Effects of nucleoside analogues and interferon treatments are analysed, and the critical drug efficiency is determined.
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Affiliation(s)
- F Fatehi Chenar
- Department of Mathematics, University of Sussex, Brighton BN1 9QH, UK
| | - Y N Kyrychko
- Department of Mathematics, University of Sussex, Brighton BN1 9QH, UK
| | - K B Blyuss
- Department of Mathematics, University of Sussex, Brighton BN1 9QH, UK.
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32
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Goyal A, Ribeiro RM, Perelson AS. The Role of Infected Cell Proliferation in the Clearance of Acute HBV Infection in Humans. Viruses 2017; 9:v9110350. [PMID: 29156567 PMCID: PMC5707557 DOI: 10.3390/v9110350] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2017] [Revised: 11/14/2017] [Accepted: 11/16/2017] [Indexed: 12/17/2022] Open
Abstract
Around 90-95% of hepatitis B virus (HBV) infected adults do not progress to the chronic phase and, instead, recover naturally. The strengths of the cytolytic and non-cytolytic immune responses are key players that decide the fate of acute HBV infection. In addition, it has been hypothesized that proliferation of infected cells resulting in uninfected progeny and/or cytokine-mediated degradation of covalently closed circular DNA (cccDNA) leading to the cure of infected cells are two major mechanisms assisting the adaptive immune response in the clearance of acute HBV infection in humans. We employed fitting of mathematical models to human acute infection data together with physiological constraints to investigate the role of these hypothesized mechanisms in the clearance of infection. Results suggest that cellular proliferation of infected cells resulting in two uninfected cells is required to minimize the destruction of the liver during the clearance of acute HBV infection. In contrast, we find that a cytokine-mediated cure of infected cells alone is insufficient to clear acute HBV infection. In conclusion, our modeling indicates that HBV clearance without lethal loss of liver mass is associated with the production of two uninfected cells upon proliferation of an infected cell.
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Affiliation(s)
- Ashish Goyal
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.
| | - Ruy M Ribeiro
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.
- Laboratório de Biomatemática, Faculdade de Medicina da Universidade de Lisboa, 1649-028 Lisboa, Portugal.
| | - Alan S Perelson
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.
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33
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3D Spatially Resolved Models of the Intracellular Dynamics of the Hepatitis C Genome Replication Cycle. Viruses 2017; 9:v9100282. [PMID: 28973992 PMCID: PMC5691296 DOI: 10.3390/v9100282] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2017] [Revised: 09/21/2017] [Accepted: 09/29/2017] [Indexed: 02/07/2023] Open
Abstract
Mathematical models of virus dynamics have not previously acknowledged spatial resolution at the intracellular level despite substantial arguments that favor the consideration of intracellular spatial dependence. The replication of the hepatitis C virus (HCV) viral RNA (vRNA) occurs within special replication complexes formed from membranes derived from endoplasmatic reticulum (ER). These regions, termed membranous webs, are generated primarily through specific interactions between nonstructural virus-encoded proteins (NSPs) and host cellular factors. The NSPs are responsible for the replication of the vRNA and their movement is restricted to the ER surface. Therefore, in this study we developed fully spatio-temporal resolved models of the vRNA replication cycle of HCV. Our simulations are performed upon realistic reconstructed cell structures-namely the ER surface and the membranous webs-based on data derived from immunostained cells replicating HCV vRNA. We visualized 3D simulations that reproduced dynamics resulting from interplay of the different components of our models (vRNA, NSPs, and a host factor), and we present an evaluation of the concentrations for the components within different regions of the cell. Thus far, our model is restricted to an internal portion of a hepatocyte and is qualitative more than quantitative. For a quantitative adaption to complete cells, various additional parameters will have to be determined through further in vitro cell biology experiments, which can be stimulated by the results deccribed in the present study.
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Understanding the Complex Patterns Observed during Hepatitis B Virus Therapy. Viruses 2017; 9:v9050117. [PMID: 28534812 PMCID: PMC5454429 DOI: 10.3390/v9050117] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2017] [Revised: 04/21/2017] [Accepted: 05/02/2017] [Indexed: 01/16/2023] Open
Abstract
Data from human clinical trials have shown that the hepatitis B virus (HBV) follows complex profiles, such as bi-phasic, tri-phasic, stepwise decay and rebound. We utilized a deterministic model of HBV kinetics following antiviral therapy to uncover the mechanistic interactions behind HBV dynamics. Analytical investigation of the model was used to separate the parameter space describing virus decay and rebound. Monte Carlo sampling of the parameter space was used to determine the virological, pharmacological and immunological factors that separate the bi-phasic and tri-phasic virus profiles. We found that the level of liver infection at the start of therapy best separates the decay patterns. Moreover, drug efficacy, ratio between division of uninfected and infected cells, and the strength of cytotoxic immune response are important in assessing the amount of liver damage experienced over time and in quantifying the duration of therapy leading to virus resolution in each of the observed profiles.
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35
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Abstract
In this paper, a diffusive hepatitis B virus (HBV) infection model with a discrete time delay is presented and analyzed, where the spatial mobility of both intracellular capsid covered HBV DNA and HBV and the intracellular delay in the reproduction of infected hepatocytes are taken into account. We define the basic reproduction number [Formula: see text] that determines the dynamical behavior of the model. The local and global stability of the spatially homogeneous steady states are analyzed by using the linearization technique and the direct Lyapunov method, respectively. It is shown that the susceptible uninfected steady state is globally asymptotically stable whenever [Formula: see text] and is unstable whenever [Formula: see text]. Also, the infected steady state is globally asymptotically stable when [Formula: see text]. Finally, numerical simulations are carried out to illustrate the results obtained.
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Affiliation(s)
- Kalyan Manna
- Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati 781039, Assam, India
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36
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Ciupe SM, Heffernan JM. In-host modeling. Infect Dis Model 2017; 2:188-202. [PMID: 29928736 PMCID: PMC6001971 DOI: 10.1016/j.idm.2017.04.002] [Citation(s) in RCA: 31] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2017] [Revised: 04/24/2017] [Accepted: 04/26/2017] [Indexed: 01/14/2023] Open
Abstract
Understanding the mechanisms governing host-pathogen kinetics is important and can guide human interventions. In-host mathematical models, together with biological data, have been used in this endeavor. In this review, we present basic models used to describe acute and chronic pathogenic infections. We highlight the power of model predictions, the role of drug therapy, and advantage of considering the dynamics of immune responses. We also present the limitations of these models due in part to the trade-off between the complexity of the model and their predictive power, and the challenges a modeler faces in determining the appropriate formulation for a given problem.
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Affiliation(s)
- Stanca M. Ciupe
- Department of Mathematics, Virginia Tech, Blacksburg, VA, USA
| | - Jane M. Heffernan
- Centre for Disease Modelling, Department of Mathematics & Statistics, York University, Toronto, ON, Canada
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37
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Song L, Ma C, Li Q, Fan A, Wang K. Global dynamics of a viral infection model with full logistic terms and antivirus treatments. INT J BIOMATH 2016. [DOI: 10.1142/s1793524517500127] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, mathematical analysis of the global dynamics of a viral infection model in vivo is carried out. Though the model is originally to study hepatitis C virus (HCV) dynamics in patients with high baseline viral loads or advanced liver disease, similar models still hold significance for other viral infection, such as hepatitis B virus (HBV) or human immunodeficiency virus (HIV) infection. By means of Volterra-type Lyapunov functions, we know that the basic reproduction number [Formula: see text] is a sharp threshold para-meter for the outcomes of viral infections. If [Formula: see text], the virus-free equilibrium is globally asymptotically stable. If [Formula: see text], the system is uniformly persistent, the unique endemic equilibrium appears and is globally asymptotically stable under a sufficient condition. Other than that, for the global stability of the unique endemic equilibrium, another sufficient condition is obtained by Li–Muldowney global-stability criterion. Using numerical simulation techniques, we further find that sustained oscillations can exist and different maximum de novo hepatocyte influx rate can induce different global dynamics along with the change of overall drug effectiveness. Finally, some biological implications of our findings are given.
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Affiliation(s)
- Lijuan Song
- Department of Mathematics, School of Biomedical Engineering, Third Military Medical University, Chongqing 400038, P. R. China
| | - Cui Ma
- Department of Mathematics, School of Biomedical Engineering, Third Military Medical University, Chongqing 400038, P. R. China
| | - Qiang Li
- Center for Hypertension and Metabolic Diseases, Department of Hypertension and Endocrinology, Daping Hospital, Third Military Medical University, Chongqing 400038, P. R. China
- Chongqing Institute of Hypertension, Chongqing 400042, P. R. China
| | - Aijun Fan
- Chongqing Academy of Science and Technology, Chongqing 401123, P. R. China
| | - Kaifa Wang
- Department of Mathematics, School of Biomedical Engineering, Third Military Medical University, Chongqing 400038, P. R. China
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38
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Modelling the Impact of Cell-To-Cell Transmission in Hepatitis B Virus. PLoS One 2016; 11:e0161978. [PMID: 27560827 PMCID: PMC4999077 DOI: 10.1371/journal.pone.0161978] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2016] [Accepted: 08/15/2016] [Indexed: 12/11/2022] Open
Abstract
Cell-free virus is a well-recognized and efficient mechanism for the spread of hepatitis B virus (HBV) infection in the liver. Cell-to-cell transmission (CCT) can be a more efficient means of virus propagation. Despite experimental evidence implying CCT occurs in HBV, its relative impact is uncertain. We develop a 3-D agent-based model where each hepatocyte changes its viral state according to a dynamical process driven by cell-free virus infection, CCT and intracellular replication. We determine the relative importance of CCT in the development and resolution of acute HBV infection in the presence of cytolytic (CTL) and non-CTL mechanisms. T cell clearance number is defined as the minimum number of infected cells needed to be killed by each T cell at peak infection that results in infection clearance within 12 weeks with hepatocyte turnover (HT, number of equivalent livers) ≤3. We find that CCT has very little impact on the establishment of infection as the mean cccDNA copies/cell remains between 15 to 20 at the peak of the infection regardless of CCT strength. In contrast, CCT inhibit immune-mediated clearance of acute HBV infection as higher CCT strength requires higher T cell clearance number and increases the probability of T cell exhaustion. An effective non-CTL inhibition can counter these negative effects of higher strengths of CCT by supporting rapid, efficient viral clearance and with little liver destruction. This is evident as the T cell clearance number drops by approximately 50% when non-CTL inhibition is increased from 10% to 80%. Higher CCT strength also increases the probability of the incidence of fulminant hepatitis with this phenomenon being unlikely to arise for no CCT. In conclusion, we report the possibility of CCT impacting HBV clearance and its contribution to fulminant hepatitis.
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40
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Mathematical model of plant-virus interactions mediated by RNA interference. J Theor Biol 2016; 403:129-142. [PMID: 27188250 DOI: 10.1016/j.jtbi.2016.05.018] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2015] [Revised: 04/11/2016] [Accepted: 05/08/2016] [Indexed: 01/04/2023]
Abstract
Cross-protection, which refers to a process whereby artificially inoculating a plant with a mild strain provides protection against a more aggressive isolate of the virus, is known to be an effective tool of disease control in plants. In this paper we derive and analyse a new mathematical model of the interactions between two competing viruses with particular account for RNA interference. Our results show that co-infection of the host can either increase or decrease the potency of individual infections depending on the levels of cross-protection or cross-enhancement between different viruses. Analytical and numerical bifurcation analyses are employed to investigate the stability of all steady states of the model in order to identify parameter regions where the system exhibits synergistic or antagonistic behaviour between viral strains, as well as different types of host recovery. We show that not only viral attributes but also the propagating component of RNA-interference in plants can play an important role in determining the dynamics.
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41
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Dynamics of in vivo hepatitis D virus infection. J Theor Biol 2016; 398:9-19. [PMID: 27012516 DOI: 10.1016/j.jtbi.2016.03.018] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2015] [Revised: 03/14/2016] [Accepted: 03/14/2016] [Indexed: 12/18/2022]
Abstract
UNLABELLED Hepatitis-D virus (HDV) is a satellite virus of hepatitis-B virus (HBV) whose intracellular products are required for the completion of the HDV life cycle. HDV can replicate in a cell without the presence of HBV but needs hepatitis B surface antigen (HBsAg) to complete virus assembly and packaging. In order to better understand HDV dynamics, we developed a mathematical model and successfully simulated HBV and HDV data under a range of scenarios. Compared to HBV mono-infection, dual HDV infection resulted in lower chronic HBV DNA levels, with more marked suppression for coinfection (1 logs HBV DNA copies/ml lower) compared to superinfection (0.6 logs HBV DNA copies/ml). Although they have no effect on HBV, prenylation inhibitors may provide the best therapy for reducing HDV viremia irrespective of the stage in which they are commenced. We found that highly effective long term pegylated interferon (IFN) therapy (99.99%) eliminates HBV and HDV viremia while less effective long term IFN therapy (99%) will only produce approximately 2.03 logs and no decrease in HBV and HDV viremia respectively in both coinfection and superinfection settings. Our study also suggests that there is a substantial difference in the outcome of therapies depending upon the time of commencement. CONCLUSION Mathematical modeling of HDV infection can describe the complex interplay between this virus and HBV. Simulations suggest that HDV impacts on the feedback mechanisms that maintain cccDNA levels and that targeting these mechanisms may result in new therapeutic agents for both viruses.
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Nakabayashi J. The intracellular dynamics of hepatitis B virus (HBV) replication with reproduced virion "re-cycling". J Theor Biol 2016; 396:154-62. [PMID: 26924390 DOI: 10.1016/j.jtbi.2016.02.008] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2015] [Revised: 02/02/2016] [Accepted: 02/05/2016] [Indexed: 02/06/2023]
Abstract
Hepatitis B virus (HBV) is a causative agent of hepatitis. Clinical outcome of hepatitis type B depends on the viral titer observed in the peripheral blood of the patient. In the chronic hepatitis patient, production of HBV virion remains low level. On the other hand, the viral load prominently increases in fulminant hepatitis patient as compared with that in the chronic hepatitis patient. We previously proposed a mathematical model describing the intracellular dynamics of HBV replication. Our model clarified that there are two distinguishable replication patterns of HBV named "arrested" and "explosive" replication. In the arrested replication, the amount of virion newly reproduced from an infected cell remains low level, while the amount of virion extremely increases in the explosive replication. Viral load is drastically changed by slight alteration of expression ratio of 3.5kb RNA to 2.4kb mRNA of HBV. Though our model provided the switching mechanism determining the replication pattern of HBV, HBV dynamics is determined by not only the expression pattern of viral genes. In this study, "recycling" of HBV virion in the replication cycle is investigated as a new factor affecting the intracellular dynamics of HBV replication. A part of newly produced virion of HBV is reused as a core particle that is a resource of HBV replication. This recycling of HBV virion lowers the threshold for the explosive replication when waiting time for the next cycle of the replication is large. It is seemingly contradicting that prominent production of HBV is caused by large recycling rate and small release rate of HBV virion from infected cell to extracellular space. But the recycling of HBV virion can contribute to the positive feedback cycle of HBV replication for the explosive replication to accumulate the core particle as a resource of HBV replication in an infected cell. Accumulation of core particle in the infected cell can be risk factor for the exacerbation of hepatitis rather than rapid release of HBV virion from the infected cell.
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Affiliation(s)
- Jun Nakabayashi
- Bioinformatics Laboratory, Advanced Medical Research Center, Yokohama City University, 3-9 Fukuura, Kanazawa-ku, Yokohama-shi, Kanagawa 2360004, Japan.
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Eberhardt M, Lai X, Tomar N, Gupta S, Schmeck B, Steinkasserer A, Schuler G, Vera J. Third-Kind Encounters in Biomedicine: Immunology Meets Mathematics and Informatics to Become Quantitative and Predictive. Methods Mol Biol 2016; 1386:135-179. [PMID: 26677184 DOI: 10.1007/978-1-4939-3283-2_9] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The understanding of the immune response is right now at the center of biomedical research. There are growing expectations that immune-based interventions will in the midterm provide new, personalized, and targeted therapeutic options for many severe and highly prevalent diseases, from aggressive cancers to infectious and autoimmune diseases. To this end, immunology should surpass its current descriptive and phenomenological nature, and become quantitative, and thereby predictive.Immunology is an ideal field for deploying the tools, methodologies, and philosophy of systems biology, an approach that combines quantitative experimental data, computational biology, and mathematical modeling. This is because, from an organism-wide perspective, the immunity is a biological system of systems, a paradigmatic instance of a multi-scale system. At the molecular scale, the critical phenotypic responses of immune cells are governed by large biochemical networks, enriched in nested regulatory motifs such as feedback and feedforward loops. This network complexity confers them the ability of highly nonlinear behavior, including remarkable examples of homeostasis, ultra-sensitivity, hysteresis, and bistability. Moving from the cellular level, different immune cell populations communicate with each other by direct physical contact or receiving and secreting signaling molecules such as cytokines. Moreover, the interaction of the immune system with its potential targets (e.g., pathogens or tumor cells) is far from simple, as it involves a number of attack and counterattack mechanisms that ultimately constitute a tightly regulated multi-feedback loop system. From a more practical perspective, this leads to the consequence that today's immunologists are facing an ever-increasing challenge of integrating massive quantities from multi-platforms.In this chapter, we support the idea that the analysis of the immune system demands the use of systems-level approaches to ensure the success in the search for more effective and personalized immune-based therapies.
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Affiliation(s)
- Martin Eberhardt
- Laboratory of Systems Tumor Immunology, Department of Dermatology, University Hospital Erlangen and Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany
- Department of Dermatology, University Hospital Erlangen and Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany
| | - Xin Lai
- Laboratory of Systems Tumor Immunology, Department of Dermatology, University Hospital Erlangen and Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany
- Department of Dermatology, University Hospital Erlangen and Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany
| | - Namrata Tomar
- Laboratory of Systems Tumor Immunology, Department of Dermatology, University Hospital Erlangen and Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany
- Department of Dermatology, University Hospital Erlangen and Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany
| | - Shailendra Gupta
- Department of Systems Biology and Bioinformatics, University of Rostock, Rostock, Germany
| | - Bernd Schmeck
- Department of Medicine, Pulmonary and Critical Care Medicine, University Medical Center Marburg, Philipps University, Marburg, Germany
- Systems Biology Platform, Institute for Lung Research/iLung, German Center for Lung Research, Universities of Giessen and Marburg Lung Centre, Philipps University Marburg, Marburg, Germany
| | - Alexander Steinkasserer
- Department of Immune Modulation at the Department of Dermatology, University Hospital Erlangen, Erlangen, Germany
| | - Gerold Schuler
- Department of Dermatology, University Hospital Erlangen and Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany
| | - Julio Vera
- Laboratory of Systems Tumor Immunology, Department of Dermatology, University Hospital Erlangen and Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany.
- Department of Dermatology, University Hospital Erlangen and Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany.
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Global stability of one and two discrete delay models for chronic hepatitis B infection with HBV DNA-containing capsids. ACTA ACUST UNITED AC 2015. [DOI: 10.1007/s40314-015-0242-3] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
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45
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Packer A, Forde J, Hews S, Kuang Y. Mathematical models of the interrelated dynamics of hepatitis D and B. Math Biosci 2015; 247:38-46. [PMID: 24513247 DOI: 10.1016/j.mbs.2013.10.004] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2013] [Revised: 10/03/2013] [Accepted: 10/14/2013] [Indexed: 12/31/2022]
Abstract
The hepatitis delta virus (HDV) is a rarest form of viral hepatitis, but has the worst outcomes for patients.It is a subviral satellite dependent on coinfection with hepatitis B (HBV) to replicate within the host liver.To date, there has been little to no modeling effort for HDV. Deriving and analyzing such a mathematical model poses difficulty as it requires the inclusion of (HBV). Here we begin with a well-studied HBV model from the literature and expand it to incorporate HDV. We investigate two models, one with and one without infected hepatocyte replication. Additionally, we consider treatment by the drug lamivudine. Comparison of model simulations with experimental results of lamivudine treatment indicate that infected cell proliferation may play a significant role in chronic HDV infection. Our results also shed light on several questions surrounding HDV and illustrate the need for more data.
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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.
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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
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Modelling Hepatotoxicity of Antiretroviral Therapy in the Liver during HIV Monoinfection. ACTA ACUST UNITED AC 2014. [DOI: 10.1155/2014/659675] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
Liver related complications are currently the leading cause of morbidity and mortality among human immunodeficiency virus (HIV) infected individuals. In HIV monoinfected individuals on therapy, liver injury has been associated with the use of antiretroviral agents as most of them exhibit some degree of toxicity. In this study we proposed a mathematical model with the aim of investigating hepatotoxicity of combinational therapy of antiretroviral drugs. Therapy efficacy and toxicity were incorporated in the model as dose-response functions. With the parameter values used in the study, protease inhibitors-based regimens were found to be more toxic than nonnucleoside reverse transcriptase inhibitors-based regimens. In both regimens, the combination of stavudine and zidovudine was the most toxic baseline nucleoside reverse transcriptase inhibitors followed by didanosine with stavudine. However, the least toxic combinations were zidovudine and lamivudine followed by didanosine and lamivudine. The study proposed that, under the same second line regimens, the most toxic first line combination gives the highest viral load and vice versa.
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Li Q, Lu F, Deng G, Wang K. Modeling the effects of covalently closed circular DNA and dendritic cells in chronic HBV infection. J Theor Biol 2014; 357:1-9. [DOI: 10.1016/j.jtbi.2014.04.037] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2013] [Revised: 04/13/2014] [Accepted: 04/29/2014] [Indexed: 12/12/2022]
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Ciupe SM, Ribeiro RM, Perelson AS. Antibody responses during hepatitis B viral infection. PLoS Comput Biol 2014; 10:e1003730. [PMID: 25078553 PMCID: PMC4117427 DOI: 10.1371/journal.pcbi.1003730] [Citation(s) in RCA: 48] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2013] [Accepted: 05/16/2014] [Indexed: 01/12/2023] Open
Abstract
Hepatitis B is a DNA virus that infects liver cells and can cause both acute and chronic disease. It is believed that both viral and host factors are responsible for determining whether the infection is cleared or becomes chronic. Here we investigate the mechanism of protection by developing a mathematical model of the antibody response following hepatitis B virus (HBV) infection. We fitted the model to data from seven infected adults identified during acute infection and determined the ability of the virus to escape neutralization through overproduction of non-infectious subviral particles, which have HBs proteins on their surface, but do not contain nucleocapsid protein and viral nucleic acids. We showed that viral clearance can be achieved for high anti-HBV antibody levels, as in vaccinated individuals, when: (1) the rate of synthesis of hepatitis B subviral particles is slow; (2) the rate of synthesis of hepatitis B subviral particles is high but either anti-HBV antibody production is fast, the antibody affinity is high, or the levels of pre-existent HBV-specific antibody at the time of infection are high, as could be attained by vaccination. We further showed that viral clearance can be achieved for low equilibrium anti-HBV antibody levels, as in unvaccinated individuals, when a strong cellular immune response controls early infection.
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Affiliation(s)
- Stanca M. Ciupe
- Department of Mathematics, Virginia Tech, Blacksburg, Virginia, United States of America
| | - Ruy M. Ribeiro
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, United States of America
| | - Alan S. Perelson
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, United States of America
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50
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Canini L, Perelson AS. Viral kinetic modeling: state of the art. J Pharmacokinet Pharmacodyn 2014; 41:431-43. [PMID: 24961742 DOI: 10.1007/s10928-014-9363-3] [Citation(s) in RCA: 57] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2014] [Accepted: 06/03/2014] [Indexed: 12/11/2022]
Abstract
Viral kinetic (VK) modeling has led to increased understanding of the within host dynamics of viral infections and the effects of therapy. Here we review recent developments in the modeling of viral infection kinetics with emphasis on two infectious diseases: hepatitis C and influenza. We review how VK modeling has evolved from simple models of viral infections treated with a drug or drug cocktail with an assumed constant effectiveness to models that incorporate drug pharmacokinetics and pharmacodynamics, as well as phenomenological models that simply assume drugs have time varying-effectiveness. We also discuss multiscale models that include intracellular events in viral replication, models of drug-resistance, models that include innate and adaptive immune responses and models that incorporate cell-to-cell spread of infection. Overall, VK modeling has provided new insights into the understanding of the disease progression and the modes of action of several drugs. We expect that VK modeling will be increasingly used in the coming years to optimize drug regimens in order to improve therapeutic outcomes and treatment tolerability for infectious diseases.
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Affiliation(s)
- Laetitia Canini
- Theoretical Biology and Biophysics, MS-K710, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
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