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Mak WY, He Q, Yang W, Xu N, Zheng A, Chen M, Lin J, Shi Y, Xiang X, Zhu X. Application of MIDD to accelerate the development of anti-infectives: Current status and future perspectives. Adv Drug Deliv Rev 2024; 214:115447. [PMID: 39277035 DOI: 10.1016/j.addr.2024.115447] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2023] [Revised: 07/27/2024] [Accepted: 09/08/2024] [Indexed: 09/17/2024]
Abstract
This review examines the role of model-informed drug development (MIDD) in advancing antibacterial and antiviral drug development, with an emphasis on the inclusion of host system dynamics into modeling efforts. Amidst the growing challenges of multidrug resistance and diminishing market returns, innovative methodologies are crucial for continuous drug discovery and development. The MIDD approach, with its robust capacity to integrate diverse data types, offers a promising solution. In particular, the utilization of appropriate modeling and simulation techniques for better characterization and early assessment of drug resistance are discussed. The evolution of MIDD practices across different infectious disease fields is also summarized, and compared to advancements achieved in oncology. Moving forward, the application of MIDD should expand into host system dynamics as these considerations are critical for the development of "live drugs" (e.g. chimeric antigen receptor T cells or bacteriophages) to address issues like antibiotic resistance or latent viral infections.
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Affiliation(s)
- Wen Yao Mak
- Department of Clinical Pharmacy and Pharmacy Administration, School of Pharmacy, Fudan University, 201203 Shanghai, China; Clinical Research Centre (Penang General Hospital), Institute for Clinical Research, National Institute of Health, Malaysia
| | - Qingfeng He
- Department of Clinical Pharmacy and Pharmacy Administration, School of Pharmacy, Fudan University, 201203 Shanghai, China
| | - Wenyu Yang
- Department of Clinical Pharmacy and Pharmacy Administration, School of Pharmacy, Fudan University, 201203 Shanghai, China
| | - Nuo Xu
- Department of Clinical Pharmacy and Pharmacy Administration, School of Pharmacy, Fudan University, 201203 Shanghai, China
| | - Aole Zheng
- Department of Clinical Pharmacy and Pharmacy Administration, School of Pharmacy, Fudan University, 201203 Shanghai, China
| | - Min Chen
- Department of Clinical Pharmacy and Pharmacy Administration, School of Pharmacy, Fudan University, 201203 Shanghai, China
| | - Jiaying Lin
- Department of Clinical Pharmacy and Pharmacy Administration, School of Pharmacy, Fudan University, 201203 Shanghai, China
| | - Yufei Shi
- Department of Clinical Pharmacy and Pharmacy Administration, School of Pharmacy, Fudan University, 201203 Shanghai, China
| | - Xiaoqiang Xiang
- Department of Clinical Pharmacy and Pharmacy Administration, School of Pharmacy, Fudan University, 201203 Shanghai, China.
| | - Xiao Zhu
- Department of Clinical Pharmacy and Pharmacy Administration, School of Pharmacy, Fudan University, 201203 Shanghai, China.
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2
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Iyaniwura SA, Cassidy T, Ribeiro RM, Perelson AS. A multiscale model of the action of a capsid assembly modulator for the treatment of chronic hepatitis B. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.07.16.603658. [PMID: 39071423 PMCID: PMC11275877 DOI: 10.1101/2024.07.16.603658] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/30/2024]
Abstract
Chronic hepatitis B virus (HBV) infection is strongly associated with increased risk of liver cancer and cirrhosis. While existing treatments effectively inhibit the HBV life cycle, viral rebound occurs rapidly following treatment interruption. Consequently, functional cure rates of chronic HBV infection remain low and there is increased interest in a novel treatment modality, capsid assembly modulators (CAMs). Here, we develop a multiscale mathematical model of CAM treatment in chronic HBV infection. By fitting the model to participant data from a phase I trial of the first-generation CAM vebicorvir, we estimate the drug's dose-dependent effectiveness and identify the physiological mechanisms that drive the observed biphasic decline in HBV DNA and RNA, and mechanistic differences between HBeAg-positive and negative infection. Finally, we demonstrate analytically and numerically that HBV RNA is more sensitive than HBV DNA to increases in CAM effectiveness.
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Affiliation(s)
- Sarafa A. Iyaniwura
- Theoretical Biology and Biophysics, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
| | - Tyler Cassidy
- School of Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom
| | - Ruy M. Ribeiro
- Theoretical Biology and Biophysics, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
| | - Alan S. Perelson
- Theoretical Biology and Biophysics, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, 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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Kitagawa K, Kim KS, Iwamoto M, Hayashi S, Park H, Nishiyama T, Nakamura N, Fujita Y, Nakaoka S, Aihara K, Perelson AS, Allweiss L, Dandri M, Watashi K, Tanaka Y, Iwami S. Multiscale modeling of HBV infection integrating intra- and intercellular viral propagation to analyze extracellular viral markers. PLoS Comput Biol 2024; 20:e1011238. [PMID: 38466770 PMCID: PMC10957078 DOI: 10.1371/journal.pcbi.1011238] [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: 06/05/2023] [Revised: 03/21/2024] [Accepted: 02/26/2024] [Indexed: 03/13/2024] Open
Abstract
Chronic infection with hepatitis B virus (HBV) is caused by the persistence of closed circular DNA (cccDNA) in the nucleus of infected hepatocytes. Despite available therapeutic anti-HBV agents, eliminating the cccDNA remains challenging. Thus, quantifying and understanding the dynamics of cccDNA are essential for developing effective treatment strategies and new drugs. However, such study requires repeated liver biopsy to measure the intrahepatic cccDNA, which is basically not accepted because liver biopsy is potentially morbid and not common during hepatitis B treatment. We here aimed to develop a noninvasive method for quantifying cccDNA in the liver using surrogate markers in peripheral blood. We constructed a multiscale mathematical model that explicitly incorporates both intracellular and intercellular HBV infection processes. The model, based on age-structured partial differential equations, integrates experimental data from in vitro and in vivo investigations. By applying this model, we roughly predicted the amount and dynamics of intrahepatic cccDNA within a certain range using specific viral markers in serum samples, including HBV DNA, HBsAg, HBeAg, and HBcrAg. Our study represents a significant step towards advancing the understanding of chronic HBV infection. The noninvasive quantification of cccDNA using our proposed method holds promise for improving clinical analyses and treatment strategies. By comprehensively describing the interactions of all components involved in HBV infection, our multiscale mathematical model provides a valuable framework for further research and the development of targeted interventions.
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Affiliation(s)
- Kosaku Kitagawa
- interdisciplinary Biology Laboratory (iBLab), Division of Natural Science, Graduate School of Science, Nagoya University, Nagoya, Japan
| | - Kwang Su Kim
- interdisciplinary Biology Laboratory (iBLab), Division of Natural Science, Graduate School of Science, Nagoya University, Nagoya, Japan
- Department of Scientific Computing, Pukyong National University, Busan, South Korea
| | - Masashi Iwamoto
- interdisciplinary Biology Laboratory (iBLab), Division of Natural Science, Graduate School of Science, Nagoya University, Nagoya, Japan
- Department of Virology II, National Institute of Infectious Diseases, Tokyo, Japan
| | - Sanae Hayashi
- Department of Gastroenterology and Hepatology, Faculty of Life Sciences, Kumamoto University, Kumamoto, Japan
| | - Hyeongki Park
- interdisciplinary Biology Laboratory (iBLab), Division of Natural Science, Graduate School of Science, Nagoya University, Nagoya, Japan
| | - Takara Nishiyama
- interdisciplinary Biology Laboratory (iBLab), Division of Natural Science, Graduate School of Science, Nagoya University, Nagoya, Japan
| | - Naotoshi Nakamura
- interdisciplinary Biology Laboratory (iBLab), Division of Natural Science, Graduate School of Science, Nagoya University, Nagoya, Japan
| | - Yasuhisa Fujita
- interdisciplinary Biology Laboratory (iBLab), Division of Natural Science, Graduate School of Science, Nagoya University, Nagoya, Japan
| | - Shinji Nakaoka
- Faculty of Advanced Life Science, Hokkaido University, Sapporo, Japan
| | - Kazuyuki Aihara
- International Research Center for Neurointelligence, The University of Tokyo Institutes for Advanced Study, The University of Tokyo, Tokyo, Japan
| | - Alan S. Perelson
- Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, United States of America
| | - Lena Allweiss
- Department of Internal Medicine, University Medical Center Hamburg-Eppendorf, Hamburg, Germany
- German Center for Infection Research (DZIF), Hamburg-Lübeck-Borstel-Riems partner sites, Germany
| | - Maura Dandri
- Department of Internal Medicine, University Medical Center Hamburg-Eppendorf, Hamburg, Germany
- German Center for Infection Research (DZIF), Hamburg-Lübeck-Borstel-Riems partner sites, Germany
| | - Koichi Watashi
- Department of Virology II, National Institute of Infectious Diseases, Tokyo, Japan
- Research Center for Drug and Vaccine Development, National Institute of Infectious Diseases, Tokyo, Japan
- Department of Applied Biological Sciences, Faculty of Science and Technology, Tokyo University of Sciences, Chiba, Japan
| | - Yasuhito Tanaka
- Department of Gastroenterology and Hepatology, Faculty of Life Sciences, Kumamoto University, Kumamoto, Japan
| | - Shingo Iwami
- interdisciplinary Biology Laboratory (iBLab), Division of Natural Science, Graduate School of Science, Nagoya University, Nagoya, Japan
- Department of Applied Biological Sciences, Faculty of Science and Technology, Tokyo University of Sciences, Chiba, Japan
- Institute of Mathematics for Industry, Kyushu University; Fukuoka, Japan
- Institute for the Advanced Study of Human Biology (ASHBi), Kyoto University; Kyoto, Japan
- NEXT-Ganken Program, Japanese Foundation for Cancer Research (JFCR), Tokyo, Japan
- Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN, Wako, Japan
- Science Groove Inc., Fukuoka, Japan
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7
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Raezah AA, Elaiw A, Alshaikh M. Global stability of secondary DENV infection models with non-specific and strain-specific CTLs. Heliyon 2024; 10:e25391. [PMID: 38352732 PMCID: PMC10862684 DOI: 10.1016/j.heliyon.2024.e25391] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2023] [Revised: 12/30/2023] [Accepted: 01/25/2024] [Indexed: 02/16/2024] Open
Abstract
Dengue virus (DENV) is a highly perilous virus that is transmitted to humans through mosquito bites and causes dengue fever. Consequently, extensive efforts are being made to develop effective treatments and vaccines. Mathematical modeling plays a significant role in comprehending the dynamics of DENV within a host in the presence of cytotoxic T lymphocytes (CTL) immune response. This study examines two models for secondary DENV infections that elucidate the dynamics of DENV under the influence of two types of CTL responses, namely non-specific and strain-specific responses. The first model encompasses five compartments, which consist of uninfected monocytes, infected monocytes, free DENV particles, non-specific CTLs, and strain-specific CTLs. In the second model, latently infected cells are introduced into the model. We posit that the CTL responsiveness is determined by a combination of self-regulating CTL response and a predator-prey-like CTL response. The model's solutions are verified to be nonnegativity and bounded and the model possesses two equilibrium states: the uninfected equilibrium EQ 0 and the infected equilibrium EQ ⁎ . Furthermore, we calculate the basic reproduction number R 0 , which determines the existence and stability of the model's equilibria. We examine the global stability by constructing suitable Lyapunov functions. Our analysis reveals that if R 0 ≤ 1 , then EQ 0 is globally asymptotically stable (G.A.S), and if R 0 > 1 , then EQ 0 is unstable while EQ ⁎ is G.A.S. To illustrate our findings analytically, we conduct numerical simulations for each model. Additionally, we perform sensitivity analysis to demonstrate how the parameter values of the proposed model impact R 0 given a set of data. Finally, we discuss the implications of including the CTL immune response and latently infected cells in the secondary DENV infection model. Our study demonstrates that incorporating the CTL immune response and latently infected cells diminishes R 0 and enhances the system's stability around EQ 0 .
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Affiliation(s)
- Aeshah A. Raezah
- Department of Mathematics, Faculty of Science, King Khalid University, Abha 62529, Saudi Arabia
| | - A.M. Elaiw
- Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
| | - M.A. Alshaikh
- Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
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8
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Kitagawa K, Kim KS, Iwamoto M, Hayashi S, Park H, Nishiyama T, Nakamura N, Fujita Y, Nakaoka S, Aihara K, Perelson AS, Allweiss L, Dandri M, Watashi K, Tanaka Y, Iwami S. Multiscale modeling of HBV infection integrating intra- and intercellular viral propagation for analyzing extracellular viral markers. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.06.06.543822. [PMID: 37333409 PMCID: PMC10274663 DOI: 10.1101/2023.06.06.543822] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/20/2023]
Abstract
Chronic infection of hepatitis B virus (HBV) is caused by the persistence of closed circular DNA (cccDNA) in the nucleus of infected hepatocytes. Despite available therapeutic anti-HBV agents, eliminating the cccDNA remains challenging. The quantifying and understanding dynamics of cccDNA are essential for developing effective treatment strategies and new drugs. However, it requires a liver biopsy to measure the intrahepatic cccDNA, which is basically not accepted because of the ethical aspect. We here aimed to develop a non-invasive method for quantifying cccDNA in the liver using surrogate markers present in peripheral blood. We constructed a multiscale mathematical model that explicitly incorporates both intracellular and intercellular HBV infection processes. The model, based on age-structured partial differential equations (PDEs), integrates experimental data from in vitro and in vivo investigations. By applying this model, we successfully predicted the amount and dynamics of intrahepatic cccDNA using specific viral markers in serum samples, including HBV DNA, HBsAg, HBeAg, and HBcrAg. Our study represents a significant step towards advancing the understanding of chronic HBV infection. The non-invasive quantification of cccDNA using our proposed methodology holds promise for improving clinical analyses and treatment strategies. By comprehensively describing the interactions of all components involved in HBV infection, our multiscale mathematical model provides a valuable framework for further research and the development of targeted interventions.
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Affiliation(s)
- Kosaku Kitagawa
- interdisciplinary Biology Laboratory (iBLab), Division of Natural Science, Graduate School of Science, Nagoya University; Nagoya, Japan
| | - Kwang Su Kim
- interdisciplinary Biology Laboratory (iBLab), Division of Natural Science, Graduate School of Science, Nagoya University; Nagoya, Japan
- Department of Scientific Computing, Pukyong National University; Busan, South Korea
| | - Masashi Iwamoto
- interdisciplinary Biology Laboratory (iBLab), Division of Natural Science, Graduate School of Science, Nagoya University; Nagoya, Japan
- Department of Virology II, National Institute of Infectious Diseases; Tokyo, Japan
| | - Sanae Hayashi
- Department of Gastroenterology and Hepatology, Faculty of Life Sciences, Kumamoto University; Kumamoto, Japan
| | - Hyeongki Park
- interdisciplinary Biology Laboratory (iBLab), Division of Natural Science, Graduate School of Science, Nagoya University; Nagoya, Japan
| | - Takara Nishiyama
- interdisciplinary Biology Laboratory (iBLab), Division of Natural Science, Graduate School of Science, Nagoya University; Nagoya, Japan
| | - Naotoshi Nakamura
- interdisciplinary Biology Laboratory (iBLab), Division of Natural Science, Graduate School of Science, Nagoya University; Nagoya, Japan
| | - Yasuhisa Fujita
- interdisciplinary Biology Laboratory (iBLab), Division of Natural Science, Graduate School of Science, Nagoya University; Nagoya, Japan
| | - Shinji Nakaoka
- Faculty of Advanced Life Science, Hokkaido University; Sapporo, Japan
| | - Kazuyuki Aihara
- International Research Center for Neurointelligence, The University of Tokyo Institutes for Advanced Study, The University of Tokyo; Tokyo, Japan
| | - Alan S. Perelson
- Theoretical Biology and Biophysics Group, Los Alamos National Laboratory; Los Alamos, USA
| | - Lena Allweiss
- Department of Internal Medicine, University Medical Center Hamburg-Eppendorf; Hamburg, Germany
- German Center for Infection Research (DZIF), Hamburg-Lübeck-Borstel-Riems partner sites; Germany
| | - Maura Dandri
- Department of Internal Medicine, University Medical Center Hamburg-Eppendorf; Hamburg, Germany
- German Center for Infection Research (DZIF), Hamburg-Lübeck-Borstel-Riems partner sites; Germany
| | - Koichi Watashi
- Department of Virology II, National Institute of Infectious Diseases; Tokyo, Japan
- Research Center for Drug and Vaccine Development, National Institute of Infectious Diseases; Tokyo, Japan
- Department of Applied Biological Sciences, Faculty of Science and Technology, Tokyo University of Sciences; Chiba, Japan
| | - Yasuhito Tanaka
- Department of Gastroenterology and Hepatology, Faculty of Life Sciences, Kumamoto University; Kumamoto, Japan
| | - Shingo Iwami
- interdisciplinary Biology Laboratory (iBLab), Division of Natural Science, Graduate School of Science, Nagoya University; Nagoya, Japan
- Department of Applied Biological Sciences, Faculty of Science and Technology, Tokyo University of Sciences; Chiba, Japan
- Institute of Mathematics for Industry, Kyushu University; Fukuoka, Japan
- Institute for the Advanced Study of Human Biology (ASHBi), Kyoto University; Kyoto, Japan
- NEXT-Ganken Program, Japanese Foundation for Cancer Research (JFCR); Tokyo, Japan
- Science Groove Inc.; Fukuoka, Japan
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9
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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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10
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Advances in Parameter Estimation and Learning from Data for Mathematical Models of Hepatitis C Viral Kinetics. MATHEMATICS 2022; 10. [DOI: 10.3390/math10122136] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
Mathematical models, some of which incorporate both intracellular and extracellular hepatitis C viral kinetics, have been advanced in recent years for studying HCV–host dynamics, antivirals mode of action, and their efficacy. The standard ordinary differential equation (ODE) hepatitis C virus (HCV) kinetic model keeps track of uninfected cells, infected cells, and free virus. In multiscale models, a fourth partial differential equation (PDE) accounts for the intracellular viral RNA (vRNA) kinetics in an infected cell. The PDE multiscale model is substantially more difficult to solve compared to the standard ODE model, with governing differential equations that are stiff. In previous contributions, we developed and implemented stable and efficient numerical methods for the multiscale model for both the solution of the model equations and parameter estimation. In this contribution, we perform sensitivity analysis on model parameters to gain insight into important properties and to ensure our numerical methods can be safely used for HCV viral dynamic simulations. Furthermore, we generate in-silico patients using the multiscale models to perform machine learning from the data, which enables us to remove HCV measurements on certain days and still be able to estimate meaningful observations with a sufficiently small error.
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11
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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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12
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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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13
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Arya RK, Verros GD, Thapliyal D. Towards a Mathematical Model for the Viral Progression in the Pharynx. Healthcare (Basel) 2021; 9:healthcare9121766. [PMID: 34946492 PMCID: PMC8701019 DOI: 10.3390/healthcare9121766] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2021] [Revised: 12/16/2021] [Accepted: 12/16/2021] [Indexed: 12/03/2022] Open
Abstract
In this work, a comprehensive model for the viral progression in the pharynx has been developed. This one-dimension model considers both Fickian diffusion and convective flow coupled with chemical reactions, such as virus population growth, infected and uninfected cell accumulation as well as virus clearance. The effect of a sterilizing agent such as an alcoholic solution on the viral progression in the pharynx was taken into account and a parametric analysis for the effect of kinetic rate parameters on virus propagation was made. Moreover, different conditions caused by further medical treatment, such as a decrease in virus yield per infected cell, were examined. It is shown that the infection fails to establish by decreasing the virus yield per infected cell. It is believed that this work could be used to further investigate the medical treatment of viral progression in the pharynx.
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Affiliation(s)
- Raj Kumar Arya
- Department of Chemical Engineering, Dr. B. R. Ambedkar National Institute of Technology, Jalandhar 144011, India;
- Correspondence: or
| | - George D. Verros
- Laboratory of Polymer and Colour Chemistry and Technology, Department of Chemistry, Aristotle University of Thessaloniki (AUTH), P.O. Box 454, Plagiari, Epanomi, 57500 Thessaloniki, Greece;
| | - Devyani Thapliyal
- Department of Chemical Engineering, Dr. B. R. Ambedkar National Institute of Technology, Jalandhar 144011, India;
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14
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Rubio FA, Yang HM. A mathematical model to evaluate the role of memory B and T cells in heterologous secondary dengue infection. J Theor Biol 2021; 534:110961. [PMID: 34774663 DOI: 10.1016/j.jtbi.2021.110961] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2021] [Revised: 10/27/2021] [Accepted: 11/08/2021] [Indexed: 11/17/2022]
Abstract
We propose a mathematical model to investigate the antibody-dependent enhancement (ADE) phenomenon during secondary dengue infection. The model consists of an ODE system that describes the interaction of the dengue virus with macrophages and memory B and T cell role during the infection. The qualitative model analysis is done in terms of memory B and T cell cloning parameters and the basic reproduction number R0. In the absence of memory B and T cell cloning, if R0<1 the dengue virus population extinguishes, while for R0>1, it tends asymptotically to a positive equilibrium. However, when we consider the memory B cell cloning, it is possible to occur dengue infection even when R0<1. Memory T cells have an essential role in eliminating the possibility of ADE occurrence when R0<1.
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Affiliation(s)
- Felipe Alves Rubio
- Institute of Mathematics, Statistics and Scientific Computing - University of Campinas, Campinas, SP, Brazil.
| | - Hyun Mo Yang
- Institute of Mathematics, Statistics and Scientific Computing - University of Campinas, Campinas, SP, Brazil
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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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Vaidya NK, Bloomquist A, Perelson AS. Modeling Within-Host Dynamics of SARS-CoV-2 Infection: A Case Study in Ferrets. Viruses 2021; 13:1635. [PMID: 34452499 PMCID: PMC8402735 DOI: 10.3390/v13081635] [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: 06/22/2021] [Revised: 07/27/2021] [Accepted: 08/09/2021] [Indexed: 12/26/2022] Open
Abstract
The pre-clinical development of antiviral agents involves experimental trials in animals and ferrets as an animal model for the study of SARS-CoV-2. Here, we used mathematical models and experimental data to characterize the within-host infection dynamics of SARS-CoV-2 in ferrets. We also performed a global sensitivity analysis of model parameters impacting the characteristics of the viral infection. We provide estimates of the viral dynamic parameters in ferrets, such as the infection rate, the virus production rate, the infectious virus proportion, the infected cell death rate, the virus clearance rate, as well as other related characteristics, including the basic reproduction number, pre-peak infectious viral growth rate, post-peak infectious viral decay rate, pre-peak infectious viral doubling time, post-peak infectious virus half-life, and the target cell loss in the respiratory tract. These parameters and indices are not significantly different between animals infected with viral strains isolated from the environment and isolated from human hosts, indicating a potential for transmission from fomites. While the infection period in ferrets is relatively short, the similarity observed between our results and previous results in humans supports that ferrets can be an appropriate animal model for SARS-CoV-2 dynamics-related studies, and our estimates provide helpful information for such studies.
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Affiliation(s)
- Naveen K. Vaidya
- Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182, USA;
- Computational Science Research Center, San Diego State University, San Diego, CA 92182, USA
- Viral Information Institute, San Diego State University, San Diego, CA 92182, USA
| | - Angelica Bloomquist
- Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182, USA;
- Computational Science Research Center, San Diego State University, San Diego, CA 92182, USA
- Viral Information Institute, San Diego State University, San Diego, CA 92182, USA
| | - Alan S. Perelson
- Los Alamos National Laboratory, Theoretical Biology and Biophysics Group, Los Alamos, NM 87545, USA;
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17
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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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18
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Ciupe SM, Vaidya NK, Forde JE. Early events in hepatitis B infection: the role of inoculum dose. Proc Biol Sci 2021; 288:20202715. [PMID: 33563115 DOI: 10.1098/rspb.2020.2715] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
The relationship between the inoculum dose and the ability of the pathogen to invade the host is poorly understood. Experimental studies in non-human primates infected with different inoculum doses of hepatitis B virus have shown a non-monotonic relationship between dose magnitude and infection outcome, with high and low doses leading to 100% liver infection and intermediate doses leading to less than 0.1% liver infection, corresponding to CD4 T-cell priming. Since hepatitis B clearance is CD8 T-cell mediated, the question of whether the inoculum dose influences CD8 T-cell dynamics arises. To help answer this question, we developed a mathematical model of virus-host interaction following hepatitis B virus infection. Our model explains the experimental data well, and predicts that the inoculum dose affects both the timing of the CD8 T-cell expansion and the quality of its response, especially the non-cytotoxic function. We find that a low-dose challenge leads to slow CD8 T-cell expansion, weak non-cytotoxic functions, and virus persistence; high- and medium-dose challenges lead to fast CD8 T-cell expansion, strong cytotoxic and non-cytotoxic function, and virus clearance; while a super-low-dose challenge leads to delayed CD8 T-cell expansion, strong cytotoxic and non-cytotoxic function, and virus clearance. These results are useful for designing immune cell-based interventions.
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Affiliation(s)
- Stanca M Ciupe
- Department of Mathematics, Virginia Tech, Blacksburg, 24060 VA, USA
| | - Naveen K Vaidya
- Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182, USA.,Computational Science Research Center, San Diego State University, San Diego, CA 92182, USA.,Viral Information Institute, San Diego State University, San Diego, CA 92182, USA
| | - Jonathan E Forde
- Department of Mathematics and Computer Science, Hobart and William Smith Colleges, Geneva, New York 14456, USA
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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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Means S, Ali MA, Ho H, Heffernan J. Mathematical Modeling for Hepatitis B Virus: Would Spatial Effects Play a Role and How to Model It? Front Physiol 2020; 11:146. [PMID: 32158403 PMCID: PMC7052012 DOI: 10.3389/fphys.2020.00146] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2019] [Accepted: 02/11/2020] [Indexed: 12/23/2022] Open
Affiliation(s)
- Shawn Means
- School of Natural and Computational Sciences, Massey University, Auckland, New Zealand
| | - Md A Ali
- Department of Mathematics and Statistics, York University, Toronto, ON, Canada
| | - Harvey Ho
- Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand
| | - Jane Heffernan
- Department of Mathematics and Statistics, York University, Toronto, ON, Canada
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21
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Fatehi F, Kyrychko YN, Blyuss KB. Stochastic dynamics in a time-delayed model for autoimmunity. Math Biosci 2020; 322:108323. [PMID: 32092469 DOI: 10.1016/j.mbs.2020.108323] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2019] [Revised: 01/21/2020] [Accepted: 02/10/2020] [Indexed: 12/18/2022]
Abstract
In this paper we study interactions between stochasticity and time delays in the dynamics of immune response to viral infections, with particular interest in the onset and development of autoimmune response. Starting with a deterministic time-delayed model of immune response to infection, which includes cytokines and T cells with different activation thresholds, we derive an exact delayed chemical master equation for the probability density. We use system size expansion and linear noise approximation to explore how variance and coherence of stochastic oscillations depend on parameters, and to show that stochastic oscillations become more regular when regulatory T cells become more effective at clearing autoreactive T cells. Reformulating the model as an Itô stochastic delay differential equation, we perform numerical simulations to illustrate the dynamics of the model and associated probability distributions in different parameter regimes. The results suggest that even in cases where the deterministic model has stable steady states, in individual stochastic realisations, the model can exhibit sustained stochastic oscillations, whose variance increases as one gets closer to the deterministic stability boundary. Furthermore, in the regime of bi-stability, whereas deterministically the system would approach one of the steady states (or periodic solutions) depending on the initial conditions, due to the presence of stochasticity, it is now possible for the system to reach both of those dynamical states with certain probability. Biological significance of this result lies in highlighting the fact that since normally in a laboratory or clinical setting one would observe a single individual realisation of the course of the disease, even for all parameters characterising the immune system and the strength of infection being the same, there is a proportion of cases where a spontaneous recovery can be observed, and similarly, where a disease can develop in a situation that otherwise would result in a normal disease clearance.
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Affiliation(s)
- Farzad Fatehi
- Department of Mathematics, University of York, York YO10 5DD, UK.
| | - Yuliya N Kyrychko
- Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, UK.
| | - Konstantin B Blyuss
- Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, UK.
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22
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Goyal A, Liao LE, Perelson AS. Within-host mathematical models of hepatitis B virus infection: Past, present, and future. ACTA ACUST UNITED AC 2019; 18:27-35. [PMID: 31930181 DOI: 10.1016/j.coisb.2019.10.003] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
Mathematical modeling has been instrumental in enhancing our understanding of the viral dynamics of hepatitis B virus (HBV) infection. We give a primer on HBV infection in humans and a brief overview of the development of within-host mathematical models of HBV infection. In the last decade, models have advanced from considering chronic HBV infections under therapy to the pathogenesis of infection. We also summarize estimates of key viral dynamic parameters that have varied greatly among studies, and show that they impact model predictions. Future directions for mathematical modeling of HBV infection are proposed to better understand emerging therapies, the HBV life cycle, predicting cure, and the mechanisms involved in the immune response to HBV infection.
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Affiliation(s)
- Ashish Goyal
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico, 87545, USA
| | - Laura E Liao
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico, 87545, USA
| | - Alan S Perelson
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico, 87545, USA
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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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Reinharz V, Churkin A, Lewkiewicz S, Dahari H, Barash D. A Parameter Estimation Method for Multiscale Models of Hepatitis C Virus Dynamics. Bull Math Biol 2019; 81:3675-3721. [PMID: 31338739 PMCID: PMC7375976 DOI: 10.1007/s11538-019-00644-7] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2018] [Accepted: 07/10/2019] [Indexed: 12/11/2022]
Abstract
Mathematical models that are based on differential equations require detailed knowledge about the parameters that are included in the equations. Some of the parameters can be measured experimentally while others need to be estimated. When the models become more sophisticated, such as in the case of multiscale models of hepatitis C virus dynamics that deal with partial differential equations (PDEs), several strategies can be tried. It is possible to use parameter estimation on an analytical approximation of the solution to the multiscale model equations, namely the long-term approximation, but this limits the scope of the parameter estimation method used and a long-term approximation needs to be derived for each model. It is possible to transform the PDE multiscale model to a system of ODEs, but this has an effect on the model parameters themselves and the transformation can become problematic for some models. Finally, it is possible to use numerical solutions for the multiscale model and then use canned methods for the parameter estimation, but the latter is making the user dependent on a black box without having full control over the method. The strategy developed here is to start by working directly on the multiscale model equations for preparing them toward the parameter estimation method that is fully coded and controlled by the user. It can also be adapted to multiscale models of other viruses. The new method is described, and illustrations are provided using a user-friendly simulator that incorporates the method.
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Affiliation(s)
- Vladimir Reinharz
- Department of Computer Science, Ben-Gurion University, Beersheba, Israel
| | - Alexander Churkin
- Department of Software Engineering, Sami Shamoon College of Engineering, Beersheba, Israel
| | - Stephanie Lewkiewicz
- Department of Mathematics, University of California at Los Angeles, Los Angeles, CA, USA
| | - Harel Dahari
- Program for Experimental and Theoretical Modeling, Division of Hepatology, Department of Medicine, Loyola University Medical Center, Maywoood, IL, USA
| | - Danny Barash
- Department of Computer Science, Ben-Gurion University, Beersheba, Israel.
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25
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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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26
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Ke R, Li H, Wang S, Ding W, Ribeiro RM, Giorgi EE, Bhattacharya T, Barnard RJO, Hahn BH, Shaw GM, Perelson AS. Superinfection and cure of infected cells as mechanisms for hepatitis C virus adaptation and persistence. Proc Natl Acad Sci U S A 2018; 115:E7139-E7148. [PMID: 29987026 PMCID: PMC6065014 DOI: 10.1073/pnas.1805267115] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
RNA viruses exist as a genetically diverse quasispecies with extraordinary ability to adapt to abrupt changes in the host environment. However, the molecular mechanisms that contribute to their rapid adaptation and persistence in vivo are not well studied. Here, we probe hepatitis C virus (HCV) persistence by analyzing clinical samples taken from subjects who were treated with a second-generation HCV protease inhibitor. Frequent longitudinal viral load determinations and large-scale single-genome sequence analyses revealed rapid antiviral resistance development, and surprisingly, dynamic turnover of dominant drug-resistant mutant populations long after treatment cessation. We fitted mathematical models to both the viral load and the viral sequencing data, and the results provided strong support for the critical roles that superinfection and cure of infected cells play in facilitating the rapid turnover and persistence of viral populations. More broadly, our results highlight the importance of considering viral dynamics and competition at the intracellular level in understanding rapid viral adaptation. Thus, we propose a theoretical framework integrating viral and molecular mechanisms to explain rapid viral evolution, resistance, and persistence despite antiviral treatment and host immune responses.
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Affiliation(s)
- Ruian Ke
- Department of Mathematics, North Carolina State University, Raleigh, NC 27695
- Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, NM 87545
| | - Hui Li
- Department of Medicine, University of Pennsylvania, Philadelphia, PA 19104
- Department of Microbiology, University of Pennsylvania, Philadelphia, PA 19104
| | - Shuyi Wang
- Department of Medicine, University of Pennsylvania, Philadelphia, PA 19104
- Department of Microbiology, University of Pennsylvania, Philadelphia, PA 19104
| | - Wenge Ding
- Department of Medicine, University of Pennsylvania, Philadelphia, PA 19104
- Department of Microbiology, University of Pennsylvania, Philadelphia, PA 19104
| | - Ruy M Ribeiro
- Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, NM 87545
- Laboratory of Biomathematics, Faculty of Medicine, University of Lisbon, 1600-276 Lisbon, Portugal
| | - Elena E Giorgi
- Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, NM 87545
| | - Tanmoy Bhattacharya
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545
- Santa Fe Institute, Santa Fe, NM 87501
| | | | - Beatrice H Hahn
- Department of Medicine, University of Pennsylvania, Philadelphia, PA 19104;
- Department of Microbiology, University of Pennsylvania, Philadelphia, PA 19104
| | - George M Shaw
- Department of Medicine, University of Pennsylvania, Philadelphia, PA 19104
- Department of Microbiology, University of Pennsylvania, Philadelphia, PA 19104
| | - Alan S Perelson
- Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, Los Alamos, NM 87545;
- Santa Fe Institute, Santa Fe, NM 87501
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27
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Reinharz V, Dahari H, Barash D. Numerical schemes for solving and optimizing multiscale models with age of hepatitis C virus dynamics. Math Biosci 2018; 300:1-13. [PMID: 29550297 PMCID: PMC5992100 DOI: 10.1016/j.mbs.2018.03.011] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2018] [Accepted: 03/07/2018] [Indexed: 12/16/2022]
Abstract
Age-structured PDE models have been developed to study viral infection and treatment. However, they are notoriously difficult to solve. Here, we investigate the numerical solutions of an age-based multiscale model of hepatitis C virus (HCV) dynamics during antiviral therapy and compare them with an analytical approximation, namely its long-term approximation. First, starting from a simple yet flexible numerical solution that also considers an integral approximated over previous iterations, we show that the long-term approximation is an underestimate of the PDE model solution as expected since some infection events are being ignored. We then argue for the importance of having a numerical solution that takes into account previous iterations for the associated integral, making problematic the use of canned solvers. Second, we demonstrate that the governing differential equations are stiff and the stability of the numerical scheme should be considered. Third, we show that considerable gain in efficiency can be achieved by using adaptive stepsize methods over fixed stepsize methods for simulating realistic scenarios when solving multiscale models numerically. Finally, we compare between several numerical schemes for the solution of the equations and demonstrate the use of a numerical optimization scheme for the parameter estimation performed directly from the equations.
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Affiliation(s)
- Vladimir Reinharz
- Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel.
| | - Harel Dahari
- The Program for Experimental & Theoretical Modeling, Division of Hepatology, Department of Medicine, Loyola University Medical Center, Maywood, IL 60153, USA
| | - Danny Barash
- Department of Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel.
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28
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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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29
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Cangelosi Q, Means SA, Ho H. A multi-scale spatial model of hepatitis-B viral dynamics. PLoS One 2017; 12:e0188209. [PMID: 29216213 PMCID: PMC5720747 DOI: 10.1371/journal.pone.0188209] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2017] [Accepted: 11/02/2017] [Indexed: 12/14/2022] Open
Abstract
Chronic hepatitis B viral infection (HBV) afflicts around 250 million individuals globally and few options for treatment exist. Once infected, the virus entrenches itself in the liver with a notoriously resilient colonisation of viral DNA (covalently-closed circular DNA, cccDNA). The majority of infections are cleared, yet we do not understand why 5% of adult immune responses fail leading to the chronic state with its collateral morbid effects such as cirrhosis and eventual hepatic carcinoma. The liver environment exhibits particularly complex spatial structures for metabolic processing and corresponding distributions of nutrients and transporters that may influence successful HBV entrenchment. We assembled a multi-scaled mathematical model of the fundamental hepatic processing unit, the sinusoid, into a whole-liver representation to investigate the impact of this intrinsic spatial heterogeneity on the HBV dynamic. Our results suggest HBV may be exploiting spatial aspects of the liver environment. We distributed increased HBV replication rates coincident with elevated levels of nutrients in the sinusoid entry point (the periportal region) in tandem with similar distributions of hepatocyte transporters key to HBV invasion (e.g., the sodium-taurocholate cotransporting polypeptide or NTCP), or immune system activity. According to our results, such co-alignment of spatial distributions may contribute to persistence of HBV infections, depending on spatial distributions and intensity of immune response as well. Moreover, inspired by previous HBV models and experimentalist suggestions of extra-hepatic HBV replication, we tested in our model influence of HBV blood replication and observe an overall nominal effect on persistent liver infection. Regardless, we confirm prior results showing a solo cccDNA is sufficient to re-infect an entire liver, with corresponding concerns for transplantation and treatment.
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Affiliation(s)
- Quentin Cangelosi
- Computational and Mathematical Engineering, Institut National des Sciences Appliquées, Toulouse, France
| | - Shawn A. Means
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
| | - Harvey Ho
- Auckland Bioengineering Institute, University of Auckland, Auckland, New Zealand
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30
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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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31
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Reinharz V, Churkin A, Dahari H, Barash D. A Robust and Efficient Numerical Method for RNA-Mediated Viral Dynamics. FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS 2017; 3:20. [PMID: 30854378 PMCID: PMC6404971 DOI: 10.3389/fams.2017.00020] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The multiscale model of hepatitis C virus (HCV) dynamics, which includes intracellular viral RNA (vRNA) replication, has been formulated in recent years in order to provide a new conceptual framework for understanding the mechanism of action of a variety of agents for the treatment of HCV. We present a robust and efficient numerical method that belongs to the family of adaptive stepsize methods and is implicit, a Rosenbrock type method that is highly suited to solve this problem. We provide a Graphical User Interface that applies this method and is useful for simulating viral dynamics during treatment with anti-HCV agents that act against HCV on the molecular level.
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Affiliation(s)
- Vladimir Reinharz
- Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel
| | - Alexander Churkin
- Department of Software Engineering, Sami Shamoon College of Engineering, Beer-Sheva, Israel
| | - Harel Dahari
- Program for Experimental and Theoretical Modeling, Division of Hepatology, Department of Medicine, Loyola University Medical Center, Maywood, IL, United States
| | - Danny Barash
- Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel
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32
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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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33
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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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34
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Nikin-Beers R, Ciupe SM. Modelling original antigenic sin in dengue viral infection. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2017; 35:257-272. [DOI: 10.1093/imammb/dqx002] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2016] [Accepted: 01/23/2017] [Indexed: 01/04/2023]
Affiliation(s)
| | - Stanca M Ciupe
- Department of Mathematics, Virginia Tech, Blacksburg, VA, USA
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35
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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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36
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37
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A Computational Model of Inhibition of HIV-1 by Interferon-Alpha. PLoS One 2016; 11:e0152316. [PMID: 27010978 PMCID: PMC4807028 DOI: 10.1371/journal.pone.0152316] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2015] [Accepted: 03/11/2016] [Indexed: 01/21/2023] Open
Abstract
Type 1 interferons such as interferon-alpha (IFNα) inhibit replication of Human immunodeficiency virus (HIV-1) by upregulating the expression of genes that interfere with specific steps in the viral life cycle. This pathway thus represents a potential target for immune-based therapies that can alter the dynamics of host-virus interactions to benefit the host. To obtain a deeper mechanistic understanding of how IFNα impacts spreading HIV-1 infection, we modeled the interaction of HIV-1 with CD4 T cells and IFNα as a dynamical system. This model was then tested using experimental data from a cell culture model of spreading HIV-1 infection. We found that a model in which IFNα induces reversible cellular states that block both early and late stages of HIV-1 infection, combined with a saturating rate of conversion to these states, was able to successfully fit the experimental dataset. Sensitivity analysis showed that the potency of inhibition by IFNα was particularly dependent on specific network parameters and rate constants. This model will be useful for designing new therapies targeting the IFNα network in HIV-1-infected individuals, as well as potentially serving as a template for understanding the interaction of IFNα with other viruses.
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38
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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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39
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Kumberger P, Frey F, Schwarz US, Graw F. Multiscale modeling of virus replication and spread. FEBS Lett 2016; 590:1972-86. [PMID: 26878104 DOI: 10.1002/1873-3468.12095] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2015] [Revised: 01/21/2016] [Accepted: 02/07/2016] [Indexed: 01/16/2023]
Abstract
Replication and spread of human viruses is based on the simultaneous exploitation of many different host functions, bridging multiple scales in space and time. Mathematical modeling is essential to obtain a systems-level understanding of how human viruses manage to proceed through their life cycles. Here, we review corresponding advances for viral systems of large medical relevance, such as human immunodeficiency virus-1 (HIV-1) and hepatitis C virus (HCV). We will outline how the combination of mathematical models and experimental data has advanced our quantitative knowledge about various processes of these pathogens, and how novel quantitative approaches promise to fill remaining gaps.
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Affiliation(s)
- Peter Kumberger
- BioQuant-Center, Heidelberg University, Germany.,Center for Modeling and Simulation in the Biosciences (BIOMS), Heidelberg University, Germany
| | - Felix Frey
- BioQuant-Center, Heidelberg University, Germany.,Institute for Theoretical Physics, Heidelberg University, Germany
| | - Ulrich S Schwarz
- BioQuant-Center, Heidelberg University, Germany.,Institute for Theoretical Physics, Heidelberg University, Germany
| | - Frederik Graw
- BioQuant-Center, Heidelberg University, Germany.,Center for Modeling and Simulation in the Biosciences (BIOMS), Heidelberg University, Germany
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40
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TCHINDA PMOUOFO, TEWA JEANJULES, MEWOLI BOULECHARD, BOWONG SAMUEL. A THEORETICAL ASSESSMENT OF THE EFFECTS OF DISTRIBUTED DELAY ON THE TRANSMISSION DYNAMICS OF HEPATITIS B. J BIOL SYST 2015. [DOI: 10.1142/s0218339015500229] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, we investigate the global dynamics of a system of delay differential equations which describes the interaction of hepatitis B virus (HBV) with both liver and blood cells. The model has two distributed time delays describing the time needed for infection of cell and virus replication. We also include the efficiency of drug therapy in inhibiting viral production and the efficiency of drug therapy in blocking new infection. We compute the basic reproduction number and find that increasing delays will decrease the value of the basic reproduction number. We study the sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. Our analysis reveals that the model exhibits the phenomenon of backward bifurcation (where a stable disease-free equilibrium (DFE) co-exists with a stable endemic equilibrium when the basic reproduction number is less than unity). Numerical simulations are presented to evaluate the impact of time-delays on the prevalence of the disease.
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Affiliation(s)
- P. MOUOFO TCHINDA
- Department of Mathematics, University of Yaounde I, P. O. Box 812 Yaounde, Cameroon
- UMI 209 IRD/UPMC UMMISCO, Bondy, France
- Project-Team GRIMCAPE, LIRIMA, CETIC Center in ICT, University of Yaounde 1, Cameroon
| | - JEAN JULES TEWA
- Department of Mathematics and Physics, National Advanced School of Engineering (Polytechnic), University of Yaounde I, P. O. Box 8390 Yaounde, Cameroon
- UMI 209 IRD/UPMC UMMISCO, Bondy, France
- Project-Team GRIMCAPE, LIRIMA, CETIC Center in ICT, University of Yaounde 1, Cameroon
| | - BOULECHARD MEWOLI
- Department of Mathematics, University of Yaounde I, P. O. Box 812 Yaounde, Cameroon
| | - SAMUEL BOWONG
- Department of Mathematics and Computer Science, Faculty of Science, University of Douala, P. O. Box 24157 Douala, Cameroon
- UMI 209 IRD/UPMC UMMISCO, Bondy, France
- Project-Team GRIMCAPE, LIRIMA, CETIC Center in ICT, University of Yaounde 1, Cameroon
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41
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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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42
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Murray JM, Goyal A. In silico single cell dynamics of hepatitis B virus infection and clearance. J Theor Biol 2014; 366:91-102. [PMID: 25476731 DOI: 10.1016/j.jtbi.2014.11.020] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2014] [Revised: 11/18/2014] [Accepted: 11/20/2014] [Indexed: 02/07/2023]
Abstract
UNLABELLED The progression of acute hepatitis B virus (HBV) to chronic infection or clearance is highly dependent on the host immune response composed of cytolytic (CTL) and non-cytolytic (non-CTL) effects. Cytolytic processes induce hepatocyte killing while non-CTL processes inhibit intracellular replication. Both effects are widely recognized and accepted. However, there are uncertainties about the assistance provided by either the loss of covalently circular closed DNA (cccDNA) during cell proliferation or the emergence of refractory cells to immune mediated clearance. We developed an agent-based mathematical model and tested the relative roles of different mechanisms of the immune system in the clearance of acute HBV infection. HBV viremia clearance time and hepatocyte turnover (HT) were used as the two major criteria in determining reasonable outcomes. Modelling results in 90% of cells containing between 1 and 17 cccDNA copies and normally distributed at the peak of infection. Variations in p36 levels, responsible for determining export of virions or recirculation to amplify cccDNA numbers, have a much greater impact on mean cccDNA level/cell at peak viremia than virus infectivity and cccDNA half-life. A strong CTL effect alone failed to clear infection with HT ≈ 10. Acute infection clearance was possible with combined CTL and non-CTL effects along with complete loss of intracellular viral components during cell proliferation resulting in the desired range of HT (0.7-1). The emergence of cells refractory to infection can reduce HT by up to 90%. However their impact was less effective than complete loss of intracellular viral components during cell proliferation. CONCLUSION the existence of refractory cells is not necessary when there is complete loss of intracellular quantities during cell proliferation but is essential with only partial clearance.
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Affiliation(s)
- John M Murray
- School of Mathematics and Statistics, UNSW, Sydney, NSW 2052, Australia.
| | - Ashish Goyal
- School of Mathematics and Statistics, UNSW, Sydney, NSW 2052, Australia
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43
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Guedj J, Rotman Y, Cotler SJ, Koh C, Schmid P, Albrecht J, Haynes-Williams V, Liang JT, Hoofnagle JH, Heller T, Dahari H. Understanding early serum hepatitis D virus and hepatitis B surface antigen kinetics during pegylated interferon-alpha therapy via mathematical modeling. Hepatology 2014; 60:1902-10. [PMID: 25098971 PMCID: PMC4245461 DOI: 10.1002/hep.27357] [Citation(s) in RCA: 50] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 02/07/2014] [Accepted: 08/05/2014] [Indexed: 12/15/2022]
Abstract
UNLABELLED There is little information on the early kinetics of hepatitis delta virus (HDV) and hepatitis B surface antigen (HBsAg) during interferon-α therapy. Here a mathematical model was developed and fitted to frequent HDV and HBsAg kinetic data from 10 patients during the first 28 weeks of pegylated-interferon-α2a (peg-IFN) therapy. Three patients achieved a complete virological response (CVR), defined as undetectable HDV 6 months after treatment stopped with loss of HBsAg and anti-HBsAg seroconversion. After initiation of therapy, a median delay of 9 days (interquartile range [IQR]: 5-15) was observed with no significant changes in HDV level. Thereafter, HDV declined in a biphasic manner, where a rapid first phase lasting for 25 days (IQR: 23-58) was followed by a slower or plateau second phase. The model predicts that the main effect of peg-IFN is to reduce HDV production/release with a median effectiveness of 96% (IQR: 93-99.8). Median serum HDV half-life (t1/2 ) was estimated as 2.9 days (IQR: 1.5-5.3) corresponding to a pretreatment production and clearance of about 10(10) (IQR: 10(9.7) -10(10.7) ) virions/day. None of the patients with flat second phase in HDV achieved CVR. HBsAg kinetics of decline paralleled the second phase of HDV decline consistent with HBsAg-productive-infected cells being the main source of production of HDV, with a median t1/2 of 135 days (IQR: 20-460). The interferon lambda-3 polymorphism (rs12979860) was not associated with kinetic parameters. CONCLUSION Modeling results provide insights into HDV-host dynamics, the relationship between serum HBsAg levels and HBsAg-infected cells, IFN's mode of action, and its effectiveness. The observation that a flat second phase in HDV and HBsAg kinetics was associated with failure to achieve CVR provides the basis to develop early stopping rules during peg-IFN treatment in HDV-infected patients.
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Affiliation(s)
- Jeremie Guedj
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los
Alamos, NM 87545
- INSERM UMR 738, University Paris Diderot, F-75018 Paris
- University Paris Diderot, Sorbonne Paris Cité, Paris, France
| | - Yaron Rotman
- Liver Diseases Branch, NIDDK, NIH, Bethesda, MD, USA
| | - Scott J. Cotler
- The Program for Experimental and Theoretical Modeling, Division of
Hepatology, Department of Medicine, Loyola University Medical Center, Maywood, IL 60153,
USA
| | | | - Peter Schmid
- National Genetics Institute, Los Angeles, CA, USA
| | | | | | - Jake T. Liang
- Liver Diseases Branch, NIDDK, NIH, Bethesda, MD, USA
| | | | - Theo Heller
- Liver Diseases Branch, NIDDK, NIH, Bethesda, MD, USA
| | - Harel Dahari
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los
Alamos, NM 87545
- The Program for Experimental and Theoretical Modeling, Division of
Hepatology, Department of Medicine, Loyola University Medical Center, Maywood, IL 60153,
USA
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44
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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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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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46
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Human systems immunology: hypothesis-based modeling and unbiased data-driven approaches. Semin Immunol 2013; 25:193-200. [PMID: 23375135 PMCID: PMC3836867 DOI: 10.1016/j.smim.2012.11.003] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/21/2012] [Accepted: 11/08/2012] [Indexed: 11/23/2022]
Abstract
Systems immunology is an emerging paradigm that aims at a more systematic and quantitative understanding of the immune system. Two major approaches have been utilized to date in this field: unbiased data-driven modeling to comprehensively identify molecular and cellular components of a system and their interactions; and hypothesis-based quantitative modeling to understand the operating principles of a system by extracting a minimal set of variables and rules underlying them. In this review, we describe applications of the two approaches to the study of viral infections and autoimmune diseases in humans, and discuss possible ways by which these two approaches can synergize when applied to human immunology.
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47
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Iwami S, Koizumi Y, Ikeda H, Kakizoe Y. Quantification of viral infection dynamics in animal experiments. Front Microbiol 2013; 4:264. [PMID: 24058361 PMCID: PMC3767920 DOI: 10.3389/fmicb.2013.00264] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2013] [Accepted: 08/16/2013] [Indexed: 12/18/2022] Open
Abstract
Analyzing the time-course of several viral infections using mathematical models based on experimental data can provide important quantitative insights regarding infection dynamics. Over the past decade, the importance and significance of mathematical modeling has been gaining recognition among virologists. In the near future, many animal models of human-specific infections and experimental data from high-throughput techniques will become available. This will provide us with the opportunity to develop new quantitative approaches, combining experimental and mathematical analyses. In this paper, we review the various quantitative analyses of viral infections and discuss their possible applications.
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Affiliation(s)
- Shingo Iwami
- Department of Biology, Faculty of Sciences, Kyushu University Fukuoka, Japan
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48
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Optimal Antiviral Treatment Strategies of HBV Infection Model with Logistic Hepatocyte Growth. ACTA ACUST UNITED AC 2013. [DOI: 10.1155/2013/912835] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
This study considers an optimal therapy strategy for HBV infection by incorporating two controls laws into a previous hepatitis B viral infection model with logistic hepatocyte growth. Our goal is to
maximize the number of healthy cells and to minimize the cost of the therapy. In this context, the existence of an optimal control is proved. The optimal control is obtained by solving the optimality system which was composed of three nonlinear ODEs with initial conditions and three nonlinear adjoint ODEs with transversality conditions. The results were analysed and interpreted numerically using MATLAB.
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49
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Block TM, Gish R, Guo H, Mehta A, Cuconati A, Thomas London W, Guo JT. Chronic hepatitis B: what should be the goal for new therapies? Antiviral Res 2013; 98:27-34. [PMID: 23391846 DOI: 10.1016/j.antiviral.2013.01.006] [Citation(s) in RCA: 99] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2012] [Revised: 01/14/2013] [Accepted: 01/28/2013] [Indexed: 02/07/2023]
Abstract
Chronic hepatitis B can currently be medically managed with either pegylated interferon-alpha (pegIFN-α) or one of the five nucleos(t)ide analog Direct Acting Antivirals (DAAs) that inhibit the hepatitis B virus (HBV) DNA polymerase. While pegIFN-α is effective in approximately one-third of the treated patients, the polymerase inhibitors significantly reduce viral load in the vast majority of those treated. However, neither pegIFN-α nor nucleosi(t)de analogs are capable of reliably eliminating the virus and achieving a cure. Moreover, the interferons and polymerase inhibitors are recommended by US, European and Asian professional society practice guidelines for use in only a subset of those infected with HBV. This subset is the population with the greatest levels of circulating viral DNA and abnormal liver function. Although this is the population at the highest risk for cirrhosis and liver cancer, those who fall outside the treatment guidelines, with low levels of viral replication and normal serum ALTs, may also benefit from antiviral therapy. The questions are thus: are new classes of drugs needed to manage chronic hepatitis B? Is a cure possible? Is a cure even necessary? It is therefore important to define the meaning of a cure and determine what the goals of new therapies should be. In this article, we address those questions and propose two operational definitions of medically attainable cures. The first is a "functional cure" based on the clinical outcome, in which the patient's life expectancy becomes the same as that of an individual who has resolved his HBV infection without therapy. Because such an outcome cannot be measured over the short term, we also define an "apparent virological cure," based on the stable off-drug suppression of HBV viremia and antigenemia and the normalization of ALTs and other laboratory tests. We suggest that such a virological cure should be the goal of future therapeutics in all patients with chronic hepatitis B. The extent to which a virological cure predicts a functional cure will only be determined by long-term follow-up.
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Affiliation(s)
- Timothy M Block
- Department of Microbiology and Immunology, Drexel University College of Medicine, 3805 Old Easton Road, Doylestown, PA 18902, USA.
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50
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Modeling the acute and chronic phases of Theiler murine encephalomyelitis virus infection. J Virol 2013; 87:4052-9. [PMID: 23365440 DOI: 10.1128/jvi.03395-12] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
Abstract
Theiler murine encephalomyelitis virus (TMEV) infection of a mouse's central nervous system is biphasic: first the virus infects motor neurons (acute phase), and this is followed by a chronic phase in which the virus infects glial cells (primarily microglia and macrophages [M]) of the spinal cord white matter, leading to inflammation and demyelination. As such, TMEV-induced demyelinating disease in mice provides a highly relevant experimental animal model for multiple sclerosis. Mathematical models have proven valuable in understanding the in vivo dynamics of persistent virus infections, such as HIV-1, hepatitis B virus, and hepatitis C virus infections. However, viral dynamic modeling has not been used for understanding TMEV infection. We constructed the first mathematical model of TMEV-host kinetics during acute and early chronic infections in mice and fit measured viral kinetic data with the model. The data fitting allowed us to estimate several unknown parameters, including the following: the rate of infection of neurons, 0.5 × 10(-8) to 5.6 × 10(-8) day(-1); the percent reduction of the infection rate due to the presence of virus-specific antibodies, which reaches 98.5 to 99.9% after day 15 postinfection (p.i.); the half-life of infected neurons, 0.1 to 1.2 days; and a cytokine-enhanced macrophage source rate of 25 to 350 M/day into the spinal cord starting at 10.9 to 12.9 days p.i. The model presented here is a first step toward building a comprehensive model for TMEV-induced demyelinating disease. Moreover, the model can serve as an important tool in understanding TMEV infectious mechanisms and may prove useful in evaluating antivirals and/or therapeutic modalities to prevent or inhibit demyelination.
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