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      Mathematical Analysis of Viral Replication Dynamics and Antiviral Treatment Strategies: From Basic Models to Age-Based Multi-Scale Modeling

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          Abstract

          Viral infectious diseases are a global health concern, as is evident by recent outbreaks of the middle east respiratory syndrome, Ebola virus disease, and re-emerging zika, dengue, and chikungunya fevers. Viral epidemics are a socio-economic burden that causes short- and long-term costs for disease diagnosis and treatment as well as a loss in productivity by absenteeism. These outbreaks and their socio-economic costs underline the necessity for a precise analysis of virus-host interactions, which would help to understand disease mechanisms and to develop therapeutic interventions. The combination of quantitative measurements and dynamic mathematical modeling has increased our understanding of the within-host infection dynamics and has led to important insights into viral pathogenesis, transmission, and disease progression. Furthermore, virus-host models helped to identify drug targets, to predict the treatment duration to achieve cure, and to reduce treatment costs. In this article, we review important achievements made by mathematical modeling of viral kinetics on the extracellular, intracellular, and multi-scale level for Human Immunodeficiency Virus, Hepatitis C Virus, Influenza A Virus, Ebola Virus, Dengue Virus, and Zika Virus. Herein, we focus on basic mathematical models on the population scale (so-called target cell-limited models), detailed models regarding the most important steps in the viral life cycle, and the combination of both. For this purpose, we review how mathematical modeling of viral dynamics helped to understand the virus-host interactions and disease progression or clearance. Additionally, we review different types and effects of therapeutic strategies and how mathematical modeling has been used to predict new treatment regimens.

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          Most cited references108

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          Tremendous progress has been made in understanding the molecular basis of the antiviral actions of interferons (IFNs), as well as strategies evolved by viruses to antagonize the actions of IFNs. Furthermore, advances made while elucidating the IFN system have contributed significantly to our understanding in multiple areas of virology and molecular cell biology, ranging from pathways of signal transduction to the biochemical mechanisms of transcriptional and translational control to the molecular basis of viral pathogenesis. IFNs are approved therapeutics and have moved from the basic research laboratory to the clinic. Among the IFN-induced proteins important in the antiviral actions of IFNs are the RNA-dependent protein kinase (PKR), the 2',5'-oligoadenylate synthetase (OAS) and RNase L, and the Mx protein GTPases. Double-stranded RNA plays a central role in modulating protein phosphorylation and RNA degradation catalyzed by the IFN-inducible PKR kinase and the 2'-5'-oligoadenylate-dependent RNase L, respectively, and also in RNA editing by the IFN-inducible RNA-specific adenosine deaminase (ADAR1). IFN also induces a form of inducible nitric oxide synthase (iNOS2) and the major histocompatibility complex class I and II proteins, all of which play important roles in immune response to infections. Several additional genes whose expression profiles are altered in response to IFN treatment and virus infection have been identified by microarray analyses. The availability of cDNA and genomic clones for many of the components of the IFN system, including IFN-alpha, IFN-beta, and IFN-gamma, their receptors, Jak and Stat and IRF signal transduction components, and proteins such as PKR, 2',5'-OAS, Mx, and ADAR, whose expression is regulated by IFNs, has permitted the generation of mutant proteins, cells that overexpress different forms of the proteins, and animals in which their expression has been disrupted by targeted gene disruption. The use of these IFN system reagents, both in cell culture and in whole animals, continues to provide important contributions to our understanding of the virus-host interaction and cellular antiviral response.
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            Treatment of infected patients with ABT-538, an inhibitor of the protease of human immunodeficiency virus type 1 (HIV-1), causes plasma HIV-1 levels to decrease exponentially (mean half-life, 2.1 +/- 0.4 days) and CD4 lymphocyte counts to rise substantially. Minimum estimates of HIV-1 production and clearance and of CD4 lymphocyte turnover indicate that replication of HIV-1 in vivo is continuous and highly productive, driving the rapid turnover of CD4 lymphocytes.
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              Telaprevir for previously untreated chronic hepatitis C virus infection.

              In phase 2 trials, telaprevir, a hepatitis C virus (HCV) genotype 1 protease inhibitor, in combination with peginterferon-ribavirin, as compared with peginterferon-ribavirin alone, has shown improved efficacy, with potential for shortening the duration of treatment in a majority of patients. In this international, phase 3, randomized, double-blind, placebo-controlled trial, we assigned 1088 patients with HCV genotype 1 infection who had not received previous treatment for the infection to one of three groups: a group receiving telaprevir combined with peginterferon alfa-2a and ribavirin for 12 weeks (T12PR group), followed by peginterferon-ribavirin alone for 12 weeks if HCV RNA was undetectable at weeks 4 and 12 or for 36 weeks if HCV RNA was detectable at either time point; a group receiving telaprevir with peginterferon-ribavirin for 8 weeks and placebo with peginterferon-ribavirin for 4 weeks (T8PR group), followed by 12 or 36 weeks of peginterferon-ribavirin on the basis of the same HCV RNA criteria; or a group receiving placebo with peginterferon-ribavirin for 12 weeks, followed by 36 weeks of peginterferon-ribavirin (PR group). The primary end point was the proportion of patients who had undetectable plasma HCV RNA 24 weeks after the last planned dose of study treatment (sustained virologic response). Significantly more patients in the T12PR or T8PR group than in the PR group had a sustained virologic response (75% and 69%, respectively, vs. 44%; P<0.001 for the comparison of the T12PR or T8PR group with the PR group). A total of 58% of the patients treated with telaprevir were eligible to receive 24 weeks of total treatment. Anemia, gastrointestinal side effects, and skin rashes occurred at a higher incidence among patients receiving telaprevir than among those receiving peginterferon-ribavirin alone. The overall rate of discontinuation of the treatment regimen owing to adverse events was 10% in the T12PR and T8PR groups and 7% in the PR group. Telaprevir with peginterferon-ribavirin, as compared with peginterferon-ribavirin alone, was associated with significantly improved rates of sustained virologic response in patients with HCV genotype 1 infection who had not received previous treatment, with only 24 weeks of therapy administered in the majority of patients. (Funded by Vertex Pharmaceuticals and Tibotec; ADVANCE ClinicalTrials.gov number, NCT00627926.).
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                Author and article information

                Contributors
                Journal
                Front Microbiol
                Front Microbiol
                Front. Microbiol.
                Frontiers in Microbiology
                Frontiers Media S.A.
                1664-302X
                11 July 2018
                2018
                : 9
                : 1546
                Affiliations
                Institute of Bioinformatics and Center for Functional Genomics of Microbes, University Medicine Greifswald , Greifswald, Germany
                Author notes

                Edited by: Thomas Dandekar, Universität Würzburg, Germany

                Reviewed by: Marc Thilo Figge, Leibniz-Institut für Naturstoff-Forschung und Infektionsbiologie, Hans Knöll Institut, Germany; Larance Ronsard, Ragon Institute of MGH, MIT and Harvard, Massachusetts Institute of Technology, United States

                *Correspondence: Carolin Zitzmann carolin.zitzmann@ 123456uni-greifswald.de

                This article was submitted to Infectious Diseases, a section of the journal Frontiers in Microbiology

                Article
                10.3389/fmicb.2018.01546
                6050366
                30050523
                be0c1ee7-d184-4a69-a8c1-fc8f26531312
                Copyright © 2018 Zitzmann and Kaderali.

                This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

                History
                : 08 January 2018
                : 21 June 2018
                Page count
                Figures: 5, Tables: 0, Equations: 0, References: 163, Pages: 18, Words: 15906
                Funding
                Funded by: Bundesministerium für Bildung und Forschung 10.13039/501100002347
                Award ID: 031A602A
                Categories
                Microbiology
                Review

                Microbiology & Virology
                mathematical modeling,viral kinetics,viral replication,human immunodeficiency virus,hepatitis c virus,influenza a virus,antiviral therapy,immune response

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