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Special Issue "Mathematical Modeling of Viral Infections"

A special issue of Viruses (ISSN 1999-4915).

Deadline for manuscript submissions: closed (31 December 2017)

Special Issue Editors

Guest Editor
Prof. John Murray

1. School of Mathematics and Statistics, UNSW Australia, Sydney 2052, Australia
2. Cancer Research Division, Cancer Council NSW, Australia
Website | E-Mail
Interests: mathematical modelling of infectious disease
Guest Editor
Dr. Ruy Ribeiro

Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM, USA
Website | E-Mail
Interests: mathematical modeling of within-host viral infections

Special Issue Information

Dear Colleagues,

Understanding the impact of a viral infection within an individual can be difficult, as the data are often sparse and obtained from sites other than where viruses replicate. Mathematical modelling attempts to piece together the available data, and infer more about the infection than can be directly observed. Within-host viral modelling has provided important information about many infections, including human immunodeficiency virus (HIV), the hepatitis B virus, hepatitis C virus, and influenza.

This Special Issue of Viruses will present articles covering the mathematical modelling of within-host viral dynamics. We encourage submissions describing modelling of all viruses impacting humans.

Prof. John Murray
Dr. Ruy Ribeiro
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Viruses is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • within-host viral modelling
  • viral dynamics
  • mathematical modelling
  • in vivo

Published Papers (9 papers)

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Research

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Open AccessArticle A New Model for the Dynamics of Hepatitis C Infection: Derivation, Analysis and Implications
Viruses 2018, 10(4), 195; doi:10.3390/v10040195
Received: 25 January 2018 / Revised: 29 March 2018 / Accepted: 10 April 2018 / Published: 13 April 2018
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Abstract
We review various existing models of hepatitis C virus (HCV) infection and show that there are inconsistencies between the models and known behaviour of the infection. A new model for HCV infection is proposed, based on various dynamical processes that occur during the
[...] Read more.
We review various existing models of hepatitis C virus (HCV) infection and show that there are inconsistencies between the models and known behaviour of the infection. A new model for HCV infection is proposed, based on various dynamical processes that occur during the infection that are described in the literature. This new model is analysed, and three steady state branches of solutions are found when there is no stem cell generation of hepatocytes. Unusually, the branch of infected solutions that connects the uninfected branch and the pure infection branch can be found analytically and always includes a limit point, subject to a few conditions on the parameters. When the action of stem cells is included, the bifurcation between the pure infection and infected branches unfolds, leaving a single branch of infected solutions. It is shown that this model can generate various viral load profiles that have been described in the literature, which is confirmed by fitting the model to four viral load datasets. Suggestions for possible changes in treatment are made based on the model. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infections)
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Open AccessArticle Time Intervals in Sequence Sampling, Not Data Modifications, Have a Major Impact on Estimates of HIV Escape Rates
Viruses 2018, 10(3), 99; doi:10.3390/v10030099
Received: 9 December 2017 / Revised: 20 February 2018 / Accepted: 22 February 2018 / Published: 27 February 2018
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Abstract
The ability of human immunodeficiency virus (HIV) to avoid recognition by humoral and cellular immunity (viral escape) is well-documented, but the strength of the immune response needed to cause such a viral escape remains poorly quantified. Several previous studies observed a more rapid
[...] Read more.
The ability of human immunodeficiency virus (HIV) to avoid recognition by humoral and cellular immunity (viral escape) is well-documented, but the strength of the immune response needed to cause such a viral escape remains poorly quantified. Several previous studies observed a more rapid escape of HIV from CD8 T cell responses in the acute phase of infection compared to chronic infection. The rate of HIV escape was estimated with the help of simple mathematical models, and results were interpreted to suggest that CD8 T cell responses causing escape in acute HIV infection may be more efficient at killing virus-infected cells than responses that cause escape in chronic infection, or alternatively, that early escapes occur in epitopes mutations in which there is minimal fitness cost to the virus. However, these conclusions were challenged on several grounds, including linkage and interference of multiple escape mutations due to a low population size and because of potential issues associated with modifying the data to estimate escape rates. Here we use a sampling method which does not require data modification to show that previous results on the decline of the viral escape rate with time since infection remain unchanged. However, using this method we also show that estimates of the escape rate are highly sensitive to the time interval between measurements, with longer intervals biasing estimates of the escape rate downwards. Our results thus suggest that data modifications for early and late escapes were not the primary reason for the observed decline in the escape rate with time since infection. However, longer sampling periods for escapes in chronic infection strongly influence estimates of the escape rate. More frequent sampling of viral sequences in chronic infection may improve our understanding of factors influencing the rate of HIV escape from CD8 T cell responses. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infections)
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Open AccessArticle Quantitative Analysis of Hepatitis C NS5A Viral Protein Dynamics on the ER Surface
Viruses 2018, 10(1), 28; doi:10.3390/v10010028
Received: 8 November 2017 / Revised: 2 January 2018 / Accepted: 4 January 2018 / Published: 8 January 2018
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Abstract
Exploring biophysical properties of virus-encoded components and their requirement for virus replication is an exciting new area of interdisciplinary virological research. To date, spatial resolution has only rarely been analyzed in computational/biophysical descriptions of virus replication dynamics. However, it is widely acknowledged that
[...] Read more.
Exploring biophysical properties of virus-encoded components and their requirement for virus replication is an exciting new area of interdisciplinary virological research. To date, spatial resolution has only rarely been analyzed in computational/biophysical descriptions of virus replication dynamics. However, it is widely acknowledged that intracellular spatial dependence is a crucial component of virus life cycles. The hepatitis C virus-encoded NS5A protein is an endoplasmatic reticulum (ER)-anchored viral protein and an essential component of the virus replication machinery. Therefore, we simulate NS5A dynamics on realistic reconstructed, curved ER surfaces by means of surface partial differential equations (sPDE) upon unstructured grids. We match the in silico NS5A diffusion constant such that the NS5A sPDE simulation data reproduce experimental NS5A fluorescence recovery after photobleaching (FRAP) time series data. This parameter estimation yields the NS5A diffusion constant. Such parameters are needed for spatial models of HCV dynamics, which we are developing in parallel but remain qualitative at this stage. Thus, our present study likely provides the first quantitative biophysical description of the movement of a viral component. Our spatio-temporal resolved ansatz paves new ways for understanding intricate spatial-defined processes central to specfic aspects of virus life cycles. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infections)
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Open AccessArticle The Role of Infected Cell Proliferation in the Clearance of Acute HBV Infection in Humans
Viruses 2017, 9(11), 350; doi:10.3390/v9110350
Received: 25 September 2017 / Revised: 14 November 2017 / Accepted: 16 November 2017 / Published: 18 November 2017
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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
[...] Read more.
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. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infections)
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Open AccessArticle RNA Virus Evolution via a Quasispecies-Based Model Reveals a Drug Target with a High Barrier to Resistance
Viruses 2017, 9(11), 347; doi:10.3390/v9110347
Received: 20 October 2017 / Revised: 14 November 2017 / Accepted: 16 November 2017 / Published: 17 November 2017
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Abstract
The rapid occurrence of therapy-resistant mutant strains provides a challenge for anti-viral therapy. An ideal drug target would be a highly conserved molecular feature in the viral life cycle, such as the packaging signals in the genomes of RNA viruses that encode an
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The rapid occurrence of therapy-resistant mutant strains provides a challenge for anti-viral therapy. An ideal drug target would be a highly conserved molecular feature in the viral life cycle, such as the packaging signals in the genomes of RNA viruses that encode an instruction manual for their efficient assembly. The ubiquity of this assembly code in RNA viruses, including major human pathogens, suggests that it confers selective advantages. However, their impact on viral evolution cannot be assessed in current models of viral infection that lack molecular details of virus assembly. We introduce here a quasispecies-based model of a viral infection that incorporates structural and mechanistic knowledge of packaging signal function in assembly to construct a phenotype-fitness map, capturing the impact of this RNA code on assembly yield and efficiency. Details of viral replication and assembly inside an infected host cell are coupled with a population model of a viral infection, allowing the occurrence of therapy resistance to be assessed in response to drugs inhibiting packaging signal recognition. Stochastic simulations of viral quasispecies evolution in chronic HCV infection under drug action and/or immune clearance reveal that drugs targeting all RNA signals in the assembly code collectively have a high barrier to drug resistance, even though each packaging signal in isolation has a lower barrier than conventional drugs. This suggests that drugs targeting the RNA signals in the assembly code could be promising routes for exploitation in anti-viral drug design. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infections)
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Open AccessArticle 3D Spatially Resolved Models of the Intracellular Dynamics of the Hepatitis C Genome Replication Cycle
Viruses 2017, 9(10), 282; doi:10.3390/v9100282
Received: 31 July 2017 / Revised: 21 September 2017 / Accepted: 29 September 2017 / Published: 30 September 2017
Cited by 1 | PDF Full-text (5505 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
Mathematical models of virus dynamics have not previously acknowledged spatial resolution at the intracellular level despite substantial arguments that favor the consideration of intracellular spatial dependence. The replication of the hepatitis C virus (HCV) viral RNA (vRNA) occurs within special replication complexes formed
[...] Read more.
Mathematical models of virus dynamics have not previously acknowledged spatial resolution at the intracellular level despite substantial arguments that favor the consideration of intracellular spatial dependence. The replication of the hepatitis C virus (HCV) viral RNA (vRNA) occurs within special replication complexes formed from membranes derived from endoplasmatic reticulum (ER). These regions, termed membranous webs, are generated primarily through specific interactions between nonstructural virus-encoded proteins (NSPs) and host cellular factors. The NSPs are responsible for the replication of the vRNA and their movement is restricted to the ER surface. Therefore, in this study we developed fully spatio-temporal resolved models of the vRNA replication cycle of HCV. Our simulations are performed upon realistic reconstructed cell structures—namely the ER surface and the membranous webs—based on data derived from immunostained cells replicating HCV vRNA. We visualized 3D simulations that reproduced dynamics resulting from interplay of the different components of our models (vRNA, NSPs, and a host factor), and we present an evaluation of the concentrations for the components within different regions of the cell. Thus far, our model is restricted to an internal portion of a hepatocyte and is qualitative more than quantitative. For a quantitative adaption to complete cells, various additional parameters will have to be determined through further in vitro cell biology experiments, which can be stimulated by the results deccribed in the present study. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infections)
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Open AccessArticle The Mechanisms for Within-Host Influenza Virus Control Affect Model-Based Assessment and Prediction of Antiviral Treatment
Viruses 2017, 9(8), 197; doi:10.3390/v9080197
Received: 30 June 2017 / Revised: 18 July 2017 / Accepted: 24 July 2017 / Published: 26 July 2017
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Abstract
Models of within-host influenza viral dynamics have contributed to an improved understanding of viral dynamics and antiviral effects over the past decade. Existing models can be classified into two broad types based on the mechanism of viral control: models utilising target cell depletion
[...] Read more.
Models of within-host influenza viral dynamics have contributed to an improved understanding of viral dynamics and antiviral effects over the past decade. Existing models can be classified into two broad types based on the mechanism of viral control: models utilising target cell depletion to limit the progress of infection and models which rely on timely activation of innate and adaptive immune responses to control the infection. In this paper, we compare how two exemplar models based on these different mechanisms behave and investigate how the mechanistic difference affects the assessment and prediction of antiviral treatment. We find that the assumed mechanism for viral control strongly influences the predicted outcomes of treatment. Furthermore, we observe that for the target cell-limited model the assumed drug efficacy strongly influences the predicted treatment outcomes. The area under the viral load curve is identified as the most reliable predictor of drug efficacy, and is robust to model selection. Moreover, with support from previous clinical studies, we suggest that the target cell-limited model is more suitable for modelling in vitro assays or infection in some immunocompromised/immunosuppressed patients while the immune response model is preferred for predicting the infection/antiviral effect in immunocompetent animals/patients. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infections)
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Open AccessArticle Understanding the Complex Patterns Observed during Hepatitis B Virus Therapy
Viruses 2017, 9(5), 117; doi:10.3390/v9050117
Received: 17 February 2017 / Revised: 21 April 2017 / Accepted: 2 May 2017 / Published: 19 May 2017
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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.
[...] Read more.
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. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infections)
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Review

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Open AccessReview Fighting Cancer with Mathematics and Viruses
Viruses 2017, 9(9), 239; doi:10.3390/v9090239
Received: 15 July 2017 / Revised: 18 August 2017 / Accepted: 18 August 2017 / Published: 23 August 2017
Cited by 2 | PDF Full-text (3232 KB) | HTML Full-text | XML Full-text
Abstract
After decades of research, oncolytic virotherapy has recently advanced to clinical application, and currently a multitude of novel agents and combination treatments are being evaluated for cancer therapy. Oncolytic agents preferentially replicate in tumor cells, inducing tumor cell lysis and complex antitumor effects,
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After decades of research, oncolytic virotherapy has recently advanced to clinical application, and currently a multitude of novel agents and combination treatments are being evaluated for cancer therapy. Oncolytic agents preferentially replicate in tumor cells, inducing tumor cell lysis and complex antitumor effects, such as innate and adaptive immune responses and the destruction of tumor vasculature. With the availability of different vector platforms and the potential of both genetic engineering and combination regimens to enhance particular aspects of safety and efficacy, the identification of optimal treatments for patient subpopulations or even individual patients becomes a top priority. Mathematical modeling can provide support in this arena by making use of experimental and clinical data to generate hypotheses about the mechanisms underlying complex biology and, ultimately, predict optimal treatment protocols. Increasingly complex models can be applied to account for therapeutically relevant parameters such as components of the immune system. In this review, we describe current developments in oncolytic virotherapy and mathematical modeling to discuss the benefit of integrating different modeling approaches into biological and clinical experimentation. Conclusively, we propose a mutual combination of these research fields to increase the value of the preclinical development and the therapeutic efficacy of the resulting treatments. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infections)
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