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Viruses
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Mathematical Modeling of Viral Infection
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Mathematical Modeling of Viral Infection

A special issue of Viruses (ISSN 1999-4915). This special issue belongs to the section "General Virology".

Deadline for manuscript submissions: closed (16 December 2021) | Viewed by 81453

Special Issue Editors

Dr. Amber M. Smith

E-Mail Website
Guest Editor
Department of Pediatrics, University of Tennessee Health Science Center, Memphis, TN 38163, USA
Interests: respiratory infectious diseases; host–pathogen interaction; multi-pathogen infections; model prediction validation; parameter estimation
Special Issues, Collections and Topics in MDPI journals
Dr. Ruian Ke

E-Mail Website
Guest Editor
Los Alamos National Laboratory, Santa Fe, NM 87545, USA
Interests: multiscale modeling of viral and immune dynamics; treatment strategies for viral infections; HIV; HCV; influenza
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The dynamics of virus infections are complex and multifaceted, and include the mechanisms by which a virus replicates, spreads within a host, interacts with host immune responses and with other pathogens, and the extent to which the virus can be targeted by or employed as therapeutic agent. Mathematical models are essential tools that provide a quantitative understanding of viral infections and their strategies, which are often difficult to dissect through only clinical or experimental approaches. The tight and improved integration of data within modeling frameworks has enhanced the predictive capability of these models and led to new experimental and clinical designs that have led to further elucidations of complex biological interplay. In addition, recent innovations in experimental biology and a new appreciation for multiparameter quantitative datasets have enhanced model quality and provided new questions ripe for mathematical approaches.

In this Special Issue, we will showcase recent advancements in mathematical modeling of virus infections. We welcome submissions reporting any aspect of modeling virus infections.

Dr. Amber M. Smith
Dr. Ruian Ke
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 submissions that pass pre-check are 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 2600 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

  • viral dynamics
  • host-pathogen interaction
  • immune response
  • coinfection
  • oncolytic virotherapy
  • antiviral therapy
  • multiscale modeling
  • spatial modeling

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Published Papers (21 papers)

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Research

17 pages, 8999 KiB  
Article
Mathematical Modeling Finds Disparate Interferon Production Rates Drive Strain-Specific Immunodynamics during Deadly Influenza Infection
by Emily E. Ackerman, Jordan J. A. Weaver and Jason E. Shoemaker
Viruses 2022, 14(5), 906; https://0-doi-org.brum.beds.ac.uk/10.3390/v14050906 - 27 Apr 2022
Cited by 2 | Viewed by 7402
Abstract
The timing and magnitude of the immune response (i.e., the immunodynamics) associated with the early innate immune response to viral infection display distinct trends across influenza A virus subtypes in vivo. Evidence shows that the timing of the type-I interferon response and the [...] Read more.
The timing and magnitude of the immune response (i.e., the immunodynamics) associated with the early innate immune response to viral infection display distinct trends across influenza A virus subtypes in vivo. Evidence shows that the timing of the type-I interferon response and the overall magnitude of immune cell infiltration are both correlated with more severe outcomes. However, the mechanisms driving the distinct immunodynamics between infections of different virus strains (strain-specific immunodynamics) remain unclear. Here, computational modeling and strain-specific immunologic data are used to identify the immune interactions that differ in mice infected with low-pathogenic H1N1 or high-pathogenic H5N1 influenza viruses. Computational exploration of free parameters between strains suggests that the production rate of interferon is the major driver of strain-specific immune responses observed in vivo, and points towards the relationship between the viral load and lung epithelial interferon production as the main source of variance between infection outcomes. A greater understanding of the contributors to strain-specific immunodynamics can be utilized in future efforts aimed at treatment development to improve clinical outcomes of high-pathogenic viral strains. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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81 pages, 116538 KiB  
Article
Multiscale Model of Antiviral Timing, Potency, and Heterogeneity Effects on an Epithelial Tissue Patch Infected by SARS-CoV-2
by Juliano Ferrari Gianlupi, Tarunendu Mapder, T. J. Sego, James P. Sluka, Sara K. Quinney, Morgan Craig, Robert E. Stratford, Jr. and James A. Glazier
Viruses 2022, 14(3), 605; https://0-doi-org.brum.beds.ac.uk/10.3390/v14030605 - 14 Mar 2022
Cited by 6 | Viewed by 4640
Abstract
We extend our established agent-based multiscale computational model of infection of lung tissue by SARS-CoV-2 to include pharmacokinetic and pharmacodynamic models of remdesivir. We model remdesivir treatment for COVID-19; however, our methods are general to other viral infections and antiviral therapies. We investigate [...] Read more.
We extend our established agent-based multiscale computational model of infection of lung tissue by SARS-CoV-2 to include pharmacokinetic and pharmacodynamic models of remdesivir. We model remdesivir treatment for COVID-19; however, our methods are general to other viral infections and antiviral therapies. We investigate the effects of drug potency, drug dosing frequency, treatment initiation delay, antiviral half-life, and variability in cellular uptake and metabolism of remdesivir and its active metabolite on treatment outcomes in a simulated patch of infected epithelial tissue. Non-spatial deterministic population models which treat all cells of a given class as identical can clarify how treatment dosage and timing influence treatment efficacy. However, they do not reveal how cell-to-cell variability affects treatment outcomes. Our simulations suggest that for a given treatment regime, including cell-to-cell variation in drug uptake, permeability and metabolism increase the likelihood of uncontrolled infection as the cells with the lowest internal levels of antiviral act as super-spreaders within the tissue. The model predicts substantial variability in infection outcomes between similar tissue patches for different treatment options. In models with cellular metabolic variability, antiviral doses have to be increased significantly (>50% depending on simulation parameters) to achieve the same treatment results as with the homogeneous cellular metabolism. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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22 pages, 6451 KiB  
Article
Modeling the Transmission of the SARS-CoV-2 Delta Variant in a Partially Vaccinated Population
by Ugo Avila-Ponce de León, Eric Avila-Vales and Kuan-lin Huang
Viruses 2022, 14(1), 158; https://0-doi-org.brum.beds.ac.uk/10.3390/v14010158 - 16 Jan 2022
Cited by 7 | Viewed by 2928
Abstract
In a population with ongoing vaccination, the trajectory of a pandemic is determined by how the virus spreads in unvaccinated and vaccinated individuals that exhibit distinct transmission dynamics based on different levels of natural and vaccine-induced immunity. We developed a mathematical model that [...] Read more.
In a population with ongoing vaccination, the trajectory of a pandemic is determined by how the virus spreads in unvaccinated and vaccinated individuals that exhibit distinct transmission dynamics based on different levels of natural and vaccine-induced immunity. We developed a mathematical model that considers both subpopulations and immunity parameters, including vaccination rates, vaccine effectiveness, and a gradual loss of protection. The model forecasted the spread of the SARS-CoV-2 delta variant in the US under varied transmission and vaccination rates. We further obtained the control reproduction number and conducted sensitivity analyses to determine how each parameter may affect virus transmission. Although our model has several limitations, the number of infected individuals was shown to be a magnitude greater (~10×) in the unvaccinated subpopulation compared to the vaccinated subpopulation. Our results show that a combination of strengthening vaccine-induced immunity and preventative behavioral measures like face mask-wearing and contact tracing will likely be required to deaccelerate the spread of infectious SARS-CoV-2 variants. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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17 pages, 752 KiB  
Article
Modeling the Influence of Vaccine Administration on COVID-19 Testing Strategies
by Jonathan E. Forde and Stanca M. Ciupe
Viruses 2021, 13(12), 2546; https://0-doi-org.brum.beds.ac.uk/10.3390/v13122546 - 19 Dec 2021
Cited by 5 | Viewed by 2976
Abstract
Vaccination is considered the best strategy for limiting and eliminating the COVID-19 pandemic. The success of this strategy relies on the rate of vaccine deployment and acceptance across the globe. As these efforts are being conducted, the severe acute respiratory syndrome coronavirus 2 [...] Read more.
Vaccination is considered the best strategy for limiting and eliminating the COVID-19 pandemic. The success of this strategy relies on the rate of vaccine deployment and acceptance across the globe. As these efforts are being conducted, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is continuously mutating, which leads to the emergence of variants with increased transmissibility, virulence, and resistance to vaccines. One important question is whether surveillance testing is still needed in order to limit SARS-CoV-2 transmission in a vaccinated population. In this study, we developed a multi-scale mathematical model of SARS-CoV-2 transmission in a vaccinated population and used it to predict the role of testing in an outbreak with variants of increased transmissibility. We found that, for low transmissibility variants, testing was most effective when vaccination levels were low to moderate and its impact was diminished when vaccination levels were high. For high transmissibility variants, widespread vaccination was necessary in order for testing to have a significant impact on preventing outbreaks, with the impact of testing having maximum effects when focused on the non-vaccinated population. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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15 pages, 693 KiB  
Article
Modelling Mutation in Equine Infectious Anemia Virus Infection Suggests a Path to Viral Clearance with Repeated Vaccination
by Elissa J. Schwartz, Christian Costris-Vas and Stacey R. Smith?
Viruses 2021, 13(12), 2450; https://0-doi-org.brum.beds.ac.uk/10.3390/v13122450 - 06 Dec 2021
Cited by 1 | Viewed by 2706
Abstract
Equine infectious anemia virus (EIAV) is a lentivirus similar to HIV that infects horses. Clinical and experimental studies demonstrating immune control of EIAV infection hold promise for efforts to produce an HIV vaccine. Antibody infusions have been shown to block both wild-type and [...] Read more.
Equine infectious anemia virus (EIAV) is a lentivirus similar to HIV that infects horses. Clinical and experimental studies demonstrating immune control of EIAV infection hold promise for efforts to produce an HIV vaccine. Antibody infusions have been shown to block both wild-type and mutant virus infection, but the mutant sometimes escapes. Using these data, we develop a mathematical model that describes the interactions between antibodies and both wild-type and mutant virus populations, in the context of continual virus mutation. The aim of this work is to determine whether repeated vaccinations through antibody infusions can reduce both the wild-type and mutant strains of the virus below one viral particle, and if so, to examine the vaccination period and number of infusions that ensure eradication. The antibody infusions are modelled using impulsive differential equations, a technique that offers insight into repeated vaccination by approximating the time-to-peak by an instantaneous change. We use impulsive theory to determine the maximal vaccination intervals that would be required to reduce the wild-type and mutant virus levels below one particle per horse. We show that seven boosts of the antibody vaccine are sufficient to eradicate both the wild-type and the mutant strains. In the case of a mutant virus infection that is given infusions of antibodies targeting wild-type virus (i.e., simulation of a heterologous infection), seven infusions were likewise sufficient to eradicate infection, based upon the data set. However, if the period between infusions was sufficiently increased, both the wild-type and mutant virus would eventually persist in the form of a periodic orbit. These results suggest a route forward to design antibody-based vaccine strategies to control viruses subject to mutant escape. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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23 pages, 1856 KiB  
Article
Quantification of Type I Interferon Inhibition by Viral Proteins: Ebola Virus as a Case Study
by Macauley Locke, Grant Lythe, Martín López-García, César Muñoz-Fontela, Miles Carroll and Carmen Molina-París
Viruses 2021, 13(12), 2441; https://0-doi-org.brum.beds.ac.uk/10.3390/v13122441 - 04 Dec 2021
Cited by 1 | Viewed by 2572
Abstract
Type I interferons (IFNs) are cytokines with both antiviral properties and protective roles in innate immune responses to viral infection. They induce an antiviral cellular state and link innate and adaptive immune responses. Yet, viruses have evolved different strategies to inhibit such host [...] Read more.
Type I interferons (IFNs) are cytokines with both antiviral properties and protective roles in innate immune responses to viral infection. They induce an antiviral cellular state and link innate and adaptive immune responses. Yet, viruses have evolved different strategies to inhibit such host responses. One of them is the existence of viral proteins which subvert type I IFN responses to allow quick and successful viral replication, thus, sustaining the infection within a host. We propose mathematical models to characterise the intra-cellular mechanisms involved in viral protein antagonism of type I IFN responses, and compare three different molecular inhibition strategies. We study the Ebola viral protein, VP35, with this mathematical approach. Approximate Bayesian computation sequential Monte Carlo, together with experimental data and the mathematical models proposed, are used to perform model calibration, as well as model selection of the different hypotheses considered. Finally, we assess if model parameters are identifiable and discuss how such identifiability can be improved with new experimental data. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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30 pages, 9123 KiB  
Article
Mathematical Modeling of Within-Host, Untreated, Cytomegalovirus Infection Dynamics after Allogeneic Transplantation
by Elizabeth R. Duke, Florencia A. T. Boshier, Michael Boeckh, Joshua T. Schiffer and E. Fabian Cardozo-Ojeda
Viruses 2021, 13(11), 2292; https://0-doi-org.brum.beds.ac.uk/10.3390/v13112292 - 16 Nov 2021
Cited by 4 | Viewed by 2786
Abstract
Cytomegalovirus (CMV) causes significant morbidity and mortality in recipients of allogeneic hematopoietic cell transplantation (HCT). Whereas insights gained from mathematical modeling of other chronic viral infections such as HIV, hepatitis C, and herpes simplex virus-2 have aided in optimizing therapy, previous CMV modeling [...] Read more.
Cytomegalovirus (CMV) causes significant morbidity and mortality in recipients of allogeneic hematopoietic cell transplantation (HCT). Whereas insights gained from mathematical modeling of other chronic viral infections such as HIV, hepatitis C, and herpes simplex virus-2 have aided in optimizing therapy, previous CMV modeling has been hindered by a lack of comprehensive quantitative PCR viral load data from untreated episodes of viremia in HCT recipients. We performed quantitative CMV DNA PCR on stored, frozen serum samples from the placebo group of participants in a historic randomized controlled trial of ganciclovir for the early treatment of CMV infection in bone marrow transplant recipients. We developed four main ordinary differential Equation mathematical models and used model selection theory to choose between 38 competing versions of these models. Models were fit using a population, nonlinear, mixed-effects approach. We found that CMV kinetics from untreated HCT recipients are highly variable. The models that recapitulated the observed patterns most parsimoniously included explicit, dynamic immune cell compartments and did not include dynamic target cell compartments, consistent with the large number of tissue and cell types that CMV infects. In addition, in our best-fitting models, viral clearance was extremely slow, suggesting severe impairment of the immune response after HCT. Parameters from our best model correlated well with participants’ clinical risk factors and outcomes from the trial, further validating our model. Our models suggest that CMV dynamics in HCT recipients are determined by host immune response rather than target cell limitation in the absence of antiviral treatment. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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19 pages, 2299 KiB  
Article
Mathematical Modeling of Vaccines That Prevent SARS-CoV-2 Transmission
by David A. Swan, Ashish Goyal, Chloe Bracis, Mia Moore, Elizabeth Krantz, Elizabeth Brown, Fabian Cardozo-Ojeda, Daniel B. Reeves, Fei Gao, Peter B. Gilbert, Lawrence Corey, Myron S. Cohen, Holly Janes, Dobromir Dimitrov and Joshua T. Schiffer
Viruses 2021, 13(10), 1921; https://0-doi-org.brum.beds.ac.uk/10.3390/v13101921 - 24 Sep 2021
Cited by 8 | Viewed by 3420
Abstract
SARS-CoV-2 vaccine clinical trials assess efficacy against disease (VEDIS), the ability to block symptomatic COVID-19. They only partially discriminate whether VEDIS is mediated by preventing infection completely, which is defined as detection of virus in the airways (VESUSC), [...] Read more.
SARS-CoV-2 vaccine clinical trials assess efficacy against disease (VEDIS), the ability to block symptomatic COVID-19. They only partially discriminate whether VEDIS is mediated by preventing infection completely, which is defined as detection of virus in the airways (VESUSC), or by preventing symptoms despite infection (VESYMP). Vaccine efficacy against transmissibility given infection (VEINF), the decrease in secondary transmissions from infected vaccine recipients, is also not measured. Using mathematical modeling of data from King County Washington, we demonstrate that if the Moderna (mRNA-1273QS) and Pfizer-BioNTech (BNT162b2) vaccines, which demonstrated VEDIS > 90% in clinical trials, mediate VEDIS by VESUSC, then a limited fourth epidemic wave of infections with the highly infectious B.1.1.7 variant would have been predicted in spring 2021 assuming rapid vaccine roll out. If high VEDIS is explained by VESYMP, then high VEINF would have also been necessary to limit the extent of this fourth wave. Vaccines which completely protect against infection or secondary transmission also substantially lower the number of people who must be vaccinated before the herd immunity threshold is reached. The limited extent of the fourth wave suggests that the vaccines have either high VESUSC or both high VESYMP and high VEINF against B.1.1.7. Finally, using a separate intra-host mathematical model of viral kinetics, we demonstrate that a 0.6 log vaccine-mediated reduction in average peak viral load might be sufficient to achieve 50% VEINF, which suggests that human challenge studies with a relatively low number of infected participants could be employed to estimate all three vaccine efficacy metrics. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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19 pages, 2994 KiB  
Article
Personalized Virus Load Curves for Acute Viral Infections
by Carlos Contreras, Jay M. Newby and Thomas Hillen
Viruses 2021, 13(9), 1815; https://0-doi-org.brum.beds.ac.uk/10.3390/v13091815 - 13 Sep 2021
Cited by 6 | Viewed by 2472
Abstract
We introduce an explicit function that describes virus-load curves on a patient-specific level. This function is based on simple and intuitive model parameters. It allows virus load analysis of acute viral infections without solving a full virus load dynamic model. We validate our [...] Read more.
We introduce an explicit function that describes virus-load curves on a patient-specific level. This function is based on simple and intuitive model parameters. It allows virus load analysis of acute viral infections without solving a full virus load dynamic model. We validate our model on data from mice influenza A, human rhinovirus data, human influenza A data, and monkey and human SARS-CoV-2 data. We find wide distributions for the model parameters, reflecting large variability in the disease outcomes between individuals. Further, we compare the virus load function to an established target model of virus dynamics, and we provide a new way to estimate the exponential growth rates of the corresponding infection phases. The virus load function, the target model, and the exponential approximations show excellent fits for the data considered. Our virus-load function offers a new way to analyze patient-specific virus load data, and it can be used as input for higher level models for the physiological effects of a virus infection, for models of tissue damage, and to estimate patient risks. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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18 pages, 633 KiB  
Article
Intracellular Life Cycle Kinetics of SARS-CoV-2 Predicted Using Mathematical Modelling
by Dmitry Grebennikov, Ekaterina Kholodareva, Igor Sazonov, Antonina Karsonova, Andreas Meyerhans and Gennady Bocharov
Viruses 2021, 13(9), 1735; https://0-doi-org.brum.beds.ac.uk/10.3390/v13091735 - 31 Aug 2021
Cited by 13 | Viewed by 5945
Abstract
SARS-CoV-2 infection represents a global threat to human health. Various approaches were employed to reveal the pathogenetic mechanisms of COVID-19. Mathematical and computational modelling is a powerful tool to describe and analyze the infection dynamics in relation to a plethora of processes contributing [...] Read more.
SARS-CoV-2 infection represents a global threat to human health. Various approaches were employed to reveal the pathogenetic mechanisms of COVID-19. Mathematical and computational modelling is a powerful tool to describe and analyze the infection dynamics in relation to a plethora of processes contributing to the observed disease phenotypes. In our study here, we formulate and calibrate a deterministic model of the SARS-CoV-2 life cycle. It provides a kinetic description of the major replication stages of SARS-CoV-2. Sensitivity analysis of the net viral progeny with respect to model parameters enables the identification of the life cycle stages that have the strongest impact on viral replication. These three most influential parameters are (i) degradation rate of positive sense vRNAs in cytoplasm (negative effect), (ii) threshold number of non-structural proteins enhancing vRNA transcription (negative effect), and (iii) translation rate of non-structural proteins (positive effect). The results of our analysis could be used for guiding the search for antiviral drug targets to combat SARS-CoV-2 infection. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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18 pages, 4629 KiB  
Article
Modeling Within-Host Dynamics of SARS-CoV-2 Infection: A Case Study in Ferrets
by Naveen K. Vaidya, Angelica Bloomquist and Alan S. Perelson
Viruses 2021, 13(8), 1635; https://0-doi-org.brum.beds.ac.uk/10.3390/v13081635 - 18 Aug 2021
Cited by 18 | Viewed by 3603
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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25 pages, 4944 KiB  
Article
Comparative Computational Modeling of the Bat and Human Immune Response to Viral Infection with the Comparative Biology Immune Agent Based Model
by Chase Cockrell and Gary An
Viruses 2021, 13(8), 1620; https://0-doi-org.brum.beds.ac.uk/10.3390/v13081620 - 16 Aug 2021
Cited by 8 | Viewed by 2847
Abstract
Given the impact of pandemics due to viruses of bat origin, there is increasing interest in comparative investigation into the differences between bat and human immune responses. The practice of comparative biology can be enhanced by computational methods used for dynamic knowledge representation [...] Read more.
Given the impact of pandemics due to viruses of bat origin, there is increasing interest in comparative investigation into the differences between bat and human immune responses. The practice of comparative biology can be enhanced by computational methods used for dynamic knowledge representation to visualize and interrogate the putative differences between the two systems. We present an agent based model that encompasses and bridges differences between bat and human responses to viral infection: the comparative biology immune agent based model, or CBIABM. The CBIABM examines differences in innate immune mechanisms between bats and humans, specifically regarding inflammasome activity and type 1 interferon dynamics, in terms of tolerance to viral infection. Simulation experiments with the CBIABM demonstrate the efficacy of bat-related features in conferring viral tolerance and also suggest a crucial role for endothelial inflammasome activity as a mechanism for bat systemic viral tolerance and affecting the severity of disease in human viral infections. We hope that this initial study will inspire additional comparative modeling projects to link, compare, and contrast immunological functions shared across different species, and in so doing, provide insight and aid in preparation for future viral pandemics of zoonotic origin. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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16 pages, 1462 KiB  
Article
Mathematical Modelling of the Molecular Mechanisms of Interaction of Tenofovir with Emtricitabine against HIV
by Sara Iannuzzi and Max von Kleist
Viruses 2021, 13(7), 1354; https://0-doi-org.brum.beds.ac.uk/10.3390/v13071354 - 13 Jul 2021
Cited by 3 | Viewed by 2575
Abstract
The combination of the two nucleoside reverse transcriptase inhibitors (NRTI) tenofovir disoproxil fumarate (TDF) and emtricitabine (FTC) is used in most highly active antiretroviral therapies for treatment of HIV-1 infection, as well as in pre-exposure prophylaxis against HIV acquisition. Administered as prodrugs, these [...] Read more.
The combination of the two nucleoside reverse transcriptase inhibitors (NRTI) tenofovir disoproxil fumarate (TDF) and emtricitabine (FTC) is used in most highly active antiretroviral therapies for treatment of HIV-1 infection, as well as in pre-exposure prophylaxis against HIV acquisition. Administered as prodrugs, these drugs are taken up by HIV-infected target cells, undergo intracellular phosphorylation and compete with natural deoxynucleoside triphosphates (dNTP) for incorporation into nascent viral DNA during reverse transcription. Once incorporated, they halt reverse transcription. In vitro studies have proposed that TDF and FTC act synergistically within an HIV-infected cell. However, it is unclear whether, and which, direct drug–drug interactions mediate the apparent synergy. The goal of this work was to refine a mechanistic model for the molecular mechanism of action (MMOA) of nucleoside analogues in order to analyse whether putative direct interactions may account for the in vitro observed synergistic effects. Our analysis suggests that depletion of dNTP pools can explain apparent synergy between TDF and FTC in HIV-infected cells at clinically relevant concentrations. Dead-end complex (DEC) formation does not seem to significantly contribute to the synergistic effect. However, in the presence of non-nucleoside reverse transcriptase inhibitors (NNRTIs), its role might be more relevant, as previously reported in experimental in vitro studies. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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16 pages, 1565 KiB  
Article
Fitness Estimation for Viral Variants in the Context of Cellular Coinfection
by Huisheng Zhu, Brent E. Allman and Katia Koelle
Viruses 2021, 13(7), 1216; https://0-doi-org.brum.beds.ac.uk/10.3390/v13071216 - 23 Jun 2021
Viewed by 2247
Abstract
Animal models are frequently used to characterize the within-host dynamics of emerging zoonotic viruses. More recent studies have also deep-sequenced longitudinal viral samples originating from experimental challenges to gain a better understanding of how these viruses may evolve in vivo and between transmission [...] Read more.
Animal models are frequently used to characterize the within-host dynamics of emerging zoonotic viruses. More recent studies have also deep-sequenced longitudinal viral samples originating from experimental challenges to gain a better understanding of how these viruses may evolve in vivo and between transmission events. These studies have often identified nucleotide variants that can replicate more efficiently within hosts and also transmit more effectively between hosts. Quantifying the degree to which a mutation impacts viral fitness within a host can improve identification of variants that are of particular epidemiological concern and our ability to anticipate viral adaptation at the population level. While methods have been developed to quantify the fitness effects of mutations using observed changes in allele frequencies over the course of a host’s infection, none of the existing methods account for the possibility of cellular coinfection. Here, we develop mathematical models to project variant allele frequency changes in the context of cellular coinfection and, further, integrate these models with statistical inference approaches to demonstrate how variant fitness can be estimated alongside cellular multiplicity of infection. We apply our approaches to empirical longitudinally sampled H5N1 sequence data from ferrets. Our results indicate that previous studies may have significantly underestimated the within-host fitness advantage of viral variants. These findings underscore the importance of considering the process of cellular coinfection when studying within-host viral evolutionary dynamics. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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14 pages, 5411 KiB  
Article
Structural Analysis of the Novel Variants of SARS-CoV-2 and Forecasting in North America
by Elena Quinonez, Majid Vahed, Abdolrazagh Hashemi Shahraki and Mehdi Mirsaeidi
Viruses 2021, 13(5), 930; https://0-doi-org.brum.beds.ac.uk/10.3390/v13050930 - 17 May 2021
Cited by 13 | Viewed by 4441
Abstract
Background: little is known about the forecasting of new variants of SARS-COV-2 in North America and the interaction of variants with vaccine-derived neutralizing antibodies. Methods: the affinity scores of the spike receptor-binding domain (S-RBD) of B.1.1.7, B. 1.351, B.1.617, and P.1 variants in [...] Read more.
Background: little is known about the forecasting of new variants of SARS-COV-2 in North America and the interaction of variants with vaccine-derived neutralizing antibodies. Methods: the affinity scores of the spike receptor-binding domain (S-RBD) of B.1.1.7, B. 1.351, B.1.617, and P.1 variants in interaction with the neutralizing antibody (CV30 isolated from a patient), and human angiotensin-converting enzyme 2 (hACE2) receptor were predicted using the template-based computational modeling. From the Nextstrain global database, we identified prevalent mutations of S-RBD of SARS-CoV-2 from December 2019 to April 2021. Pre- and post-vaccination time series forecasting models were developed based on the prediction of neutralizing antibody affinity scores for S-RBD of the variants. Results: the proportion of the B.1.1.7 variant in North America is growing rapidly, but the rate will reduce due to high affinity (~90%) to the neutralizing antibody once herd immunity is reached. Currently, the rates of isolation of B. 1.351, B.1.617, and P.1 variants are slowly increasing in North America. Herd immunity is able to relatively control these variants due to their low affinity (~70%) to the neutralizing antibody. The S-RBD of B.1.617 has a 110% increased affinity score to the human angiotensin-converting enzyme 2 (hACE2) in comparison to the wild-type structure, making it highly infectious. Conclusion: The newly emerged B.1.351, B.1.617, and P.1 variants escape from vaccine-induced neutralizing immunity and continue circulating in North America in post- herd immunity era. Our study strongly suggests that a third dose of vaccine is urgently needed to cover novel variants with affinity scores (equal or less than 70%) to eliminate developing viral mutations and reduce transmission rates. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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23 pages, 2308 KiB  
Article
Will SARS-CoV-2 Become Just Another Seasonal Coronavirus?
by Alexander B. Beams, Rebecca Bateman and Frederick R. Adler
Viruses 2021, 13(5), 854; https://0-doi-org.brum.beds.ac.uk/10.3390/v13050854 - 07 May 2021
Cited by 9 | Viewed by 9697
Abstract
The future prevalence and virulence of SARS-CoV-2 is uncertain. Some emerging pathogens become avirulent as populations approach herd immunity. Although not all viruses follow this path, the fact that the seasonal coronaviruses are benign gives some hope. We develop a general mathematical model [...] Read more.
The future prevalence and virulence of SARS-CoV-2 is uncertain. Some emerging pathogens become avirulent as populations approach herd immunity. Although not all viruses follow this path, the fact that the seasonal coronaviruses are benign gives some hope. We develop a general mathematical model to predict when the interplay among three factors, correlation of severity in consecutive infections, population heterogeneity in susceptibility due to age, and reduced severity due to partial immunity, will promote avirulence as SARS-CoV-2 becomes endemic. Each of these components has the potential to limit severe, high-shedding cases over time under the right circumstances, but in combination they can rapidly reduce the frequency of more severe and infectious manifestation of disease over a wide range of conditions. As more reinfections are captured in data over the next several years, these models will help to test if COVID-19 severity is beginning to attenuate in the ways our model predicts, and to predict the disease. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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14 pages, 475 KiB  
Article
Modelling the Effect of MUC1 on Influenza Virus Infection Kinetics and Macrophage Dynamics
by Ke Li, Pengxing Cao and James M. McCaw
Viruses 2021, 13(5), 850; https://0-doi-org.brum.beds.ac.uk/10.3390/v13050850 - 07 May 2021
Cited by 4 | Viewed by 2464
Abstract
MUC1 belongs to the family of cell surface (cs-) mucins. Experimental evidence indicates that its presence reduces in vivo influenza viral infection severity. However, the mechanisms by which MUC1 influences viral dynamics and the host immune response are not yet well understood, limiting [...] Read more.
MUC1 belongs to the family of cell surface (cs-) mucins. Experimental evidence indicates that its presence reduces in vivo influenza viral infection severity. However, the mechanisms by which MUC1 influences viral dynamics and the host immune response are not yet well understood, limiting our ability to predict the efficacy of potential treatments that target MUC1. To address this limitation, we use available in vivo kinetic data for both virus and macrophage populations in wildtype and MUC1 knockout mice. We apply two mathematical models of within-host influenza dynamics to this data. The models differ in how they categorise the mechanisms of viral control. Both models provide evidence that MUC1 reduces the susceptibility of epithelial cells to influenza virus and regulates macrophage recruitment. Furthermore, we predict and compare some key infection-related quantities between the two mice groups. We find that MUC1 significantly reduces the basic reproduction number of viral replication as well as the number of cumulative macrophages but has little impact on the cumulative viral load. Our analyses suggest that the viral replication rate in the early stages of infection influences the kinetics of the host immune response, with consequences for infection outcomes, such as severity. We also show that MUC1 plays a strong anti-inflammatory role in the regulation of the host immune response. This study improves our understanding of the dynamic role of MUC1 against influenza infection and may support the development of novel antiviral treatments and immunomodulators that target MUC1. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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15 pages, 1702 KiB  
Article
Endogenously Produced SARS-CoV-2 Specific IgG Antibodies May Have a Limited Impact on Clearing Nasal Shedding of Virus during Primary Infection in Humans
by Shuyi Yang, Keith R. Jerome, Alexander L. Greninger, Joshua T. Schiffer and Ashish Goyal
Viruses 2021, 13(3), 516; https://0-doi-org.brum.beds.ac.uk/10.3390/v13030516 - 20 Mar 2021
Cited by 4 | Viewed by 3248
Abstract
While SARS-CoV-2 specific neutralizing antibodies have been developed for therapeutic purposes, the specific viral triggers that drive the generation of SARS-CoV-2 specific IgG and IgM antibodies remain only partially characterized. Moreover, it is unknown whether endogenously derived antibodies drive viral clearance that might [...] Read more.
While SARS-CoV-2 specific neutralizing antibodies have been developed for therapeutic purposes, the specific viral triggers that drive the generation of SARS-CoV-2 specific IgG and IgM antibodies remain only partially characterized. Moreover, it is unknown whether endogenously derived antibodies drive viral clearance that might result in mitigation of clinical severity during natural infection. We developed a series of non-linear mathematical models to investigate whether SARS-CoV-2 viral and antibody kinetics are coupled or governed by separate processes. Patients with severe disease had a higher production rate of IgG but not IgM antibodies. Maximal levels of both isotypes were governed by their production rate rather than different saturation levels between people. Our results suggest that an exponential surge in IgG levels occurs approximately 5–10 days after symptom onset with no requirement for continual antigenic stimulation. SARS-CoV-2 specific IgG antibodies appear to have limited to no effect on viral dynamics but may enhance viral clearance late during primary infection resulting from the binding effect of antibody to virus, rather than neutralization. In conclusion, SARS-CoV-2 specific IgG antibodies may play only a limited role in clearing infection from the nasal passages despite providing long-term immunity against infection following vaccination or prior infection. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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18 pages, 1179 KiB  
Article
Quantification of the Tradeoff between Test Sensitivity and Test Frequency in a COVID-19 Epidemic—A Multi-Scale Modeling Approach
by Jonathan E. Forde and Stanca M. Ciupe
Viruses 2021, 13(3), 457; https://0-doi-org.brum.beds.ac.uk/10.3390/v13030457 - 11 Mar 2021
Cited by 15 | Viewed by 3235
Abstract
Control strategies that employ real time polymerase chain reaction (RT-PCR) tests for the diagnosis and surveillance of COVID-19 epidemic are inefficient in fighting the epidemic due to high cost, delays in obtaining results, and the need of specialized personnel and equipment for laboratory [...] Read more.
Control strategies that employ real time polymerase chain reaction (RT-PCR) tests for the diagnosis and surveillance of COVID-19 epidemic are inefficient in fighting the epidemic due to high cost, delays in obtaining results, and the need of specialized personnel and equipment for laboratory processing. Cheaper and faster alternatives, such as antigen and paper-strip tests, have been proposed. They return results rapidly, but have lower sensitivity thresholds for detecting virus. To quantify the effects of the tradeoffs between sensitivity, cost, testing frequency, and delay in test return on the overall course of an outbreak, we built a multi-scale immuno-epidemiological model that connects the virus profile of infected individuals with transmission and testing at the population level. We investigated various randomized testing strategies and found that, for fixed testing capacity, lower sensitivity tests with shorter return delays slightly flatten the daily incidence curve and delay the time to the peak daily incidence. However, compared with RT-PCR testing, they do not always reduce the cumulative case count at half a year into the outbreak. When testing frequency is increased to account for the lower cost of less sensitive tests, we observe a large reduction in cumulative case counts, from 55.4% to as low as 1.22% half a year into the outbreak. The improvement is preserved even when the testing budget is reduced by one half or one third. Our results predict that surveillance testing that employs low-sensitivity tests at high frequency is an effective tool for epidemic control. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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20 pages, 1998 KiB  
Article
Modeling the Molecular Impact of SARS-CoV-2 Infection on the Renin-Angiotensin System
by Fabrizio Pucci, Philippe Bogaerts and Marianne Rooman
Viruses 2020, 12(12), 1367; https://0-doi-org.brum.beds.ac.uk/10.3390/v12121367 - 30 Nov 2020
Cited by 12 | Viewed by 2948
Abstract
SARS-CoV-2 infection is mediated by the binding of its spike protein to the angiotensin-converting enzyme 2 (ACE2), which plays a pivotal role in the renin-angiotensin system (RAS). The study of RAS dysregulation due to SARS-CoV-2 infection is fundamentally important for a better understanding [...] Read more.
SARS-CoV-2 infection is mediated by the binding of its spike protein to the angiotensin-converting enzyme 2 (ACE2), which plays a pivotal role in the renin-angiotensin system (RAS). The study of RAS dysregulation due to SARS-CoV-2 infection is fundamentally important for a better understanding of the pathogenic mechanisms and risk factors associated with COVID-19 coronavirus disease and to design effective therapeutic strategies. In this context, we developed a mathematical model of RAS based on data regarding protein and peptide concentrations; the model was tested on clinical data from healthy normotensive and hypertensive individuals. We used our model to analyze the impact of SARS-CoV-2 infection on RAS, which we modeled through a downregulation of ACE2 as a function of viral load. We also used it to predict the effect of RAS-targeting drugs, such as RAS-blockers, human recombinant ACE2, and angiotensin 1–7 peptide, on COVID-19 patients; the model predicted an improvement of the clinical outcome for some drugs and a worsening for others. Our model and its predictions constitute a valuable framework for in silico testing of hypotheses about the COVID-19 pathogenic mechanisms and the effect of drugs aiming to restore RAS functionality. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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20 pages, 4903 KiB  
Article
Convolutional Neural Network Based Approach to In Silico Non-Anticipating Prediction of Antigenic Distance for Influenza Virus
by Majid Forghani and Michael Khachay
Viruses 2020, 12(9), 1019; https://0-doi-org.brum.beds.ac.uk/10.3390/v12091019 - 12 Sep 2020
Cited by 10 | Viewed by 3619
Abstract
Evaluation of the antigenic similarity degree between the strains of the influenza virus is highly important for vaccine production. The conventional method used to measure such a degree is related to performing the immunological assays of hemagglutinin inhibition. Namely, the antigenic distance between [...] Read more.
Evaluation of the antigenic similarity degree between the strains of the influenza virus is highly important for vaccine production. The conventional method used to measure such a degree is related to performing the immunological assays of hemagglutinin inhibition. Namely, the antigenic distance between two strains is calculated on the basis of HI assays. Usually, such distances are visualized by using some kind of antigenic cartography method. The known drawback of the HI assay is that it is rather time-consuming and expensive. In this paper, we propose a novel approach for antigenic distance approximation based on deep learning in the feature spaces induced by hemagglutinin protein sequences and Convolutional Neural Networks (CNNs). To apply a CNN to compare the protein sequences, we utilize the encoding based on the physical and chemical characteristics of amino acids. By varying (hyper)parameters of the CNN architecture design, we find the most robust network. Further, we provide insight into the relationship between approximated antigenic distance and antigenicity by evaluating the network on the HI assay database for the H1N1 subtype. The results indicate that the best-trained network gives a high-precision approximation for the ground-truth antigenic distances, and can be used as a good exploratory tool in practical tasks. Full article
(This article belongs to the Special Issue Mathematical Modeling of Viral Infection)
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