Special Issue Information

Dear Colleagues,

The current COVID-19 pandemic has made it clear that mathematical modeling in conjunction with computational techniques and statistical analysis plays an important role in the qualitative and quantitative understanding of epidemics. Because of the current pandemic, there has been a great and rapid advance in scientific knowledge for these types of epidemic emergencies. Population scale models have provided valuable information for public health authorities at local and national levels, allowing them to assess the effect of different non-pharmaceutical interventions. Moreover, models have been used to analyze the effects of vaccination programs and the appearance of new SARS-CoV-2 variants. At the within-host level, models of viral dynamics have helped to assess the possibility of re-purposing antivirals in order to treat the emerging epidemic. In order to be prepared for the next pandemic, we need to continue to refining mathematical tools for analyzing viral dynamics. Furthermore, a big challenge that we face is the integration of models for within-hosts and between-hosts.

In this Special Issue, we will include recent developments of mathematical modeling techniques for viral infections, covering both the within-host dynamics and population-level dynamics.

Dr. Gilberto Gonzalez-Parra
Dr. Hana Dobrovolny
Guest Editors

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Keywords

mathematical modeling
epidemics
viral dynamics
coinfection
antiviral therapy
multiscale modeling
dynamical systems
vaccination
mutation

Published Papers (3 papers)

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Research

16 pages, 3676 KiB

Open AccessArticle

Treatment of Respiratory Viral Coinfections

by Paul Alexander and Hana M. Dobrovolny

Epidemiologia 2022, 3(1), 81-96; https://0-doi-org.brum.beds.ac.uk/10.3390/epidemiologia3010008 - 23 Feb 2022

Cited by 1 | Viewed by 2524

Abstract

With the advent of rapid multiplex PCR, physicians have been able to test for multiple viral pathogens when a patient presents with influenza-like illness. This has led to the discovery that many respiratory infections are caused by more than one virus. Antiviral treatment of viral coinfections can be complex because treatment of one virus will affect the time course of the other virus. Since effective antivirals are only available for some respiratory viruses, careful consideration needs to be given on the effect treating one virus will have on the dynamics of the other virus, which might not have available antiviral treatment. In this study, we use mathematical models of viral coinfections to assess the effect of antiviral treatment on coinfections. We examine the effect of the mechanism of action, relative growth rates of the viruses, and the assumptions underlying the interaction of the viruses. We find that high antiviral efficacy is needed to suppress both infections. If high doses of both antivirals are not achieved, then we run the risk of lengthening the duration of coinfection or even of allowing a suppressed virus to replicate to higher viral titers. Full article

(This article belongs to the Special Issue Mathematical Modeling for Understanding Viral Infections Within-Host and Between-Host)

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13 pages, 738 KiB

Open AccessArticle

On Deterministic and Stochastic Multiple Pathogen Epidemic Models

by Fernando Vadillo

Epidemiologia 2021, 2(3), 325-337; https://0-doi-org.brum.beds.ac.uk/10.3390/epidemiologia2030025 - 12 Aug 2021

Cited by 1 | Viewed by 2416

Abstract

In this paper, we consider a stochastic epidemic model with two pathogens. In order to analyze the coexistence of two pathogens, we compute numerically the expectation time until extinction (the mean persistence time), which satisfies a stationary partial differential equation with degenerate variable coefficients, related to backward Kolmogorov equation. I use the finite element method in order to solve this equation, and we implement it in FreeFem++. The main conclusion of this paper is that the deterministic and stochastic epidemic models differ considerably in predicting coexistence of the two diseases and in the extinction outcome of one of them. Now, the main challenge would be to find an explanation for this result. Full article

(This article belongs to the Special Issue Mathematical Modeling for Understanding Viral Infections Within-Host and Between-Host)

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23 pages, 3547 KiB

Open AccessArticle

Analysis of Delayed Vaccination Regimens: A Mathematical Modeling Approach

by Gilberto Gonzalez-Parra

Epidemiologia 2021, 2(3), 271-293; https://0-doi-org.brum.beds.ac.uk/10.3390/epidemiologia2030021 - 20 Jul 2021

Cited by 11 | Viewed by 3914

Abstract

The first round of vaccination against coronavirus disease 2019 (COVID-19) began in early December of 2020 in a few countries. There are several vaccines, and each has a different efficacy and mechanism of action. Several countries, for example, the United Kingdom and the USA, have been able to develop consistent vaccination programs where a great percentage of the population has been vaccinated (May 2021). However, in other countries, a low percentage of the population has been vaccinated due to constraints related to vaccine supply and distribution capacity. Countries such as the USA and the UK have implemented different vaccination strategies, and some scholars have been debating the optimal strategy for vaccine campaigns. This problem is complex due to the great number of variables that affect the relevant outcomes. In this article, we study the impact of different vaccination regimens on main health outcomes such as deaths, hospitalizations, and the number of infected. We develop a mathematical model of COVID-19 transmission to focus on this important health policy issue. Thus, we are able to identify the optimal strategy regarding vaccination campaigns. We find that for vaccines with high efficacy (>70%) after the first dose, the optimal strategy is to delay inoculation with the second dose. On the other hand, for a low first dose vaccine efficacy, it is better to use the standard vaccination regimen of 4 weeks between doses. Thus, under the delayed second dose option, a campaign focus on generating a certain immunity in as great a number of people as fast as possible is preferable to having an almost perfect immunity in fewer people first. Therefore, based on these results, we suggest that the UK implemented a better vaccination campaign than that in the USA with regard to time between doses. The results presented here provide scientific guidelines for other countries where vaccination campaigns are just starting, or the percentage of vaccinated people is small. Full article

(This article belongs to the Special Issue Mathematical Modeling for Understanding Viral Infections Within-Host and Between-Host)

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