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Viruses
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Mathematical Modeling of the COVID-19 Pandemic
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Mathematical Modeling of the COVID-19 Pandemic

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

Deadline for manuscript submissions: closed (30 April 2023) | Viewed by 13566

Special Issue Editors

Prof. Dr. Thanasis Fokas

E-Mail Website
Guest Editor
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK
Interests: linear and nonlinear ODEs and PDEs; medical imaging; asymtotic analysis; complex variables; modelling
Dr. George Kastis

E-Mail Website
Guest Editor
Research Center of Mathematics, Academy of Athens, GR-11527 Athens, Greece
Interests: PET and SPECT imaging; small-animal imaging; multimodality imaging; molecular imaging; image reconstruction
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematical models that are capable of identifying probable causes of a disease process, predicting the disease dynamics, and suggesting optimal intervention measures have a long history. The earliest example of such a model was published by the famous mathematician Daniel Bernoulli in 1776, and this mathematical model was used to compute the death rate of a chickenpox epidemic that occurred in London. Seminal development in epidemiological modelling occurred in 1927, with the introduction of the so-called compartmental models. The COVID-19 pandemic has stimulated a renewed interest in a variety of mathematical approaches, including the following: (i) Two important generalizations of the classical compartmental models, namely, the metapopulation models, which subdivide the various populations into appropriate subpopulations (for example, according to age groups and geographical regions), as well as the agent-based models, which explicitly capture the interaction structure of individuals. (ii) Data-driven forecasting models, which use a variety of statistical methods, as well as deep learning, to attempt to predict the outcomes of an epidemic.

This Special Issue will review the implementation of some of these approaches to the CODID-19 pandemic.

Prof. Dr. Thanasis Fokas
Dr. George Kastis
Guest Editors

Manuscript Submission Information

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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

  • predictive models of COVID-19
  • COVID-19 forecasting
  • COVID-19 mechanistic models
  • COVID-19 statistical models
  • COVID-19 deep Learning
  • COVID-19 agent-based models
  • COVID-19 health Geography
  • COVID-19 spatial epidemiology

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Published Papers (5 papers)

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Research

26 pages, 9494 KiB  
Article
A Model for Reinfections and the Transition of Epidemics
by Yannis C. Yortsos and Jincai Chang
Viruses 2023, 15(6), 1340; https://doi.org/10.3390/v15061340 - 8 Jun 2023
Cited by 1 | Viewed by 1664
Abstract
Reinfections of infected individuals during a viral epidemic contribute to the continuation of the infection for longer periods of time. In an epidemic, contagion starts with an infection wave, initially growing exponentially fast until it reaches a maximum number of infections, following which [...] Read more.
Reinfections of infected individuals during a viral epidemic contribute to the continuation of the infection for longer periods of time. In an epidemic, contagion starts with an infection wave, initially growing exponentially fast until it reaches a maximum number of infections, following which it wanes towards an equilibrium state of zero infections, assuming that no new variants have emerged. If reinfections are allowed, multiple such infection waves might occur, and the asymptotic equilibrium state is one in which infection rates are not negligible. This paper analyzes such situations by expanding the traditional SIR model to include two new dimensionless parameters, ε and θ, characterizing, respectively, the kinetics of reinfection and a delay time, after which reinfection commences. We find that depending on these parameter values, three different asymptotic regimes develop. For relatively small θ, two of the regimes are asymptotically stable steady states, approached either monotonically, at larger ε (corresponding to a stable node), or as waves of exponentially decaying amplitude and constant frequency, at smaller ε (corresponding to a spiral). For θ values larger than a critical, the asymptotic state is a periodic pattern of constant frequency. However, when ε is sufficiently small, the asymptotic state is a wave. We delineate these regimes and analyze the dependence of the corresponding population fractions (susceptible, infected and recovered) on the two parameters ε and θ and on the reproduction number R0. The results provide insights into the evolution of contagion when reinfection and the waning of immunity are taken into consideration. A related byproduct is the finding that the conventional SIR model is singular at large times, hence the specific quantitative estimate for herd immunity it predicts will likely not materialize. Full article
(This article belongs to the Special Issue Mathematical Modeling of the COVID-19 Pandemic)
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18 pages, 597 KiB  
Article
A COVID-19 Infection Model Considering the Factors of Environmental Vectors and Re-Positives and Its Application to Data Fitting in Japan and Italy
by Shimeng Dong, Jinlong Lv, Wanbiao Ma and Boralahala Gamage Sampath Aruna Pradeep
Viruses 2023, 15(5), 1201; https://doi.org/10.3390/v15051201 - 19 May 2023
Viewed by 2962
Abstract
COVID-19, which broke out globally in 2019, is an infectious disease caused by a novel strain of coronavirus, and its spread is highly contagious and concealed. Environmental vectors play an important role in viral infection and transmission, which brings new difficulties and challenges [...] Read more.
COVID-19, which broke out globally in 2019, is an infectious disease caused by a novel strain of coronavirus, and its spread is highly contagious and concealed. Environmental vectors play an important role in viral infection and transmission, which brings new difficulties and challenges to disease prevention and control. In this paper, a type of differential equation model is constructed according to the spreading functions and characteristics of exposed individuals and environmental vectors during the virus infection process. In the proposed model, five compartments were considered, namely, susceptible individuals, exposed individuals, infected individuals, recovered individuals, and environmental vectors (contaminated with free virus particles). In particular, the re-positive factor was taken into account (i.e., recovered individuals who have lost sufficient immune protection may still return to the exposed class). With the basic reproduction number R0 of the model, the global stability of the disease-free equilibrium and uniform persistence of the model were completely analyzed. Furthermore, sufficient conditions for the global stability of the endemic equilibrium of the model were also given. Finally, the effective predictability of the model was tested by fitting COVID-19 data from Japan and Italy. Full article
(This article belongs to the Special Issue Mathematical Modeling of the COVID-19 Pandemic)
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27 pages, 3602 KiB  
Article
A Modified PINN Approach for Identifiable Compartmental Models in Epidemiology with Application to COVID-19
by Haoran Hu, Connor M. Kennedy, Panayotis G. Kevrekidis and Hong-Kun Zhang
Viruses 2022, 14(11), 2464; https://doi.org/10.3390/v14112464 - 7 Nov 2022
Cited by 8 | Viewed by 2645
Abstract
Many approaches using compartmental models have been used to study the COVID-19 pandemic, with machine learning methods applied to these models having particularly notable success. We consider the Susceptible–Infected–Confirmed–Recovered–Deceased (SICRD) compartmental model, with the goal of estimating the unknown infected compartment I, [...] Read more.
Many approaches using compartmental models have been used to study the COVID-19 pandemic, with machine learning methods applied to these models having particularly notable success. We consider the Susceptible–Infected–Confirmed–Recovered–Deceased (SICRD) compartmental model, with the goal of estimating the unknown infected compartment I, and several unknown parameters. We apply a variation of a “Physics Informed Neural Network” (PINN), which uses knowledge of the system to aid learning. First, we ensure estimation is possible by verifying the model’s identifiability. Then, we propose a wavelet transform to process data for the network training. Finally, our central result is a novel modification of the PINN’s loss function to reduce the number of simultaneously considered unknowns. We find that our modified network is capable of stable, efficient, and accurate estimation, while the unmodified network consistently yields incorrect values. The modified network is also shown to be efficient enough to be applied to a model with time-varying parameters. We present an application of our model results for ranking states by their estimated relative testing efficiency. Our findings suggest the effectiveness of our modified PINN network, especially in the case of multiple unknown variables. Full article
(This article belongs to the Special Issue Mathematical Modeling of the COVID-19 Pandemic)
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11 pages, 613 KiB  
Article
Susceptibility to Resurgent COVID-19 Outbreaks Following Vaccine Rollouts: A Modeling Study
by Georgios Neofotistos, Mattia Angeli, Marios Mattheakis and Efthimios Kaxiras
Viruses 2022, 14(10), 2237; https://doi.org/10.3390/v14102237 - 12 Oct 2022
Viewed by 1804
Abstract
Using the recently proposed Susceptible–Asymptomatic–Infected–Vaccinated–Removed (SAIVR) model, we study the impact of key factors affecting COVID-19 vaccine rollout effectiveness and the susceptibility to resurgent epidemics. The SAIVR model expands the widely used Susceptible–Infectious–Removed (SIR) model for describing epidemics by adding compartments to include [...] Read more.
Using the recently proposed Susceptible–Asymptomatic–Infected–Vaccinated–Removed (SAIVR) model, we study the impact of key factors affecting COVID-19 vaccine rollout effectiveness and the susceptibility to resurgent epidemics. The SAIVR model expands the widely used Susceptible–Infectious–Removed (SIR) model for describing epidemics by adding compartments to include the asymptomatic infected (A) and the vaccinated (V) populations. We solve the model numerically to make predictions on the susceptibility to resurgent COVID-19 epidemics depending on initial vaccination coverage, importation loads, continuing vaccination, and more contagious SARS-CoV-2 variants, under persistent immunity and immunity waning conditions. The parameters of the model represent reported epidemiological characteristics of the SARS-CoV-2 virus such as the disease spread in countries with high levels of vaccination coverage. Our findings help explain how the combined effects of different vaccination coverage levels and waning immunity lead to distinct patterns of resurgent COVID-19 epidemics (either surges or endemic), which are observed in countries that implemented different COVID-19 health policies and achieved different vaccinated population plateaus after the vaccine rollouts in the first half of 2021. Full article
(This article belongs to the Special Issue Mathematical Modeling of the COVID-19 Pandemic)
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37 pages, 4512 KiB  
Article
On the Parametrization of Epidemiologic Models—Lessons from Modelling COVID-19 Epidemic
by Yuri Kheifetz, Holger Kirsten and Markus Scholz
Viruses 2022, 14(7), 1468; https://doi.org/10.3390/v14071468 - 2 Jul 2022
Cited by 7 | Viewed by 2945
Abstract
Numerous prediction models of SARS-CoV-2 pandemic were proposed in the past. Unknown parameters of these models are often estimated based on observational data. However, lag in case-reporting, changing testing policy or incompleteness of data lead to biased estimates. Moreover, parametrization is time-dependent due [...] Read more.
Numerous prediction models of SARS-CoV-2 pandemic were proposed in the past. Unknown parameters of these models are often estimated based on observational data. However, lag in case-reporting, changing testing policy or incompleteness of data lead to biased estimates. Moreover, parametrization is time-dependent due to changing age-structures, emerging virus variants, non-pharmaceutical interventions, and vaccination programs. To cover these aspects, we propose a principled approach to parametrize a SIR-type epidemiologic model by embedding it as a hidden layer into an input-output non-linear dynamical system (IO-NLDS). Observable data are coupled to hidden states of the model by appropriate data models considering possible biases of the data. This includes data issues such as known delays or biases in reporting. We estimate model parameters including their time-dependence by a Bayesian knowledge synthesis process considering parameter ranges derived from external studies as prior information. We applied this approach on a specific SIR-type model and data of Germany and Saxony demonstrating good prediction performances. Our approach can estimate and compare the relative effectiveness of non-pharmaceutical interventions and provide scenarios of the future course of the epidemic under specified conditions. It can be translated to other data sets, i.e., other countries and other SIR-type models. Full article
(This article belongs to the Special Issue Mathematical Modeling of the COVID-19 Pandemic)
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