Reaction–Diffusion Equations in Mathematical Models Arising in Epidemiology

Author:

Davydovych Vasyl’1,Dutka Vasyl’2,Cherniha Roman13ORCID

Affiliation:

1. Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka Street, 01601 Kyiv, Ukraine

2. Bakul Institute for Superhard Materials, National Academy of Sciences of Ukraine, 2 Avtozavods’ka Street, 04074 Kyiv, Ukraine

3. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK

Abstract

The review is devoted to an analysis of mathematical models used for describing epidemic processes. Our main focus is on the models that are based on partial differential equations (PDEs), especially those that were developed and used for the COVID-19 pandemic modeling. Most of our attention is given to the studies in which not only results of numerical simulations are presented but analytical results as well. In particular, traveling fronts (waves), exact solutions, and the estimation of key epidemic parameters of the epidemic models with governing PDEs (typically reaction–diffusion equations) are discussed. The review may serve as a valuable resource for researchers and practitioners in the field of mathematical modeling in epidemiology.

Funder

National Research Foundation of Ukraine

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

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