Abstract
A mathematical model incorporating diffusion is developed to describe the spatial spread of COVID-19 epidemics in geographical regions. The dynamics of the spatial spread are based on community transmission of the virus. The model is applied to the outbreak of the COVID-19 epidemic in Brazil.
Highlights
Coronavirus disease 2019 (COVID-19) firstly identified in December 2019 has infected over 20 million people worldwide as of September 2021 [11, 26]
Reaction-diffusion equations have been used extensively to model the spatial spread of epidemic diseases
The authors in [3] use a kinetic transport model to simulate the outbreak of COVID-19 epidemic in Italy; the authors in [24] use a diffusive compartmental model to simulate the spatial spread of COVID-19 in three cities of Italy, USA, and Brazil
Summary
Coronavirus disease 2019 (COVID-19) firstly identified in December 2019 has infected over 20 million people worldwide as of September 2021 [11, 26]. Reaction-diffusion equations have been used extensively to model the spatial spread of epidemic diseases (see, for example, [1, 2, 6, 13, 19, 18, 29, 32, 37, 49, 50, 53]). We will use a reaction-diffusion model to simulate the community transmission of COVID-19, which plays a major role in the geographical spread of the epidemics. Reaction-diffusion equations, epidemic models, spatial transmission, COVID-19. The proofs of the mathematical results are presented in the appendix
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