Well-posedness and qualitative analysis of a SEIR model with spatial diffusion for COVID-19 spreading

Authors

  • José Paulo Carvalho dos Santos Institute of Exact Sciences, Federal University of Alfenas, UNIFAL-MG, Alfenas, Minas Gerais, Brazil
  • Evandro Monteiro Institute of Exact Sciences, Federal University of Alfenas, UNIFAL-MG, Alfenas, Minas Gerais, Brazil
  • José Claudinei Ferreira Institute of Exact Sciences, Federal University of Alfenas, UNIFAL-MG, Alfenas, Minas Gerais, Brazil
  • Nelson Henrique Teixeira Lemes Institute of Chemistry, Federal University of Alfenas, UNIFAL-MG, Alfenas, Minas Gerais, Brazil
  • Diego Samuel Rodrigues School of Technology, University of Campinas, UNICAMP, Limeira, São Paulo, Brazil

DOI:

https://doi.org/10.55630/j.biomath.2023.07.207

Keywords:

Abstract differential equations, COVID-19, SEIR compartmental model, Semigroup theory

Abstract

In this paper, we study the well-posedness and the qualitative behavior of equilibria of a SEIR epidemic models with spatial diffusion for the spreading of COVID-19. The well-posedness of the model is proved using both the Semigroup Theory of sectorial operators and existence results for abstract parabolic differential equations. The asymptotical local stability of both disease-free and endemic equilibria are established using standard linearization theory, and confirmed by illustrative numerical simulations. The asymptotical global stability of both disease-free and endemic equilibria are established using a Lyapunov function.

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Published

2023-07-28

Issue

Vol. 12 No. 1 (2023)

Section

Original Articles

License

Copyright (c) 2023 José Paulo Carvalho dos Santos, Evandro Monteiro, José Claudinei Ferreira, Nelson Henrique Teixeira Lemes, Diego Samuel Rodrigues

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