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.
Authors: José Paulo Carvalho dos Santos, Evandro Ziggiatti Monteiro, José Claudinei Ferreira, Nelson H. T. Lemes, Diego Samuel Rodrigues
DOI: https://doi.org/10.55630/j.biomath.2023.07.207
Publish Year: 2023
