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Paper details
Number 2 - June 2022
Volume 32 - 2022
Global behavior of a multi-group SEIR epidemic model with spatial diffusion in a heterogeneous environment
Pengyan Liu, Hong-Xu Li
Abstract
In this paper, we propose a multi-group SEIR epidemic model with spatial diffusion, where the model parameters are
spatially heterogeneous. The positivity and ultimate boundedness of the solution, as well as the existence of a global
attractor of the associated solution semiflow, are established. The definition of the basic reproduction number is given by
utilizing the next generation operator approach, whereby threshold-type results on the global dynamics in terms of this
number are established. That is, when the basic reproduction number is less than one, the disease-free steady state is
globally asymptotically stable, while if it is greater than one, uniform persistence of this model is proved. Finally, the
feasibility of the main theoretical results is shown with the aid of numerical examples for a model with two groups.
Keywords
global stability, multi-group epidemic model, spatial heterogeneity, spatial diffusion