Open Access

Global Behavior of a Multi–Group Seir Epidemic Model with Spatial Diffusion in a Heterogeneous Environment

International Journal of Applied Mathematics and Computer Science's Cover Image
International Journal of Applied Mathematics and Computer Science
Towards Self-Healing Systems through Diagnostics, Fault-Tolerance and Design (Special section, pp. 171-269), Marcin Witczak and Ralf Stetter (Eds.)


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.

Publication timeframe:
4 times per year
Journal Subjects:
Mathematics, Applied Mathematics