Mathematics

Hopf bifurcation in three-dimensional SIRS-model with diffusion

P. M. Kravets

The Dept. of Technical Cybernetics, Samara State Aerospace University, Samara, 443001, Russian Federation

Abstract: In this paper, modified 3D epidemiologic SIRS model with the so-called saturation incidence is considered. In the course of research the considered model was enlarged by means of adding spatial constituent and diffusion process. The aim of the work is to prove the existence of spatial heterogeneous periodic solutions in the system that takes place when bifurcation of periodic solutions happens not only along temporal but spatial variable and to simulate them numerically.

Keywords: epidemiology, SIRS-model, saturation incidence, Hopf bifurcation, diffusion.

UDC: 517.9

Received: 22.03.2013
Revised: 22.03.2013