Impact of migration on epidemiological dynamics with saturated incidence rate

Ali Al-Qahtani; Shaban Aly; Fatma Hussien;


Recently an SIS epidemic reaction-diffusion model with Neumann (or no-flux) boundary condition has been proposed and studied by several authors to understand the dynamics of disease transmission in a spatially heterogeneous environment in which the individuals are subject to a random movement. In this paper an SIS epidemiological model with saturated incidence rate is proposed to describe the dynamics of disease spread among identical patches due to population migration. First the stability conditions for the endemic equilibrium for the corresponding kinetic system and reaction-diffusion system without diffusion are analyzed and proved. Moreover, we prove that at a critical value of the bifurcation parameter the positive endemic equilibrium becomes linear non-constant stationary solutions only when diffusion also plays a role in the reaction-diffusion system, which shows that the strong effects of diffusion on the Turing instability. Numerical simulations are provided to illustrate and extend the theoretical results.

Vol. 19 (2018), No. 1, pp. 49-61

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