Author(s)

Miaomiao Zhang, Hui Cao^*

School of Mathematics & Data Science, Shaanxi University of Science & Technology, Xi’an, China.

In order to analyze the impact of dispersal on disease transmission, we establish an SIS epidemic integrodifference model with a nonlinear incidence function. Firstly, the discrete-time SIS epidemic model is established and studied, including the existence and stability of equilibria, the existence of a flip bifurcation, and chaos. Secondly, the SIS epidemic integrodifference model is built based on the discrete-time SIS epidemic model with dispersal. The dynamic analysis of the model includes the existence and stability of equilibria, the existence of a traveling wave solution, and a minus-one bifurcation. Finally, the results suggest that dispersal causes the system to become more unstable and accelerates the spread of the disease when the equilibrium is unstable. Numerical examples are provided to demonstrate the theoretical results.

Integrodifference Model, Flip Bifurcation, Travelling Wave Solution, Minus-One Bifurcation

Zhang, M. and Cao, H. (2023) Dynamical Analysis of an SIS Epidemic Integrodifference Model. Journal of Applied Mathematics and Physics, 11, 3464-3483. doi: 10.4236/jamp.2023.1111220.