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Castillo-Chavez, C. and Yakubu, A.A. (2002) Discrete-Time SIS Models with Simple and Complex Population Dynamics. In: Castillo-Chavez, C., Blower, S., van den Driessche, P., Kirschner, D. and Yakubu, A.A., Eds., Mathematical Approaches for Emerging and Reemerging Infectious Diseases: A Introduction, Springger-Verlag, New York, 153-163.
https://doi.org/10.1007/978-1-4757-3667-0_9

has been cited by the following article:

• TITLE: Dynamical Analysis of an SIS Epidemic Integrodifference Model

  AUTHORS: Miaomiao Zhang, Hui Cao

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

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.11, November 20, 2023

  ABSTRACT: 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.