Relaxation Oscillation and Canard Explosion for a SIRS Model with Nonlinear Incidence Rate

• Wang Xiaoling ^[2] ; Li Shimin ^[1]
  1. [1] Hangzhou Normal University

     Hangzhou Normal University

     China

     
  2. [2] Guangdong University of Finance and Economics
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 4, 2022
• Idioma: inglés
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• Resumen

  • In this paper, we study a susceptible-infectious-recovered model with a nonlinear incidence rate. Assume that the infected individual has large immunity failure rate, then it becomes a slow–fast system. Using geometry singular perturbation theory, we revealed that it exhibits rich dynamics, such as supercritical Hopf bifurcation, canard explosion and relaxation oscillation.