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Oseledets, V.I. (1968) A Multiplicative Ergodic Theorem. Lyapunov Characteristic Numbers for Dynamical Systems. Transactions of the Moscow Mathematical Society, 19, 197-231.

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• TITLE: Stochastic Bifurcation of an SIS Epidemic Model with Treatment and Immigration

  AUTHORS: Weipeng Zhang, Dan Gu

  KEYWORDS: Epidemic Model, Stochastic Averaging Method, Singular Boundary Theory, Stochastic Bifurcation

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.6, June 28, 2024

  ABSTRACT: In this paper, we investigate an SIS model with treatment and immigration. Firstly, the two-dimensional model is simplified by using the stochastic averaging method. Then, we derive the local stability of the stochastic system by computing the Lyapunov exponent of the linearized system. Further, the global stability of the stochastic model is analyzed based on the singular boundary theory. Moreover, we prove that the model undergoes a Hopf bifurcation and a pitchfork bifurcation. Finally, several numerical examples are provided to illustrate the theoretical results.