Symmetry (May 2020)

Dynamical Behavior of a Stochastic SIRC Model for Influenza A

  • Tongqian Zhang,
  • Tingting Ding,
  • Ning Gao,
  • Yi Song

DOI
https://doi.org/10.3390/sym12050745
Journal volume & issue
Vol. 12, no. 5
p. 745

Abstract

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In this paper, a stochastic SIRC epidemic model for Influenza A is proposed and investigated. First, we prove that the system exists a unique global positive solution. Second, the extinction of the disease is explored and the sufficient conditions for extinction of the disease are derived. And then the existence of a unique ergodic stationary distribution of the positive solutions for the system is discussed by constructing stochastic Lyapunov function. Furthermore, numerical simulations are employed to illustrate the theoretical results. Finally, we give some further discussions about the system.

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