Dynamical analysis of a stochastic SIRS epidemic model with saturating contact rate | Zendy

Yang Chen | Zendy; Wencai Zhao | Zendy

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Dynamical analysis of a stochastic SIRS epidemic model with saturating contact rate

Author(s) -

Yang Chen,

Wencai Zhao

Publication year - 2020

Publication title -

mathematical biosciences and engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.451

H-Index - 45

eISSN - 1551-0018

pISSN - 1547-1063

DOI - 10.3934/mbe.2020316

Subject(s) - extinction (optical mineralogy) , epidemic model , eigenvalues and eigenvectors , noise (video) , stability (learning theory) , environmental noise , mathematics , intensity (physics) , statistical physics , control theory (sociology) , computer science , physics , artificial intelligence , demography , population , control (management) , quantum mechanics , machine learning , sociology , acoustics , optics , image (mathematics) , sound (geography)

In this paper, a stochastic SIRS epidemic model with saturating contact rate is constructed. First, for the deterministic system, the stability of the equilibria is discussed by using eigenvalue theory. Second, for the stochastic system, the threshold conditions of disease extinction and persistence are established. Our results indicate that a large environmental noise intensity can suppress the spread of disease. Conversely, if the intensity of environmental noise is small, the system has a stationary solution which indicates the disease is persistent. Eventually, we introduce some computer simulations to validate the theoretical results.

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