Theoretical Analysis on a Diffusive SIS Epidemic Model with Logistic Source, Saturated Incidence Rate and Spontaneous Infection Mechanism

Hongmin Zhang (), Jian Zhang and Xin Huo
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Hongmin Zhang: School of Science, Qiqihar University, Qiqihar 161006, China
Jian Zhang: School of Science, Qiqihar University, Qiqihar 161006, China
Xin Huo: School of Mathematical Sciences, Harbin Normal University, Harbin 150025, China

Mathematics, 2025, vol. 13, issue 8, 1-15

Abstract: In this paper, we study a diffusive SIS epidemic model with a logistic source, saturation rate, and spontaneous infection mechanism. Based on the uniform bounds of parabolic system, the global attractivity of the endemic equilibrium is established in a homogeneous environment. Moreover, we prove the existence of the endemic equilibrium via the topological degree theory. We mainly analyze the effects of dispersal, saturation, and spontaneous infection on the limiting behaviors of the endemic equilibrium. These results show that spontaneous infection and the logistic source can enhance the persistence of infectious disease, causing the disease to become more threatening.

Keywords: SIS epidemic model with logistic source; saturation; spatially heterogeneous; global stability; asymptotic profile (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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