Work

Dynamics of stochastic SIQS model based on nonlinear incidence: disease extinction and stationary distribution under degenerate diffusion

Year: 2025

Type: book-chapter

Abstract: This paper investigated the dynamical behaviors of the SIQS (susceptible, infected, isolated, and again susceptible) infectious disease model with nonlinear incidence rate and degenerate diffusion in a stochastic environment. By introducing nonlinear contagion rate, the model was able to more realistically reflect the complexity of real-world disease transmission, including the effects of social behavior, medical resource constraints, and public health interventions. It was proved that the infectious disease will be extinct when $ R_0^s < 1 $. Furthermore, by utilizing Markov semigroup theory, we obtained that there existed stationary distribution for the system when $ R_0^s > 1 $. Numerical simulations were conducted by introducing three different forms of nonlinear incidence rates (standard incidence, non-monotonic incidence, Beddington-DeAngelis incidence) to verify our results.

Source: Electronic Research Archive

DOI: 10.3934/era.2025193

Authors: Shuantu He, Zhongyi Xiang

Institution: Hubei University for Nationalities

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

SDG: Good health and well-being

Open Access status: gold

Estimated APC paid: $1,000