Certain aspects of the SIS stochastic epidemic model

The SIS model is a fundamental tool in epidemiology for understanding the spread of infectious diseases. This article focuses on the stochastic SIS model, introducing randomness through the disease transmission parameter. The study investigates the behavior of the model, revealing the conditions for...

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Bibliographic Details
Published in:Applied mathematical modelling 2024-04, Vol.128, p.272-286
Main Authors: de Jesús Cabral-García, Gabriela, Villa-Morales, José
Format: Article
Language:English
Subjects:
asymptotic behaviour
First moment
some real-world SIS epidemic models
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Summary:The SIS model is a fundamental tool in epidemiology for understanding the spread of infectious diseases. This article focuses on the stochastic SIS model, introducing randomness through the disease transmission parameter. The study investigates the behavior of the model, revealing the conditions for the recurrence or extinction of the disease. In particular, it addresses the calculation of the conditional expected time for the disease to exceed a certain threshold, using both Laplace transforms and numerical techniques for its specific application. Real-world phenomena are discussed, and a method for determining the most suitable stochastic parameter is proposed, with examples such as gonorrhea and pneumococcus. •A stochastic SIS model is obtained by varying the parameters.•The conditional expected value of the first passage is deduced.•Asymptotic behavior is explored, addressing previous conjectures in the literature.•A methodology is proposed to identify suitable stochastic parameters.•A method is presented to calculate the conditional expected value.
ISSN:0307-904X
DOI:10.1016/j.apm.2024.01.027