Stochastic modeling of spreading an infection with standard incidence rate

Parsamanesh, Mahmood; Abukhaled, Marwan

doi:10.47974/JSMS-1271

Open Access Research Article

Stochastic modeling of spreading an infection with standard incidence rate

^*Mahmood ParsamaneshCorresponding authormparsamanesh@tvu.ac.irDepartment of Mathematics National University of Skills (NUS)Tehran, IranView full profile → , Marwan AbukhaledDepartment of Mathematics and Statistics American University of SharjahSharjah, United Arab EmiratesView full profile →

* Corresponding author · click or hover a name for details

pp. 1221–1241Vol. 27Issue 6September 2024DOI: 10.47974/JSMS-1271XML

Received:: 12 Sep 2023
Published Online:: 19 Sep 2024
Article type:: Research Article
Language:: EN
Article no.:: JSMS-1271
Pages:: 1221–1241

Abstract

This paper studies and models the random spread of an infection in a population. It extends the traditional deterministic modeling approach by incorporating discrete-time stochastic modeling using Markov chains. The probability of extinction and disease persistence is then investigated using the branching chain method, with a focus on a quantity in the non-random model, which is called the basic reproductive number. Moreover, the random model is transformed into a system of stochastic differential equations by approximating the probability distribution function using the forward Kolmogorov equation. An equivalent stochastic differential system is also introduced and examined for the stochastic model. Finally, numerical simulations of the stochastic models are conducted to evaluate the theoretical findings presented in the paper.

Keywords

Stochastic epidemic model Vaccination Markov chain model Stochastic differential system Extinction probability

Subject Classifications

60J1060H35

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