https://doi.org/10.1140/epjp/s13360-025-06300-5
Regular Article
A novel time-delayed stochastic epidemic modeling approach incorporating Crowley–Martin incidence and nonlinear holling type II treatment rate
1
Laboratory of Mathematics Modeling and Applications (LaMMA), University of Adrar, 01000, Adrar, Algeria
2
Department of Mathematics, Faculty of Education, Sana’a University, Sanaa, Yemen
3
Jadara University Research Center, Jadara University, Irbid, Jordan
4
Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa, Pakistan
5
Department of Clinical Laboratory Sciences, College of Applied Medical Sciences, King Khalid University, Abha, Saudi Arabia
6
IT4Innovations, VSB–Technical University of Ostrava, Ostrava, Czech Republic
7
Applied Science Research Center, Applied Science Private University, Amman, Jordan
Received:
16
October
2024
Accepted:
4
April
2025
Published online:
6
May
2025
Mathematical modeling of infectious disease is essential for understanding the impact of various epidemiological factors and stochastic influences on disease spread. In this study, we investigate a stochastic compartmental epidemic model with time delays, featuring a Crowley–Martin (C-M) incidence rate alongside a holling type II (HT-II) treatment rate. Initially, we demonstrate the existence and uniqueness of a positive global solution to the model. Subsequently, we establish sufficient conditions that lead to the extinction of the disease. A suitability constructed Lyapunov function is used to confirm the presence of a stationary distribution (SD). In epidemiology, the presence of a stationary distribution indicates that the disease will persist over the long term. Additionally, the Fokker–Planck equation is solved to obtain the exact analytical form of the probability density function (PDF) that describes the behavior of the stochastic model near its unique endemic quasi-equilibrium. In statistical analysis, the explicit density function can capture and represent all the dynamical features of an epidemic model. Finally, a comprehensive simulation is provided to support and illustrate our theoretical results, offering practical insights into the model’s behavior. This work contributes to the development of more accurate predictive models that can assist public health policymakers in designing effective disease control strategies and intervention plans to mitigate the spread of infectious diseases.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
