Stationary Distribution of Stochastic SEIRS Epidemic Model with Saturated Incidence Rate and Saturated Treatment Function
DOI:
https://doi.org/10.21123/bsj.2024.11183Keywords:
Extinction, Lyapunov function, Mathematical modelling, Stationary distribution, Stochastic SEIRS epidemic modelAbstract
This investigation aims to enhance and broaden the mathematical model that governs a dynamic stochastic SEIRS (Susceptible, Exposed, Infective, and Recovery) epidemic. This complex model integrates crucial components, including a saturated incidence rate and saturated treatment function, which are fundamental in molding epidemic dynamics. The objective is to explore the presence and uniqueness of a positive global solution through the application of a meticulously designed Lyapunov function, facilitating a more profound analysis of the intricacies of the systems. This analytical framework enables us to uncover the interactions among disease transmission, treatment dynamics, and stochastic influences. This theoretical framework assumes that treatment responses are directly related to incidence cases within the healthcare system as long as they remain within the system. A key aspect of our contribution lies in defining the stochastic basic reproduction number as a critical threshold that determines the course of the epidemic. Under conditions characterized by low noise levels and , it establishes the prerequisites for the appearance of an ergodic stationary distribution, offering insights into the potential long-term trends in disease dissemination. Conversely, in scenarios characterized by high noise intensity , our analysis sheds light on the inevitable eradication of the disease. To further enhance the theoretical underpinning, our research integrates extensive numerical simulations. These simulations not only confirm the validity of our theoretical findings but also provide a dynamic visualization of the implications of the model. The dual methodology of theoretical analysis and simulations contributes to a nuanced understanding of stochasticity and epidemic dynamics.
Received 14/03/2024
Revised 24/06/2024
Accepted 26/06/2024
Published Online First 20/12/2024
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