Numerical treatment of stochastic-deterministic SIRS epidemic differential model with impact of saturated incidence using implicit/stochastic RK and Euler-Maruyama computing paradigm

Abstract

This investigation involves the numerical exploration of both stochastic and deterministic SIRS epidemic models with saturated incidence rates. The implicit Runge-Kutta method, Euler-Maruyama method, and stochastic Runge-Kutta methods are employed to analyze the dynamic patterns of the epidemic. The deterministic model is formulated using an ordinary differential system and is deep-seated in the well-established classical SIRS epidemic framework. A stochastic model is formulated by incorporating the elements of white noise in order to explain the effect of random environmental fluctuation. The proposed numerical experiments are efficiently used to assess the impact of environmentally induced changes on the SIRS epidemic model transmission dynamics. The incidence of transmission of each type of population is predicted by varying the rate of recruiting new susceptible populations, the rate of immunity decay, the rate of natural mortality, mortality due to disease, and the rate of recovery of infected individuals. The deterministic modelling solutions are approximated using the state-of-the-art implicit Runge-Kutta method, while the probabilistic versions of the model are explored using the Euler-Maruyama and stochastic Runge-Kutta techniques. Both deterministic and stochastic disease models are extensively compared and analyzed in the light of sundry scenarios of environmental changes with the view of obtaining an insight into the trends in disease transmission.