Stochastic Analysis of a Rotavirus Epidemic Model With Delay-Dependent Transmission Attenuation and an Efficient NSFD Scheme

This paper develops and analyzes a stochastic rotavirus epidemic model incorporating a delay-dependent exponential attenuation factor in the nonlinear transmission rate. The attenuation term is used to represent the reduction in effective disease transmission caused by delayed intervention, response, or control effects. The main objective is to investigate threshold dynamics and construct a dynamically consistent stochastic numerical scheme that preserves qualitative properties of the continuous system. Stochastic differential equations with delay-dependent transmission attenuation are used in the study to evaluate the dynamics of rotavirus illness. When designing the stochastic delayed model, the entire population is divided into five compartments: Rotavirus Susceptibility S, Maternal Immunity M, Rotavirus Vaccinated V, Rotavirus Infected I, and Rotavirus Recovered R. A thorough study is conducted of the delayed model’s continuous analysis as well as dynamical aspects such as existence, boundedness, positivity, and uniqueness. With the restriction of the reproduction number, the asymptotic behavior of both local and global stability around derived equilibrium studies is examined. It is examined that the stochastic delayed model has a unique global positive solution. Furthermore, it was revealed that the only stochastic nonstandard finite difference scheme that is dynamically consistent and convergent to its derived equilibrium states is the one that was suggested. It compares the results with the current approaches in the literature and complies with all dynamical properties. Only the suggested stochastic nonstandard finite difference scheme is consistent, free of step size, and converges around their generated equilibrium states, according to the results. Only the nonstandard finite difference scheme converges with its mean trajectory deterministic, according to the scheme comparison simulations that are shown. Every other conventional scheme under consideration deviates from its basic characteristics, such as positivity and boundedness. At last, for susceptible, infected rotavirus, the delayed consequences of the model’s stochasticity were examined.