A non-standard computational method for stochastic anthrax epidemic model

Abstract

This study employing a non-standard computational method for a stochastic anthrax epidemic model can enhance accuracy, evaluate control measures, and identify critical factors. The mathematical modeling of an anthrax disease includes the four-compartment of the population as susceptible animals (s), infected animals (i), carcasses animals (c), and grams spores of animals in the environment (a). The continuous model analysis (equilibria, reproduction number, and local stability of equilibria) is studied rigorously. The stochastic model is based on transition probabilities and parametric perturbation techniques. The fundamental properties of the model with standard computational methods such as Euler Maruyama, stochastic Euler, and stochastic Runge Kutta are studied. Unfortunately, these methods are time-dependent and even valid for short-period analysis of the disease. In comparison, the non-standard computational method, like the non-standard finite difference method nonstandard finite difference in the sense of stochastic, is designed for the given model. The non-standard computational method and its dynamical properties (positivity, boundedness, and dynamical consistency) are studied thoroughly. In the end, numerical results of the non-standard computational method with the existing standard computational methods are provided. These benefits contribute to a more comprehensive understanding of anthrax epidemiology and support effective decision-making in public health interventions.