Stochastic Analysis For Some Non-Linear Epidemic Models

Stochastic calculus has emerged as a robust mathematical framework for modeling complex biological systems characterized by inherent randomness and uncertainty. Unlike traditional deterministic models, which often fail to capture the variability observed in biological processes, stochastic calculus allows for directly incorporating noise and random fluctuations into the modeling equations. This approach is efficient in areas such as population dynamics, gene expression, neural activity, and the spread of infectious diseases, where biological systems are influenced by numerous random factors at both the microscopic and macroscopic levels. By utilizing tools such as stochastic differential equations (SDEs) and the Itô calculus, researchers can describe the temporal evolution of biological systems in a manner that accounts for both the deterministic trends and stochastic perturbations.