131Stochastic approach to a SIR model with two target classes

The present work presents a stochastic approach to a dual compartmental SIR model that takes into account the awareness of the disease among the population. Building on this framework, the susceptible population is categorized into two groups, vigilant and ignorant individuals. It is assumed that these two populations interact freely without any restrictions. The model exhibits two equilibrium points. To analyze the disease transmission potential, the basic reproduction number is derived using the next generation matrix (NGM) method. The model is then extended into a stochastic differential equation (SDE) by incorporating additive noise into the equations governing the state variables. This stochastic extension allows for the investigation of population dynamics under random environmental fluctuations. The findings indicate that higher noise intensity induces greater variability in the population, which potentially fluctuates the system dynamics.