INVESTIGATION OF DETERMINISTIC AND STOCHASTIC SIR EPIDEMIOLOGICAL MODEL WITH NONLINEAR INCIDENCE RATE

In this study, an expanded SIR-type model is provided that takes behavioral and environmental factors into account when analyzing the dynamics of transmission. Equilibrium points and their local stability are explored in a deterministic framework, and the fundamental reproduction number is also calculated. The model is then reconstructed using a discrete-time Markov chain (DTMC) technique to represent the random character of illness propagation in real-world settings. The evolution of the epidemic can be analyzed probabilistically using transition probabilities thanks to this stochastic framework. Numerical simulations are used to verify the outcomes of the deterministic and stochastic versions, and a comparison of their predictive tendencies is made. The results have demonstrated the need to include stochasticity in epidemiological models, particularly when taking variability and uncertainty in transmission dynamics into consideration. This dual viewpoint gives useful insights for public health policies as well as a fuller knowledge of how diseases spread.