A Stochastic SIR Epidemic with Nonlinear Power Functions and Logistic Growth

Abstract

This research conducts a comprehensive analytical investigation into a stochastic SIR epidemic model that integrates nonlinear power functions and logistic growth dynamics. We examine the intricacies of model behavior, demonstrating its capability to produce a positive global solution. Utilizing precisely defined Lyapunov functions, we demonstrate the essential prerequisites for establishing the ergodicity of this particular model. Furthermore, the research deduces adequate criteria for predicting the eventual eradication of infectious diseases within this theoretical framework. Ultimately, we supplement the study with numerical simulations to elucidate and substantiate the analytical findings. This work contributes to comprehending epidemic systems with nuanced growth patterns and intricate disease transmission mechanisms, offering insights into real-world epidemic potential behaviors and outcomes.