A novel SIRS epidemic model for two diseases incorporating treatment functions, media coverage, and three types of noise

The paper introduces an innovative stochastic SIRS epidemic model to address the dynamics of dual diseases in response to the escalating threat of rapidly spreading epidemics. The model incorporates crucial factors such as media coverage and treatment functions, while also considering real -world complexities through the integration of three types of noises. The study explores the model using stopping time concepts and Lyapunov functions and confirms a globally positive solution. Reproduction numbers established are employed to derive extinction criteria for the diseases, along with identifying conditions for the persistence of one or both. Theoretical findings evaluate validation through efficient simulations using the Milstein method, enabling the authors to extract meaningful results from the model.