Mathematical Analysis of SIR Stochastic Epidemic Model With Media Effects and Threshold Reinforcement

ABSTRACT A stochastic nonlinear (susceptible–infected–recovered) mathematical model has been developed to investigate the effects of therapeutic interventions, preventive strategies and public health awareness campaigns disseminated through media on the transmission dynamics of infectious diseases within a population. By incorporating the inherent stochasticity of the model parameters, the existence and uniqueness of globally defined solutions have been rigorously established. The asymptotic properties of the equilibrium solutions within the stochastic framework have been analyzed to elucidate their biological significance. Furthermore, the model stability and asymptotic behavior near the endemic equilibrium have been systematically examined. Explicit sufficient conditions for both disease eradication and persistence have been analytically derived and impact of prominent factor as noise intensity for stochastic model has been obtained. Numerical simulations have been conducted to validate the theoretical findings, providing deeper insights into the complex interplay between stochastic perturbations and epidemiological dynamics.