Long-Term Dynamics of a Stochastic SIRV Model for TB with Random Disturbances

We investigate the long-term behavior of an epidemic using a stochastic SIRV (Susceptible-Infectious-Recovered-Vaccinated) model that incorporates time dependent parameters and random perturbations. The model is motivated by tuberculosis (TB) transmission dynamics and includes vaccination of newborns as a key intervention strategy. Random environmental fluctuations are modeled via Wiener processes, and the systems stochastic stability is analyzed. We derive conditions for the existence of a unique global solution and examine the extinction and persistence of the disease under stochastic influences. Numerical simulations are provided to illustrate the theoretical results and to explore the impact of parameter variability and noise intensity on the epidemic’s evolution. This work contributes to the understanding of how random disturbances affect long-term epidemic dynamics and can inform public health strategies under uncertainty. This project has received funding through the MSCA4Ukraine project (AvH ID:1233636), which is funded by the European Union.