On a stochastic generalized delayed SIR model with vaccination and treatment

In this paper we consider a stochastic susceptible-infectious-recovered (SIR) epidemiological model which is obtained on the basis of the deterministic SIR epidemiological model with general incidence rate, distributed delay, general treatment and vaccination. For our model we first prove existence and uniqueness of the global positive solution and then we consider conditions under which disease survives in population by proving the existence of ergodic stationary distribution. Also, the stochastic model adopts the disease-free equilibrium from it is deterministic analogue, and we investigate conditions under which it is stable in probability. Finally, the numerical simulations with real life date are carried out to illustrate the theoretical results.