An SIR epidemic model with time-varying pulse control schemes and saturated infectious force

Vaccination and treatment policies are two methods used to control the spread of disease. In this paper, we study an SIR epidemic model with time-varying pulse vaccination of the susceptible and time-varying pulse treatment of the infected population. Owing to the seasonal fluctuations in transmission of many disease, we propose the model with periodic saturation incidence. The Threshold value R0R0 is established. We demonstrate that the disease dies out for R0<1R0<1, whereas it is permanent for R0>1R0>1.