(SI10-057) Effect of Time-delay on an SIR Type Model For Infectious Diseases with Saturated Treatment

This study presents the complex dynamics of an SIR epidemic model incorporating a constant time-delay in incidence rate with saturated type of treatment rate. The system is studied to observe the effect of time lag in the asymptotic stability of endemic equilibrium states. We also establish global asymptotic stability of both disease-free and endemic equilibrium states by Lyapunov direct method with the help of suitable Lyapunov functionals. The existences of periodic solutions are ensured for the suitable choice of delay parameter. Finally, we perform numerical simulations supporting the analytical findings as well as to observe the effect of time-delay. The theoretical and numerical results together show delay can have both stabilizing and destabilizing effects on the system. Moreover, we observe that infection may die out from the population when the corresponding system without delay has two endemic equilibrium for appropriate choice of time-delay