Effect of Disease-Induced Death Rate and Latent Period on Global Stability for SIRS Epidemic Models with General Incidence Rate

In this paper, We study a class of delayed SIRS epidemic dynamical models with a general nonlinear incidence rate representing the transfer from susceptible class to infected class. Besides we incorporate a surviving probability from susceptibles to infectious. Throughout the paper, Lyapunov and Euler's stability tools are used to establish the global and local stability for both disease-free and endemic equilibriums depending on reproduction number value R0 and disease-induced death rate. Finally, a sensitivity analysis over basic reproduction number with respect to controllable model's parameters and numerical simulations are presented to illustrate and explain our theoretical results.