Investigating the dynamics of a delayed stage-structured epidemic model with saturated incidence and treatment functions

This paper investigates the dynamics of a stage-structured SI epidemic system with a saturated incidence rate and a saturated treatment function. Two discrete time delays are incorporated to represent the time required for immature to be mature, and the infected individuals to move into recover class, respectively. A thorough investigation of endogenous equilibrium states of the SI system has been conducted, and the characteristics of the dynamical system around these states, including local stability and Hopf bifurcation, have been studied. Using sensitivity analysis, the model is evaluated to determine which parameters play greater roles in the model results and subsequently which of them may be used to control the disease. Finally, some numerical simulations have been conducted to confirm the analytical results.