Threshold dynamics of difference equations for SEIR model with nonlinear incidence function and infinite delay.

In this research, we explore the global conduct of age-structured SEIR system with nonlinear incidence functional (NIF), where a threshold behavior is obtained. More precisely, we will analyze the investigated model differently, where we will rewrite it as a difference equations with infinite delay by the help of the characteristic method. Using standard conditions on the nonlinear incidence functional that can fit with a vast class of a well-known incidence functionals, we investigated the global asymptotic stability (GAS) of the disease-free equilibrium (DFE) using a Lyapunov functional (LF) for . The total trajectory method is utilized for avoiding proving the local behavior of equilibria. Further, in the case we achieved the persistence of the infection and the GAS of the endemic equilibrium state (EE) using the weakly -persistence theory, where a proper LF is obtained. The achieved results are checked numerically using graphical representations.