Some asymptotic properties of SEIRS models with nonlinear incidence and random delays

TThis paper presents the dynamics of mosquitoes and humans, with general nonlinear incidence rate and multiple distributed delays for the disease. The model is a SEIRS system of delay differential equations. The normalized dimensionless version is derived; analytical techniques are applied to find conditions for deterministic extinction and permanence of disease. The BRN $R^{*}_{0}$ and ESPR $E(e^{-(\mu_{v}T_{1}+\mu T_{2})})$ are computed. Conditions for deterministic extinction and permanence are expressed in terms of $R^{*}_{0}$ and $E(e^{-(\mu_{v}T_{1}+\mu T_{2})})$, and applied to a P.vivax malaria scenario. Numerical results are given.