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

Abstract: 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.