Some asymptotic properties of SEIRS models with nonlinear incidence and random delays - Wanduku, Divine; Oluyede, B.O. (Nonlinear Analysis: Modelling and Control, 2020)
This 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  R0* and  ESPR E(e–(μvT1+μT2)) are computed. Conditions for deterministic extinction and permanence are expressed in terms of R0* and E(e–(μvT1+μT2)) and applied to a P. vivax malaria scenario. Numerical results are given.
Keywords: endemic equilibrium; basic reproduction number; permanence in the mean; Lyapunov functionals techniques; extinction rate