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

TL;DR

This paper analyzes the long-term behavior of a SEIRS epidemic model with nonlinear infection rates and multiple delays, deriving conditions for disease extinction or persistence, and applying findings to malaria.

Contribution

It introduces a SEIRS model with nonlinear incidence and distributed delays, providing analytical conditions for disease extinction and permanence, and applies these to a malaria scenario.

Findings

Derived conditions for disease extinction and permanence.

Computed basic reproduction number and delay-related expectation.

Numerical simulations illustrating theoretical results.

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.