Some asymptotic properties of SEIRS models with nonlinear incidence and random delays
Articles
Divine Wanduku
Georgia Southern University
https://orcid.org/0000-0002-5499-2311
B.O. Oluyede
Georgia Southern University
Published 2020-05-01
https://doi.org/10.15388/namc.2020.25.16660
PDF

Keywords

endemic equilibrium
basic reproduction number
permanence in the mean
Lyapunov functionals techniques
extinction rate

How to Cite

WandukuD. and OluyedeB. (2020) “Some asymptotic properties of SEIRS models with nonlinear incidence and random delays”, Nonlinear Analysis: Modelling and Control, 25(3), pp. 461–481. doi: 10.15388/namc.2020.25.16660.

Abstract

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.

PDF
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Please read the Copyright Notice in Journal Policy