Some asymptotic properties of SEIRS models withnonlinear incidence and random delays

Divine Wanduku; Broderick O. Oluyede

doi:10.15388/namc.2020.25.16660

Some asymptotic properties of SEIRS models withnonlinear incidence and random delays

Divine Wanduku, Broderick O. Oluyede

Mathematical Sciences

Georgia Southern University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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+µT} ^{2 )} ) 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.

Original language	American English
Journal	Nonlinear Analysis: Modelling and Control
Volume	25
DOIs	https://doi.org/10.15388/namc.2020.25.16660
State	Published - May 1 2020

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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+µT 2 ) ) 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.",

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AU - Oluyede, Broderick O.

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N2 - 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+µT 2 ) ) 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.

AB - 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+µT 2 ) ) 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.

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/739

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DO - 10.15388/namc.2020.25.16660

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VL - 25

JO - Nonlinear Analysis: Modelling and Control

JF - Nonlinear Analysis: Modelling and Control

ER -

Some asymptotic properties of SEIRS models withnonlinear incidence and random delays

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