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

Divine Wanduku; Broderick O. Oluyede

doi:10.15388/namc.2020.25.16660

Some asymptotic properties of seirs models with nonlinear 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

1 Downloads (Pure)

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	English
Pages (from-to)	461-481
Number of pages	21
Journal	Nonlinear Analysis: Modelling and Control
Volume	25
Issue number	3
DOIs	https://doi.org/10.15388/namc.2020.25.16660
State	Published - 2020

Scopus Subject Areas

Analysis
Applied Mathematics

Keywords

Basic reproduction number
Endemic equilibrium
Extinction rate
Lyapunov functionals techniques
Permanence in the mean

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

Access to Document

10.15388/namc.2020.25.16660

Cite this

@article{ad8d141ee06a41239e7adf1c4fd278be,

title = "Some asymptotic properties of seirs models with nonlinear incidence and random delays",

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.",

keywords = "Basic reproduction number, Endemic equilibrium, Extinction rate, Lyapunov functionals techniques, Permanence in the mean",

author = "Divine Wanduku and Oluyede, \{Broderick O.\}",

note = "Publisher Copyright: {\textcopyright} 2020 Authors.",

year = "2020",

doi = "10.15388/namc.2020.25.16660",

language = "English",

volume = "25",

pages = "461--481",

journal = "Nonlinear Analysis: Modelling and Control",

issn = "1392-5113",

publisher = "Vilnius University Press",

number = "3",

}

TY - JOUR

T1 - Some asymptotic properties of seirs models with nonlinear incidence and random delays

AU - Wanduku, Divine

AU - Oluyede, Broderick O.

PY - 2020

Y1 - 2020

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.

KW - Basic reproduction number

KW - Endemic equilibrium

KW - Extinction rate

KW - Lyapunov functionals techniques

KW - Permanence in the mean

UR - https://www.scopus.com/pages/publications/85083304979

U2 - 10.15388/namc.2020.25.16660

DO - 10.15388/namc.2020.25.16660

M3 - Article

SN - 1392-5113

VL - 25

SP - 461

EP - 481

JO - Nonlinear Analysis: Modelling and Control

JF - Nonlinear Analysis: Modelling and Control

IS - 3

ER -

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

Abstract

Scopus Subject Areas

Keywords

UN SDGs

Access to Document

Other files and links

Fingerprint

Cite this