Complete Global Analysis of a Two-Scale Network SIRS Epidemic Dynamic Model with Distributed Delay and Random Perturbations

Divine Wanduku

doi:10.1016/j.amc.2016.09.001

Complete Global Analysis of a Two-Scale Network SIRS Epidemic Dynamic Model with Distributed Delay and Random Perturbations

Divine Wanduku

Mathematical Sciences

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

27 Scopus citations

Abstract

A stochastic SIRS epidemic dynamic model with distributed time delay for vector-borne diseases in two-scale network structured populations is presented. The distributed delay accounts for the varying incubation period of the disease. Furthermore, the disease dynamics is influenced by random environmental perturbations in the disease transmission process as well as the two-scale human mobility process. The basic reproduction numbers at three human–vector contact levels in the two-scale population are computed, and the results for the stochastic asymptotic stability of the equilibria are presented. Moreover, the asymptotic stability results are exhibited in several real life scenarios and the significance of the results are presented. Numerical simulation results are presented.

Original language	American English
Journal	Applied Mathematics and Computation
Volume	294
DOIs	https://doi.org/10.1016/j.amc.2016.09.001
State	Published - Feb 1 2017

Disciplines

Education
Mathematics

Keywords

Disease-free steady state
Intra- and inter-regional visiting times
Lyapunov functional technique
Stochastic asymptotic stability
Threshold value

UN SDGs

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

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10.1016/j.amc.2016.09.001License: Unspecified

https://doi.org/10.1016/j.amc.2016.09.001

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title = "Complete Global Analysis of a Two-Scale Network SIRS Epidemic Dynamic Model with Distributed Delay and Random Perturbations",

abstract = "A stochastic SIRS epidemic dynamic model with distributed time delay for vector-borne diseases in two-scale network structured populations is presented. The distributed delay accounts for the varying incubation period of the disease. Furthermore, the disease dynamics is influenced by random environmental perturbations in the disease transmission process as well as the two-scale human mobility process. The basic reproduction numbers at three human–vector contact levels in the two-scale population are computed, and the results for the stochastic asymptotic stability of the equilibria are presented. Moreover, the asymptotic stability results are exhibited in several real life scenarios and the significance of the results are presented. Numerical simulation results are presented.",

keywords = "Disease-free steady state, Intra- and inter-regional visiting times, Lyapunov functional technique, Stochastic asymptotic stability, Threshold value",

author = "Divine Wanduku",

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year = "2017",

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doi = "10.1016/j.amc.2016.09.001",

language = "American English",

volume = "294",

journal = "Applied Mathematics and Computation",

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T1 - Complete Global Analysis of a Two-Scale Network SIRS Epidemic Dynamic Model with Distributed Delay and Random Perturbations

AU - Wanduku, Divine

PY - 2017/2/1

Y1 - 2017/2/1

N2 - A stochastic SIRS epidemic dynamic model with distributed time delay for vector-borne diseases in two-scale network structured populations is presented. The distributed delay accounts for the varying incubation period of the disease. Furthermore, the disease dynamics is influenced by random environmental perturbations in the disease transmission process as well as the two-scale human mobility process. The basic reproduction numbers at three human–vector contact levels in the two-scale population are computed, and the results for the stochastic asymptotic stability of the equilibria are presented. Moreover, the asymptotic stability results are exhibited in several real life scenarios and the significance of the results are presented. Numerical simulation results are presented.

AB - A stochastic SIRS epidemic dynamic model with distributed time delay for vector-borne diseases in two-scale network structured populations is presented. The distributed delay accounts for the varying incubation period of the disease. Furthermore, the disease dynamics is influenced by random environmental perturbations in the disease transmission process as well as the two-scale human mobility process. The basic reproduction numbers at three human–vector contact levels in the two-scale population are computed, and the results for the stochastic asymptotic stability of the equilibria are presented. Moreover, the asymptotic stability results are exhibited in several real life scenarios and the significance of the results are presented. Numerical simulation results are presented.

KW - Disease-free steady state

KW - Intra- and inter-regional visiting times

KW - Lyapunov functional technique

KW - Stochastic asymptotic stability

KW - Threshold value

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/389

UR - https://doi.org/10.1016/j.amc.2016.09.001

U2 - 10.1016/j.amc.2016.09.001

DO - 10.1016/j.amc.2016.09.001

M3 - Article

SN - 0096-3003

VL - 294

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Complete Global Analysis of a Two-Scale Network SIRS Epidemic Dynamic Model with Distributed Delay and Random Perturbations

Abstract

Disciplines

Keywords

UN SDGs

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