Global Analysis of a Stochastic Two-Scale Network Human Epidemic Dynamic Model with Varying Immunity Period

Divine Wanduku; G. S. Ladde

doi:10.4236/jamp.2017.55101

Global Analysis of a Stochastic Two-Scale Network Human Epidemic Dynamic Model with Varying Immunity Period

Divine Wanduku, G. S. Ladde

Mathematical Sciences

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Abstract

A stochastic SIR epidemic dynamic model with distributed-time-delay, for a two-scale dynamic population is derived. The distributed time delay is the varying naturally acquired immunity period of the removal class of individuals who have recovered from the infection, and have acquired natural immunity to the disease. We investigate the stochastic asymptotic stability of the disease free equilibrium of the epidemic dynamic model, and verify the impact on the eradication of the disease.

Original language	American English
Journal	Journal of Applied Mathematics and Physics
Volume	5
DOIs	https://doi.org/10.4236/jamp.2017.55101
State	Published - May 27 2017

Keywords

Disease-Free Steady State
Lyapunov Functional Technique
Positively Self Invariant Set
Stochastic Asymptotic Stability
Threshold Value

DC Disciplines

Mathematics

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title = "Global Analysis of a Stochastic Two-Scale Network Human Epidemic Dynamic Model with Varying Immunity Period",

abstract = " A stochastic SIR epidemic dynamic model with distributed-time-delay, for a two-scale dynamic population is derived. The distributed time delay is the varying naturally acquired immunity period of the removal class of individuals who have recovered from the infection, and have acquired natural immunity to the disease. We investigate the stochastic asymptotic stability of the disease free equilibrium of the epidemic dynamic model, and verify the impact on the eradication of the disease.",

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N2 - A stochastic SIR epidemic dynamic model with distributed-time-delay, for a two-scale dynamic population is derived. The distributed time delay is the varying naturally acquired immunity period of the removal class of individuals who have recovered from the infection, and have acquired natural immunity to the disease. We investigate the stochastic asymptotic stability of the disease free equilibrium of the epidemic dynamic model, and verify the impact on the eradication of the disease.

AB - A stochastic SIR epidemic dynamic model with distributed-time-delay, for a two-scale dynamic population is derived. The distributed time delay is the varying naturally acquired immunity period of the removal class of individuals who have recovered from the infection, and have acquired natural immunity to the disease. We investigate the stochastic asymptotic stability of the disease free equilibrium of the epidemic dynamic model, and verify the impact on the eradication of the disease.

KW - Disease-Free Steady State

KW - Lyapunov Functional Technique

KW - Positively Self Invariant Set

KW - Stochastic Asymptotic Stability

KW - Threshold Value

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DO - 10.4236/jamp.2017.55101

M3 - Article

VL - 5

JO - Journal of Applied Mathematics and Physics

JF - Journal of Applied Mathematics and Physics

ER -

Global Analysis of a Stochastic Two-Scale Network Human Epidemic Dynamic Model with Varying Immunity Period

Abstract

Keywords

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