The Existence and Stability Analysis of the Equilibria in Dengue Disease Infection Model

In this paper we formulate an SIR (Susceptible - Infective - Recovered) model of Dengue fever transmission with constant recruitment. We found a threshold parameter K0, known as the Basic Reproduction Number (BRN). This model has two equilibria, disease-free equilibrium and endemic equilibrium. By c...

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Published in:Journal of physics. Conference series 2015-06, Vol.622 (1), p.12039
Main Authors: Anggriani, N, Supriatna, A K, Soewono, E
Format: Article
Language:English
Subjects:
Asymptotic properties
Dengue fever
Equilibrium
Liapunov functions
Physics
Stability analysis
Viral diseases
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description In this paper we formulate an SIR (Susceptible - Infective - Recovered) model of Dengue fever transmission with constant recruitment. We found a threshold parameter K0, known as the Basic Reproduction Number (BRN). This model has two equilibria, disease-free equilibrium and endemic equilibrium. By constructing suitable Lyapunov function, we show that the disease- free equilibrium is globally asymptotic stable whenever BRN is less than one and when it is greater than one, the endemic equilibrium is globally asymptotic stable. Numerical result shows the dynamic of each compartment together with effect of multiple bio-agent intervention as a control to the dengue transmission.
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subjects Asymptotic properties
Dengue fever
Equilibrium
Liapunov functions
Physics
Stability analysis
Viral diseases
title The Existence and Stability Analysis of the Equilibria in Dengue Disease Infection Model
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