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

3rd International Conference on Science & Engineering in Mathematics, Chemistry and Physics 2015

数学;化学;物理学

Anggriani, N.^1 ; Supriatna, A.K.^1 ; Soewono, E.^2

Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jl. Raya Bandung-Sumedang km 21, Jatinangor

45363, Indonesia^1

Industrial and Financial Mathematics Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung

40132, Indonesia^2

关键词: Basic reproduction number;    Dengue fevers;    Disease-free equilibrium;    Endemic equilibrium;    Existence and stability;    Infection models;    Numerical results;    Threshold parameters;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/622/1/012039/pdf
DOI  :  10.1088/1742-6596/622/1/012039

来源: IOP

【 摘 要 】

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.