SIR Model Analysis for Transmission of Dengue Fever Disease with Climate Factors Using Lyapunov Function

Abstract

The aim of this paper is to discuss the dynamic system of SIR model with climate factors for transmission characteristics of dengue fever in closed population. Human population is divided into three types, which are susceptible population, infected population, and recovered population, while mosquito population is divided into two kinds that are susceptible population and infected population contaminated by dengue fever virus. Five nonlinear differential equations are analyzed to obtain the equilibrium of the system and the basic reproduction number R0. Next, the stability of the equilibrium of the system is dissected with three theorems using lyapunov. The results will be in the form of the disease-free equilibrium, the endemic equilibrium, and the basic reproduction number. The basic reproduction number R0 is influenced by climate factors. If R0 ≤ 1, the disease-free equilibrium will be asymptotically stable, whereas if R0 > 1, the endemic equilibrium will become asymptotically stable instead. Based on the results, the dengue fever transmission is affected greatly by the climate of a region.