A SIR Mathematical Model of Dengue Transmission and its Simulation

Abstract

The Mathematical model that was developed is a SIR model human-mosquito-mosquito eggs, the rate of displacement of latent mosquitoes become infected mosquito was assumed constant and non-infected eggs were produced by infected mosquitoes and susceptible mosquitoes, while infected eggs were produced by infected mosquitoes. In addition, the temperature factor used in producing susceptible mosquitoes and infected mosquitoes from eggs. The analysis shows two equilibrium state, disease-free equilibrium and endemic equilibrium. The simulation was conducted to show dynamic population where Ro<1 and Ro>1. The result shows the disease-free equilibrium which is stable when Ro<1 and the endemic equilibrium which is stable when Ro>1. This also shows mosquito mortality rate towards the desease in population. If mosquito mortality rate is increased, the basic reproduction number is decreasing, so it can prevent spread in population.