MODEL MATEMATIKA PENYEBARAN DBD TIPE SIR

Abstract

Based on emerging DHF cases occur various solutions for the prevention and control of the transmission of dengue, one of them is to create a mathematical model. The Mathematical model that was developed is a SIR (Susceptible (S), Infected (I) and recovered (R)),, where the rate of displacement of latent mosquitoes become infected mosquito is assumed constant and healthy mosquito eggs produced by infected mosquitoes and susceptible mosquitoes, while the mosquito is infected eggs produced only by infected mosquitoes. In the SIR model, an analysis is performed to assess the stability of the equilibrium point and numerical simulations. Numeric simulation was introduced to show the stability at the equilibrium state considered basic reproduction number ℛ0 .There are two equilibrium points. The first equilibrium point is a the disease-free equilibrium which is stable, ℛ0<1. The second equilibrium point is called an endemic equilibrium, which is stable, ℛ0>1. The numerical simulations show that increasing mosquitoes mortality rate makes ℛ0, infected human, latent mosquito, infected mosquito, infected egg are decrease, so as to help suppress the spread of the disease in the population.