Solusi Numerik Masalah Kontrol Optimum Penyebaran Penyakit Influenza A

Abstract

Influenza A is an acute respiratory disease caused by a virus H1N1. The virus is mainly transmitted by air and can be contagious from human to human. In this work, a mathematical model of SIR is used to describe the disease transmission, where the population is divided into three classes namely susceptible, infected, and recovered. Analysis was performed on two cases, those are models without and with control, i.e. vaccination treatments. The model of H1N1 transmission is applied at regency and city of Bogor with a total population of six million people. Model without control provides two equilibrium points, where from stability threshold for disease free equilibrium point is obtained a basic reproductive number . The disease will die out if and may become endemic if . On the model with administration of control we minimized the infected population and the vaccination cost. Numerical solutions of nonlinear system of differential equations derived from the conditions of Pontryagin minimum principle are conducted by Runge-Kutta 4th order method. The results of numerical simulation show that the model without control administration, basic reproductive number causes more infected individuals than that of . Meanwhile, the effect of the treatment above decreased the number of H1N1 infected down to .