Analysis and simulation of mathematical model for typhus disease in Makassar

Abstract

The aims of the research is to build a mathematical model for typhus; Analyse and determine the basic reproduction number of the model; model simulations to predict the number of Typhus cases in Makassar City. This stage of the study examines the mathematical model of Typhus transmission by including food and flies as variables, which are the Susceptible-Exposed-Infected-Recovered (SEIR) model; analysed the SEIR model using the matrix generation method, then the model simulation using Maple with secondary data on the number of Typhus cases in Makassar City obtained from the Makassar Health Office. The results obtained are the SEIR model for typhus transmission by including flies and food as a variable which is an eight dimension non-linear differential equation model. This study also provides the analysis results of the SEIR model that Makassar is not worried an area Makassar for Typhus disease, this means the disease Typhus still exists in Makassar, while the calculation results of the basic reproduction number is .R0=0.137≤1, it can be concluded that the spread of typhus in Makassar is at an alarming stage, because a person suffering from typhus does not cause another person to suffer from Typhus. Model simulation results can predict the number of cases of Typhus so that early prevention can be done immediately and become the government's attention to prevent the spread of typhus in Makassar City