Stability analysis model of Bacillus antracis using SEIQR population compartment with quarantine in Indonesia

Abstract

In Indonesia there are many breeders of cattle that are actually used as a livelihood so that Indonesia is prone to the spread of anthrax disease. This disease can be transmitted through indirect contacts such as deep impurities, saliva and the like. Anthrax disease is a type of disease caused by bacteria and there is a link between livestock and humans as the host. Anthrax disease with quarantine special factors can be modelled with SEIQR where existed from susceptible, exposed, symptomatic infected, quarantine and recovered compartment with research method used that is quantitative method, so different with disease models caused by bacteria in general.In this study we will determine the qualitative analysis of the anthrax disease distribution model with goal of research are to obtain model transmission Anthrax, to find equilibrium point of model and to find the basic reproduction number R 0, where R0 aims to determine the spread of disease or the absence of disease spread through endemic equilibrium stability analysis. The goal from this research is compare stability analysis between model with quarantine and model without quarantine use Routh-Hurwitz criteria to prove that E 1 and E 2 are asymptotic stability equilibrium so from this research conclude that quarantine population can speed up recovered population to be free disease condition from Anthrax.