Mathematical analysis on SEIR-type model of the Tuberculosis disease spread with vaccination and treatment elements

Abstract

Tuberculosis (TB) is one of the most contagious diseases that cause many deaths. TB disease is caused by Mycobacterium tuberculosis bacteria that commonly affect the lungs and other organs such as lymph nodes, intestines, kidneys, womb, bones and brain. World Health Organization (WHO) stated that in 2015 there are 60% of TB cases found in developing countries including India, Indonesia, China, Nigeria, Pakistan and South Africa. By 2015 the TB death rate is 1.4 million. One way to reduce the spread of TB disease is vaccination and treatment. The treatment given is in the form of several types of drugs that should be taken by infected individuals within a certain period of time. Therefore, it is necessary to do a scientifically acceptable analysis of the spread of TB disease. Mathematical model for analyzing the spread of TB disease have been widely developed. One is SEIR type. In this model the population is divided into four groups, namely S for susceptible individuals, E for exposed individuals, I for infected individuals, R for recovered individuals. This article discusses the model of SEIR type TB disease with vaccination and treatment.