Abstract. Tuberculosis (TB) is a contagious disease which can cause death. The disease is caused by Mycobacterium Tuberculosis which generally affects lungs and other organs such as lymph gland, intestine, kidneys, uterus, bone, and brain. The spread of TB occurs through the bacteria-contaminated air which is inhaled into the lungs. The symptoms of the TB patients are cough, chest pain, shortness of breath, appetite lose, weight lose, fever, cold, and fatigue. World Health Organization (WHO) reported that Indonesia placed the second in term of the most TB cases after India which has 23 % cases while China is reported to have 10 % cases in global. TB has become one of the greatest death threats in global. One way to countermeasure TB disease is by administering vaccination. However, a medication is needed when one has already infected. The medication can generally take 6 months of time which consists of two phases, inpatient and outpatient. Mathematical models to analyze the spread of TB have been widely developed. One of them is the SEIR type model. In this model the population is divided into four groups, which are suspectible (S), exposed (S), infected (I), recovered (R). In fact, a TB patient needs to undergo medication with a period of time in order to recover. This article discusses a model of TB spread with considering the term of recovery (time delay). The model is developed in SIR type where the population is divided into three groups, suspectible (S), infected (I), and recovered (R). Here, the vaccine is given to the susceptible group and the time delay is considered in the group undergoing the medication.
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.
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