Mathematical Modelling of Pulmonary and Extra-pulmonary Tuberculosis
Journal Title: INTERNATIONAL JOURNAL OF MATHEMATICS TRENDS AND TECHNOLOGY - Year 2013, Vol 4, Issue 9
Abstract
Tuberculosis (TB) is a big public health problem in India. As per WHO TB-report 2011, India accounts for one fourth (approximately 26%) of the global TB incident cases. Each year nearly 20,00000 people in India develop TB, of which around 870000 are infectious cases. It is estimated that every day approximately 1000 Indians die due to TB. In this paper, a mathematical model is formulated for tuberculosis using ordinary differential equations which is similar to SEIR epidemic model. The entire population is divided into five compartments viz. susceptible (S), exposed (E), infectious with pulmonary tuberculosis (I) and extra-pulmonary tuberculosis (X) and treated (T). Basic reproduction number R0is defined and a relation is established for it. Steady state conditions are derived showing that when 0 R 1there is a disease free equilibrium which is locally asymptotically stable whereas for 0 R 1there exists an endemic equilibrium. Sensitivity of R0 to each parameter is analysed.
Authors and Affiliations
Nita H. Shah#1 and Jyoti Gupta
Keywords
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