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Modeling and Analysis of Malt-Drug Resistance Tuberculosis in Densly Populated Areas
American Journal of Applied Mathematics
Volume 4, Issue 1, February 2016, Pages: 1-10
Received: Nov. 18, 2015; Accepted: Dec. 4, 2015; Published: Jan. 4, 2016
Authors
Dancho Desaleng, School of Mathematical and Statistical Sciences Hawassa University, Hawassa, Ethiopia
Purnachandra Rao Koya, School of Mathematical and Statistical Sciences Hawassa University, Hawassa, Ethiopia
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Abstract
Tuberculosis is an airborne disease caused by the bacterium called mycobacterium tuberculosis. We have compartmentalized the population based on the exposed level to the disease and described the flow using a flowchart. Mathematical model is developed to describe the population dynamics of the compartments. The migration of people from infected class to exposed class, due to failure of continuing the medicine for any reason, is called here as Malt – drug resistance tuberculosis. The equilibrium points identified are disease free, endemic and epidemic. Equilibrium point analysis is made and has been included. Formula for reproduction number is derived. Numerical simulation study of the Mathematical model is conducted using ode45 function of MATLAB software. It is shown that the propagation of the disease is more in the more populated areas and less in the less populated areas.
Keywords
Tuberculosis, Mathematical Modeling, Equilibrium Points, Basic Reproduction Number, Stability Analysis, Numerical Simulation
Dancho Desaleng, Purnachandra Rao Koya, Modeling and Analysis of Malt-Drug Resistance Tuberculosis in Densly Populated Areas, American Journal of Applied Mathematics. Vol. 4, No. 1, 2016, pp. 1-10. doi: 10.11648/j.ajam.20160401.11
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