Mathematical Model of Tuberculosis with Drug Resistance to the First and Second Line of Treatment

Authors : Virendra Kumar Gupta, Sandeep Kumar Tiwari, Shivram Sharma, Lakhan Nagar

Pages : 94-106

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Publication Date : 2018-02-27

Article Type : Research

Abstract :This study proposed a mathematical model of tuberculosis with drug resistance to a first and second line of treatment. The basic reproduction number for the model using next generation method is obtained. The equilibrium point of the model was investigated and also found the global stability of the disease free equilibrium and endemic equilibrium for the model. This study shows the effect of resistance rate of the first and second line of treatment to the infected and resistant population. If basic reproduction number is less than one, the disease free equilibrium is globally asymptotically stable and if basic reproduction number is greater than one, then the endemic equilibrium is a globally asymptotically stable. 
Keywords : Tuberculosis, Mycobacterium tuberculosis bacteria, Mtb, , developed multi-drug resistant, MDR, , Basic reproduction number, Stability