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

Year 2018, Issue: 21, 94 - 106, 27.02.2018

Virendra Kumar Gupta Sandeep Kumar Tiwari Shivram Sharma , Lakhan Nagar

https://izlik.org/JA65HC97SA

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

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