Virendra Kumar GUPTA, Sandeep Kumar TİWARİ, Shivram SHARMA, Lakhan NAGAR

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

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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[1] D. Morse, Brothwell and PJ. Ucko, (1964), Tuberculosis in Ancient Egypt, Am Rev Respir. Dis., 90: 524-541.
[2] D. Young, J. Stark and D. Kirschner, (2008), System Biology of Persistent Infection: Tuberculosis as a Case Study, Nature Reviews Microbiology, 6: 520-528.
[3] E. Klein, R. Laxminarayan, D. Smith and C. Gilligan, (2007), Economic incentives and Mathematical Models of Disease, Environment and Development Economics, 12: 707-732.
[4] H. Waaler, and S. Anderson, (1962), The Use of Mathematical Models in the Study of the Epidemiology of Tuberculosis, American Journal of Public Health, 52: 1002-1013.
[5] J. Semenza, J. Suk and S. Tsolova, (2010), Social Determinants of Infectious Diseases: A Public Health Priority, Euro Surveil, 15 : 1-3.
[6] J. Trauer, J. Denholm and E. McBryde, (2014), Construction of a Mathematical Model for Tuberculosis Transmission in Highly Endemic Regions of the Asia-Pacific. Journal of Theoretical Biology, 358 : 74-84.
[7] K. Zaman, (2010), Tuberculosis: A Global Health Problem. Journal of Health Population and Nutrition, 28: 111-113.
[8] R. Ullah, G. Zaman , and S. Islam, (2013), Stability Analysis of a General SIR Epidemic Model, VFAST Transaction on Mathematics, 1: 16-20.
[9] S. Sharma, V.H. Badshah, and V.K. Gupta, (2017), Analysis of a SIRI Epidemic Model with Modified Nonlinear incidence Rate and Latent Period, Asian journal of Mathematics and statistics, 10: 1-12.
[10] T. M. Daniel, (2006), History of Tuberculosis, Respiratory Medicine, 100: 1862-1870.
[11] T. Cohen, and M. Murray, (2004) Modelling Epidemics of Multidrug-Resistant m. Tuberculosis of Heterogeneous Fitness. Nature Medicine, 10: 1117-1121.

Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2014
Yayıncı: Naim Çağman

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