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

Yıl 2018, Sayı: 21, 94 - 106, 27.02.2018

Öz

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. 

Kaynakça

  • [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.
Yıl 2018, Sayı: 21, 94 - 106, 27.02.2018

Öz

Kaynakça

  • [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.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Araştırma Makalesi
Yazarlar

Virendra Kumar Gupta Bu kişi benim

Sandeep Kumar Tiwari Bu kişi benim

Shivram Sharma

Lakhan Nagar Bu kişi benim

Yayımlanma Tarihi 27 Şubat 2018
Gönderilme Tarihi 11 Şubat 2018
Yayımlandığı Sayı Yıl 2018 Sayı: 21

Kaynak Göster

APA Gupta, V. K., Tiwari, S. K., Sharma, S., Nagar, L. (2018). Mathematical Model of Tuberculosis with Drug Resistance to the First and Second Line of Treatment. Journal of New Theory(21), 94-106.
AMA Gupta VK, Tiwari SK, Sharma S, Nagar L. Mathematical Model of Tuberculosis with Drug Resistance to the First and Second Line of Treatment. JNT. Şubat 2018;(21):94-106.
Chicago Gupta, Virendra Kumar, Sandeep Kumar Tiwari, Shivram Sharma, ve Lakhan Nagar. “Mathematical Model of Tuberculosis With Drug Resistance to the First and Second Line of Treatment”. Journal of New Theory, sy. 21 (Şubat 2018): 94-106.
EndNote Gupta VK, Tiwari SK, Sharma S, Nagar L (01 Şubat 2018) Mathematical Model of Tuberculosis with Drug Resistance to the First and Second Line of Treatment. Journal of New Theory 21 94–106.
IEEE V. K. Gupta, S. K. Tiwari, S. Sharma, ve L. Nagar, “Mathematical Model of Tuberculosis with Drug Resistance to the First and Second Line of Treatment”, JNT, sy. 21, ss. 94–106, Şubat 2018.
ISNAD Gupta, Virendra Kumar vd. “Mathematical Model of Tuberculosis With Drug Resistance to the First and Second Line of Treatment”. Journal of New Theory 21 (Şubat 2018), 94-106.
JAMA Gupta VK, Tiwari SK, Sharma S, Nagar L. Mathematical Model of Tuberculosis with Drug Resistance to the First and Second Line of Treatment. JNT. 2018;:94–106.
MLA Gupta, Virendra Kumar vd. “Mathematical Model of Tuberculosis With Drug Resistance to the First and Second Line of Treatment”. Journal of New Theory, sy. 21, 2018, ss. 94-106.
Vancouver Gupta VK, Tiwari SK, Sharma S, Nagar L. Mathematical Model of Tuberculosis with Drug Resistance to the First and Second Line of Treatment. JNT. 2018(21):94-106.


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