DOI: https://doi.org/10.14710/jfma.v4i2.12049

ANALYSIS OF TUBERCULOSIS DYNAMICAL MODEL WITH DIFFERENT EFFECTS OF TREATMENT

*Anindita Henindya Permatasari  -  DIponegoro University, Indonesia
Robertus Heri Soelistyo Utomo  -  DIponegoro University, Indonesia

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Abstract
A tuberculosis model that integrates pre-infection and active infection stages along with two treatment parameters was studied. The model also considered the death rate due to pre-tuberculosis infection. The basic reproduction ratio was used to investigate the local and global stability of the equilibrium point. The local stability of uninfected equilibrium was analysed using Routh Hurwitz criteria. The existence of endemic equilibrium was given. After we achieved the endemic equilibrium, the global stability of the endemic equilibrium was analyzed using the Lyapunov function. A numerical simulation was studied to illustrate the effect of the treatment on the spread of the tuberculosis disease.

 

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
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  1. Loddenkemper R, Lipman M, Zumla A, "Clinical Aspects of Adult Tuberculosis", Cold Spring Harb Perspect Med, vol. 6, no. 1, 2015
  2. K.G. Simon, K. Iyawoo, "Management Issue in Tuberculosis in the Asia-Pasific Region", Medical Progress CMP Medica, vol. 32, no.10, pp.486–490, 2005
  3. World Health Organization, Global Tuberculosis Report 2015, Geneva: World Health Organization, 2015
  4. World Health Organization, Global Tuberculosis Report 2013, Geneva : World Health Organization, 2013
  5. US Preventive Services Task Force. "Screening for Latent Tuberculosis Infection in Adults: US Preventive Services Task Force Recommendation Statement". JAMA., vol. 316, no. 9, pp. 962–969, 2016
  6. H. Getahun, A. Matteelli, R.E.Chaisson, et al, "Latent Mycobacterium Tuberculosis Infection", N Engl J Med, vol. 372, pp. 2127–2135, 2015
  7. K.J. Seung, S. Keshavjee, M.L. Rich, "Multidrug-Resistant Tuberculosis and Extensively Drug-Resistant Tuberculosis", Cold Spring Harb Perspect Med., vol. 5, no. 9, 2015
  8. S. Bowong and J.J Tewa, "Global Analysis of a Dynamical Model for Transmission of Tuberculosis with a General Contact Rate", J. Commun. Nonlinear Sci. Numer. Simul., vol. 15, pp. 3621-3631, 2010
  9. H.F. Huo, S.J. Dang, Y.N. Li, "Stability of a two-strain tuberculosis model with general contact rate", Abst. Appl. Anal., vol. 2010, pp. 1-31, 2010
  10. Y. Yu, Y. Shi, and W. Yao, , J. Infect. Dis. Model., vol. 3, pp. 362–372, 2018
  11. Diekmann, R., and Heesterbeek, JAP., John Wiley and Sons, Chichester, UK, 2000
  12. S. Bowong and J.J Tewa, "Mathematical Analysis of a Tuberculosis Model with Differential Inefectivity ", J. Commun. Nonlinear Sci. Numer. Simul., vol. 14, pp. 4010–4021, 2009
  13. H.F. Huo and L.X. Feng, "Global Stability of an Epidemic Model with Incomplete Treatment and Vaccination", Discrete Dyn. Nat. Soc., vol. 2012, pp. 1–14, 2012
  14. H.F. Huo and M.X. Zou, "Modelling Effects of Treatment at Home on Tuberculosis Transmission Dynamics", J. Appl. Math. Model., vol. 40, pp. 9474–9484, 2016
  15. P. Rodriguesa, M.G.M. Gomesa, C. Rebelo, "Drug Resistance in Tuberculosis-a Reinfection Model", Theor. Popul. Biol., vol. 71, pp. 196-212, 2007
  16. R.M.G.J Houben, P.J. Dodd, "The Global Burden of Latent Tuberculosis Infection: A Re-Estimation Using Mathematical Modelling", PLoS Med., vol. 13, 2016
  17. A. Agyeman, R. Ofori, "Tuberculosis—an overview ", J. Public Health Emerg. , vol. 1, no.7, 2017
  18. F A Taqiya et al, "Local Stability Analysis for Tuberculosis Epidemic with SI1I2R Model", J. Phys.: Conf. Ser., vol. 1943, 012132, 2021
  19. N A Lestari et al, "Local Stability Analysis for Tuberculosis Epidemic Model with Different Infection Stages and Treatments", J. Phys.: Conf. Ser., vol. 1943, 012120, 2021
  20. K.P Wijaya, Sutimin, E. Soewono, and T. Gotz, " On the Existence of a Nontrivial Equilibrium in Relation to the Basic Reproductive Number", Int. J. Appl. Math. Comput. Sci., vol. 27, no. 3, 2017
  21. Sutimin, R. Herdiana, R.H.S. Utomo, and A.H. Permatasari, "Stability Analysis of Tuberculosis Epidemic Model with Saturated Infection Force ", E3S Web of Conferences, vol. 202, 12023, 2020
  22. Z. Ma, J. Liu, J. Li, “Stability Analysis for Differential Infectivity Epidemic Models”, Nonlinear Analysis RWA, vol. 4, pp. 841-856, 2003
  23. A. Iggidr, J. Mbang, G. Sallet, J.J. Tewa, “Multi-compartment models”, Discrete Contin. Dyn. Syst. Supp., vol. 2007, pp. 506-519, 2007
  24. C.C. McCluskey, “Lyapunov functions for tuberculosis models with fast and slow progression”, Math. Biosci. Eng., vol. 3, pp. 603-614, 2006
  25. H. Guo, M.Y. Li, “Global dynamics of a staged progression model for infectious diseases”, Math. Biosci. Eng., vol. 3, pp. 513-525, 2006
  26. J. Liu, T. Zhang, “Global stability for a tuberculosis model”, Math. Comp. Model., vol 54, pp 836-845, 2011

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