DOI: https://doi.org/10.14710/jfma.v5i2.15723

MATHEMATICAL ANALYSIS OF A TUBERCULOSIS MODEL WITH TWO DIFFERENT STAGES OF INFECTION

*Anindita Henindya Permatasari scopus  -  Dept. of Mathematics, Diponegoro University, Indonesia
Robertus Heri Soelistyo Utomo  -  Dept. of Mathematics, Diponegoro University, Indonesia

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Abstract

Tuberculosis is an infectious disease. This disease causes death and the world notes that Tuberculosis has a high mortality rate. A mathematical model of Tuberculosis with  two infection stages of individuals, pre infected and actively infected, is studied in this paper. The rate of treatment considered in this model. The stability analysis of the equilibrium is determined by the basic reproduction ratio. Routh Hurwitz linearization is used for investigate the local stability of uninfected equilibrium. While the global stability of endemic equilibrium is investigated by construct Lyapunov function. The effect of treatment in pre infected and actively infected stages can reduce the spread rate of Tuberculosis as shown in numerical simulation.

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
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  2. Maartens G, Wilkinson RJ, “Tuberculosis”, Lancet, vol. 370, pp. 2030-2043, 2007
  3. World Health Organization. 2015. Global Tuberculosis Report. Geneva, Switzerland: WHO
  4. Padmanesan Narasimhan, James Wood, Chandini Raina MacIntyre, Dilip Mathai Pulmonary Medicine, vol. 2013, no. 11, 2013
  5. Getahun H, Matteelli A, Chaisson RE, et al. “Latent Mycobacterium tuberculosis infection”, N Engl J Med, vol. 372, no. 22, pp. 2127–2135, 2015
  6. Churchyard GJ, Swindells S. “Controlling latent TB tuberculosis infection in high-burden countries: a neglected strategy to end TB”, PLoS Med, vol. 16, 2019
  7. Mack U, Migliori GB, Sester M, et al. “LTBI: latent tuberculosis infection or lasting immune responses to M. tuberculosis? A TBNET consensus statement”, Eur Respir J, vol. 33, pp. 956–973, 2009
  8. Houben RMGJ, Dodd PJ, “The global burden of latent tuberculosis infection: a re-estimation using mathematical modelling”, PLoS Med, vol. 13, 2016
  9. Agyeman A, Ofori R. “Tuberculosis—an overview”, J. Public Health Emerg, vol. 1, no. 7, pp. 1-11, 2017
  10. Bowong, S and Tewa, J J. “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
  11. Bowong, S and Tewa, J J. “Mathematical analysis of a tuberculosis model with differential inefectivity”, J. Commun. Nonlinear Sci. Numer. Simul., vol. 14, pp. 4010–4021, 2009
  12. Huo, H F and Feng, L X. “Global stability of an epidemic model with incomplete treatment and vaccination”, Discret. Dyn. Nat. Soc., vol. 2012, pp. 1-14, 2012
  13. Huo, H F and Zou, M X. J. Appl. Math. Model, vol. 40, pp. 9474–84, 2016
  14. Wijaya, KP., Sutimin, Soewono, E., and Gotz, T. “On the existence of a nontrivial equilibrium in relation to the basic reproductive number”, Int. J. Appl. Math. Comput. Sci., vol. 27, no. 3, pp. 623-636, 2017
  15. Diekmann, R., and Heesterbeek, JAP. (2000). Mathematical Epidemiology of Infectious Diseases. John Wiley and Sons, Chichester
  16. Taqiya, F A, et al. “Local stability analysis for tuberculosis epidemic with SI1I2R model”, J. Phys.: Conf. Ser., vol. 1943, no. 012132, 2021
  17. Lestari, N A, et al. “Local stability analysis for tuberculosis epidemic model with different infection stages and treatments”, J. Phys.: Conf. Ser., vol. 1943, no. 012120, 2021
  18. Z. Ma, J. Liu, J. Li, “Stability Analysis for Differential Infectivity Epidemic Models”, Nonlinear Analysis RWA, vol. 4, pp. 841-856, 2003
  19. A. Iggidr, J. Mbang, G. Sallet, J.J. Tewa, “Multi-compartment models”, Discrete Contin. Dyn. Syst. Supp., vol. 2007, pp. 506-519, 2007
  20. C.C. McCluskey, “Lyapunov functions for tuberculosis models with fast and slow progression”, Math. Biosci. Eng., vol. 3, pp. 603-614, 2006
  21. H. Guo, M.Y. Li, “Global dynamics of a staged progression model for infectious diseases”, Math. Biosci. Eng., vol. 3, pp. 513-525, 2006
  22. J. Liu, T. Zhang, “Global stability for a tuberculosis model”, Math. Comp. Model., vol 54, pp 836-845, 2011

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