Handika Lintang Saputra(1), Sutimin Sutimin(2), Sutrisno Sutrisno(3*)

(1) Departemen Matematika, Universitas Diponegoro
(2) Departemen Matematika, Universitas Diponegoro
(3) Departemen Matematika, Universitas Diponegoro
(*) Corresponding Author


This paper deals with the analysis of tuberculosis disease spread model with saturated infection rate and the treatment effect. We analyze the dynamical behavior of the model to observe the stability peroperty of the model’s equilibrium points. The Routh-Hurwitz Theorem is used to analyze the local stability peroperty of the free disease equilibrium point whereas Transcritical Bifurcation principle is used to analyze the local stability property of the endemic equilibrium pont. The result show that the local stability property of the equilibrium points is depending on the basic reproduction number value calculated by the next generation matrix (NGM). When the basic reproduction number is less than 1, the free disease equilibrium point is locally asymptotically stable, and when it is greater than 1, the endemic equilibrium point is locally asymptotically stable. Numeric simulation results were presented to describe the evolution of the dynamical behavior and to understand the treatment effectiveness for the tuberculosis disease of the population. From the simulation results, it was derived that the treatment in the infected subpopulation had a better result than the one in latent.

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[1] Whang, S., Choi, S. and Jung, E., A dynamic model for tuberculosis transmission and optimal treatment strategies in South Korea, J. Theor. Biol., 279 (2011), 120-31.

[2] World Health Organization, Global Tuberculosis Report 2018, World Health Organization (2018),

[3] Esteva, L. and Matias, M., A Model for Vector Transmitted Diseases with Saturation Incidence, J. Biol. Syst., 9 (2001), 235–245.

[4] Zhang, J., Jia, J., and Song, X., Analysis of an SEIR epidemic model with saturated incidence and saturated treatment function, Sci. World J., 2014 (2014), 1-11.

[5] Elkhaiar, S. and Kaddar, A., Stability Analysis of an SEIR Model with Treatment, Res. Appl. Math., 1 (2017), 1-16.

[6] Fengying Wei, Rui Xue, Stability and extinction of SEIR epidemic models with generalized nonlinear incidence, Mathematics and Computers in Simulation, 170 (2020), 1-15.

[7] Bowong, S.and Tewa, J. J., Mathematical analysis of a tuberculosis model with differential infectivity, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 4010-4021.

[8] Huo, H. F. and Zou, M. X., Modelling effects of treatment at home on tuberculosis transmission dynamics, Appl. Math. Model., 40 (2016), 9474–9484.

[10] Yang, H. M., The basic reproduction number obtained from Jacobian and next generation matrices - A case study of dengue transmission modelling, BioSystems, 126 (2014), 52-75.

[11] Van Den Driessche, P. and Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.

[12] Gunawan, Bifurkasi Mundur pada Model Epidemi SEIV dengan Laju Insiden Nonlinear, J. Mat. Murni dan Terap. Epsilon, 10 (2016), 1–13.

[13] Manda, E. C., Within Host Dynamics for Treatment of R5 HIV Infection in the Langerhans, PhD Thesis, African Institute for Mathematical Sciences (AIMS), 2015.


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