International Journal of Mathematical Sciences and Computing(IJMSC)

ISSN: 2310-9025 (Print), ISSN: 2310-9033 (Online)

Published By: MECS Press

IJMSC Vol.6, No.3, Jun. 2020

A SEIRS Model of Tuberculosis Infection Model with Vital Dynamics, Early Treatment for Latent Patients and Treatment of Infective

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Sulayman Fatima, Amit Mishra

Index Terms

Tuberculosis Transmission; Control Strategy; Disease Free Equilibrium; Effective Reproduction Number; Stability.


Tuberculosis is one of the most destructive bacteria in human being and the second cause of mortality after HIV/AIDS in the whole world. In this research work, a SEIRS of mathematical model for the transmission of tuberculosis incorporating vital dynamics, early therapy of patient with tuberculosis were studied and a model for treatment of infective as controls was developed. The effective reproduction number and the disease-free equilibrium was also analysed for the stability. The results revealed that the two controls reduce effective number below unity. Furthermore, it shows that early therapy of patient with tuberculosis is more effective in mitigating the spread of tuberculosis burden.

Cite This Paper

Sulayman Fatima, Amit Mishra," A SEIRS Model of Tuberculosis Infection Model with Vital Dynamics, Early Treatment for Latent Patients and Treatment of Infective", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.6, No.3, pp.42-52, 2020. DOI: 10.5815/ijmsc.2020.03.05


[1] Nyerere N, Luboobi LS, Nkansah-Gyekye Y. Modeling the effect of screening and treatment on the transmission of tuberculosis infections. Mathematical theory and Modeling. 2014;4(7):51-62.

[2] Bhunu CP, Garira W, Mukandavire Z, Zimba M. Tuberculosis transmission model with  chemoprophylaxis and treatment. Bulletin of Mathematical Biology. 2008 May 1;70(4):1163-91.

[3] Van den Driessche P, Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical biosciences. 2002 Nov 1;180(1-2):29-48.

[4] Castillo-Chavez C, Song B. Dynamical models of tuberculosis and their applications. Mathematical biosciences and engineering. 2004 Sep 1;1(2):361-404.

[5] Ugwa KA, Agwu IA. Mathematical Analysis Of The Endemic Equilibrium Of Thetransmission Dynamics Of Tuberculosis. International Journal of Scientific & Technology Research. 2013 Dec 25;2(12):263-9.

[6] Grange JM, Zumla A. The global emergency of tuberculosis: what is the cause?. The journal of the Royal Society for the Promotion of Health. 2002 Jun;122(2):78-81.

[7] WHO, Report, Global tuberculosis control: epidemiology, strategy, financing. Geneva:World Health Organization; 2009.

[8] Ziv E, Daley CL, Blower S. Potential public health impact of new tuberculosis vaccines. Emerging infectious diseases. 2004 Sep;10(9):1529.

[9] Daniel TM. The history of tuberculosis. Respiratory medicine. 2006 Nov 1;100(11):1862-70.

[10] Bhunu CP, Garira W. A two strain tuberculosis transmission model with therapy and    quarantine. Mathematical Modelling and Analysis. 2009 Jan 1;14(3):291-312.

[11] Feng Z, Huang W, Castillo-Chavez C. On the role of variable latent periods in mathematical models for tuberculosis. Journal of dynamics and differential equations. 2001 Apr 1;13(2):425-52.

[12] Liu L, Wang Y. A mathematical study of a TB model with treatment interruptions and two latent periods. Computational and mathematical methods in medicine. 2014;2014.

[13] Maliyoni M, Mwamtobe PM, Hove-Musekwa SD, Tchuenche JM. Modelling the role of diagnosis, treatment, and health education on multidrug-resistant tuberculosis dynamics. ISRN Biomathematics. 2012 Aug 16;2012.

[14] ADELEYE ES. Modelling The impact of BCG vaccines on tuberculosis epidemics. Journal of Mathematical Modelling and Application. 2014 Apr 22;1(9):49-55.

[15] Diekmann O, Heesterbeek JA. Mathematical epidemiology of infectious diseases: model building, analysis and interpretation. John Wiley & Sons; 2000 Apr 7.

[16] Feng Z, Castillo-Chavez C, Capurro AF. A model for tuberculosis with exogenous reinfection. Theoretical population biology. 2000 May 1;57(3):235-47.

[17] Blower SM, Mclean AR, Porco TC, Small PM, Hopewell PC, Sanchez MA, Moss AR. The intrinsic transmission dynamics of tuberculosis epidemics. Nature medicine. 1995 Aug;1(8):815.

[18] Picon PD, Bassanesi SL, Caramori ML, Ferreira RL, Jarczewski CA, Vieira PR. Risk factors for recurrence of tuberculosis. Jornal brasileiro de pneumologia. 2007 Oct;33(5):572-8.

[19] Dye C, Williams BG. Criteria for the control of drug-resistant tuberculosis. Proceedings of the National Academy of Sciences. 2000 Jul 5;97(14):8180-5.

[20] Dye C, Scheele S, Dolin P, Pathania V, Raviglione MC. for the WHO Global Surveillance and Monitoring Project. Global burden of tuberculosis: estimated incidence, prevalence, and mortality by country. Jama. 1999 Aug 18;282(7):677-86.

[21] Kuta FA, Somma SA, Tech M. Local Stability Analysis of a Tuberculosis Model incorporating Extensive Drug Resistant Subgroup FY Eguda, Ph. D.; NI Akinwande Ph. D. 2; S. Abdulrahman Ph. D. 2.

[22] Ronoh M, Jaroudi R, Fotso P, Kamdoum V, Matendechere N, Wairimu J, Auma R, Lugoye J. A mathematical model of tuberculosis with drug resistance effects. Applied Mathematics. 2016 Jul 25;7(12):1303.

[23] Sensitivity analysis of the parameters of a mathematical model of Hepatitis B virus transmission.

[24] Sulayman F. Modelling and analysis of the spread of cholera disease in Nigeria with environmental control. Research thesis, 2014 -

[25] Rohaeti E, Wardatun S, Andriyati A. Stability Analysis Model of Spreading and Controlling of Tuberculosis. Applied Mathematical Sciences. 2015;9(52):2559-66.

[26] Kar TK, Mondal PK. Global dynamics of a tuberculosis epidemic model and the influence of backward bifurcation. Journal of Mathematical Modelling and Algorithms. 2012 Dec 1;11(4):433-59.

[27] World Health Organization. Global tuberculosis report 2013. World Health Organization; 2013.