Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30576
Vaccinated Susceptible Infected and Recovered (VSIR) Mathematical Model to Study the Effect of Bacillus Calmette-Guerin (BCG) Vaccine and the Disease Stability Analysis

Authors: Muhammad Shahid, Asif Mansoor, Muhammad Liaquat Ali, Nasir-uddin Khan, Mushtaq Hussain


Tuberculosis (TB) remains a leading cause of infectious mortality. It is primarily transmitted by the respiratory route, individuals with active disease may infect others through airborne particles which releases when they cough, talk, or sing and subsequently inhale by others. In order to study the effect of the Bacilli Calmette-Guerin (BCG) vaccine after vaccination of TB patient, a Vaccinated Susceptible Infected and Recovered (VSIR) mathematical model is being developed to achieve the desired objectives. The mathematical model, so developed, shall be used to quantify the effect of BCG Vaccine to protect the immigrant young adult person. Moreover, equations are to be established for the disease endemic and free equilibrium states and subsequently utilized in disease stability analysis. The stability analysis will give a complete picture of disease annihilation from the total population if the total removal rate from the infectious group should be greater than total number of dormant infections produced throughout infectious period.

Keywords: Bacillus Calmette-Guerin vaccine, disease-free equilibrium state, VSIR Quantification, disease stability analysis

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1189


[1] World Health Organization. Tuberculosis, Fact Sheet No.104. Retrieved from:, (Accessed on: March, 2007).
[2] Okyere, E, 2006.Deterministic Compartmental Models for HIV and TB, African Institute for Mathematical Sciences. Retrieved from :http//
[3] Global stability result for tuberculosis epidemic models research journal of mathematics and statistics 4(1): 14:20-2012 ISSN 2040-750.
[4] Colditz, G.A., T.F. Brewer, C.S. Berkey, M. Wilson and. Mosteller, 1995. ‘The efficacy of bacillus Calmette-grin vaccination of new born and infants in the prevention of tuberculosis: Meta-analyses of the published literature’. Pediatrics, jul:96(1 Pt 1): 29-35
[5] Rieder, H.L., 1999. ‘Epidemiologic Basis of Tuberculosis’.1st Ed., International Union Against Tuberculosis and Lung Disease, ISBN 2- 9504238-8-4 Ch:3, pp. 63-81.
[6] A.I. Enagi, M.O. Ibrahim, “Preventing Mother to Child Transmission of Tuberculosis Using Bacillus Calmette-Guérin Vaccine: A Deterministic Modeling Approach”, Research Journal of Mathematics and Statistics 3(2): 67-71, 2011 ISSN: 2040-7505© Maxwell Scientific Organization, 2011. Okyere, E., 2006.
[7] Vincent Ele Asor, Chidiebere Ugwu, “A New Mathematical Model to Simulate Infectious Disease Dynamics in Rivers State, Nigeria – I.”, Koriko and Yusuf, 2008. IJCSI International Journal of Computer Science Issues, Vol. 8, Issue 2, March 2011. ISSN (Online): 1694-0814.
[8] Hao Wang, Mathematical Modeling I preliminary, .pp 51-52.