Vaccinated Susceptible Infected and Recovered (VSIR) Mathematical Model to Study the Effect of Bacillus Calmette-Guerin (BCG) Vaccine and the Disease Stability Analysis
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
 World Health Organization. Tuberculosis, Fact Sheet No.104. Retrieved
(Accessed on: March, 2007).
 Okyere, E, 2006.Deterministic Compartmental Models for HIV and TB,
African Institute for Mathematical Sciences. Retrieved from
 Global stability result for tuberculosis epidemic models research journal
of mathematics and statistics 4(1): 14:20-2012 ISSN 2040-750.
 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
 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.
 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.
 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.
 Hao Wang, Mathematical Modeling I preliminary, .pp 51-52.