Mathematical Transmission of Tuberculosis (TB) with Detection of Infected Undetected
I. A. Olopade *
Department of Mathematics and Statistics, Federal University Wukari, P.M.B. 1020, Wukari, Taraba State, Nigeria.
S. O. Ajao
Department of Mathematics and Computer Science, Elizade University, P.M.B. 002, Ilara-Mokin, Ondo State, Nigeria.
G. A. Adeniran
Department of Physical Sciences, Chrisland University, P.M.B. 2131, Abeokuta, Ogun State, Nigeria.
A. K. Adamu
Department of Mathematics and Statistics, Federal University Wukari, P.M.B. 1020, Wukari, Taraba State, Nigeria.
S. O. Adewale
Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology (LAUTECH), P.M.B. 4000, Ogbomoso, Oyo State, Nigeria.
O. R. Aderele
Department of Mathematics and Statistics, College of Applied sciences, Lagos State University of Science and Technology, Ikorodu, Lagos, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Six (6) new compartmental epidemiological models were developed to investigate the detection of undetected infected and the parameters that fuel the increase of Basic Reproduction Number ( ) in the dynamical spread of Tuberculosis (TB). Qualitative analysis of the model reveals well posedness and uniqueness of the solution. Basic reproduction number ( ) was computed by next generation matrix as well as the stability of model equilibrium. It was established that the model has two equilibrium points, namely; disease-free equilibrium which is locally asymptotically stable whenever and unstable otherwise, giving rise to the existence of the endemic equilibrium whenever .
Sensitivity analysis of the parameters in basic reproduction number was carried out to determine the parameters that fuel the spread of TB in the society. Analysis shows that effective contact rate and fast progressor are the major parameters that increase the basic reproduction number most. This analysis will help the medical practitioners to provide adequate intervention strategies and to work on the parameters that increase the spread of the disease.
Keywords: Tassel, Mycobacterium tuberculosis, Wood, critical points, Seeding,, basic reproduction number, epigeal germination, sensitivity, simulation