TITLE:
Mathematical Analysis of the Transmission Dynamics of Tuberculosis
AUTHORS:
Jannatun Nayeem, Israt Sultana
KEYWORDS:
TUBERCULOSIS Model, SIR Model, Equilibria, Stability, Castillo-Chavez Theorem, Disease Dynamics, Disease Endemic Equilibrium
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.9 No.3,
August
30,
2019
ABSTRACT: We develop a dynamical model to understand the underlying dynamics of
TUBERCULOSIS infection at population level. The model, which integrates
the treatment of individuals, the infections of latent and recovery individuals,
is rigorously analyzed to acquire insight into its dynamical features. The
phenomenon resulted due to the exogenous infection of TUBERCULOSIS
disease. The mathematical analysis reveals that the model exhibits a backward
bifurcation when TB treatment remains of infected class. It is shown that, in
the absence of treatment, the model has a disease-free equilibrium (DEF)
which is globally asymptotically stable (GAS) and the associated reproduction
threshold is less than unity. Further, the model has a unique endemic equilibrium
(EEP), for a special case, whenever the associated reproduction threshold
quantity exceeds unity. For a special case, the EEP is GAS using the
central manifold theorem of Castillo-Chavez.