TITLE:
A Mathematical Model of Tuberculosis with Drug Resistance Effects
AUTHORS:
Marilyn Ronoh, Rym Jaroudi, Patrick Fotso, Victor Kamdoum, Nancy Matendechere, Josephine Wairimu, Rose Auma, Jonnes Lugoye
KEYWORDS:
Tuberculosis, Mtb, MDR, Reproduction Number, DFE, EE, Stability
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.12,
July
25,
2016
ABSTRACT: Despite the enormous progress in prevention
and treatment, tuberculosis disease remains a leading cause of death worldwide
and one of the major sources of concern is the drug resistant strain, MDR-TB
(multidrug resistant tuberculosis) and XDR-TB (extensively drug resistant
tuberculosis). In this work, we extend the standard SEIRS epidemiology model of
tuberculosis to include MDR-TB. For that, we considered compartments of
susceptible, exposed, infected, resistant to a first line of treatment and
recovered humans and we modeled the natural growth, the interactions between
these populations and the effects of treatments. We calculate the basic
reproduction number, , using the next generation method. The DFE and the EE are
established and their stability analysis done to show that they are locally and
globally asymptotically stable. Numerical analysis for the model with and
without delay is done and demonstrated that in the case of patients with both
active tuberculosis and MDR tuberculosis, both strains will still persist due
to lack of permanent immunity to tuberculosis while the recovered can still
lose their immunity to become susceptible again.