Sensitivity Analysis of Mathematical Modelling of Tuberculosis Disease With Resistance to Drug Treatments

Abstract

Drug resistance to the line of treatment is also of concerns in the control of Tuberculosis
disease in the world [11], an individual with drug resistance will still retain the disease even
after several treatment. In this study, we consider a mathematical model of a tuberculosis
disease with resistance to the first line of treatment, taking into consideration population of
children and adults. We considered six different compartment (S1S2EIRHR), an extension of
SEIR model by introducing two different susceptible classes (S1S2) and drug resistance(RH) to
the first line of treatment. The system was described by an ordinary differential equation, which
was solved algebraically to obtained the equilibrium point (disease free and endemic equilibrium
point). The next generation matrix was employed to evaluate the basic reproduction number
and column reduction matrix to get the local stability of the systems. It was observed that
the age group had bigger effect on the control of TB. The drug resistance had a little effect
on the total control of the disease. At the end, three effective measure were found,that would
help reach the major goal of the World Health Organization(WHO)which includes: to reduce
the exposed rate of the disease especially in the adults, increase the recovery rate and reduce
the transmission rate of the adults.