A Mathematical Model of Tuberculosis with Drug Resistance Effects

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.