Mathematical analysis of a three-strain tuberculosis transmission model

Abstract

In recent years, bacteria have become resistant to antibiotics, leading to a decline in the effectiveness of antibiotics in treating infectious diseases. A mathematical model for multi-strain tuberculosis transmission dynamics to assess the burden of drug-sensitive, multidrug-resistant and extensively drug-resistant tuberculosis is formulated and analyzed. Each single strain submodel is shown to exhibit backward bifurcation when the threshold parameter is less than unity. Both analytical and numerical results show that resistance to drugs increase with increase in drug use, that is, active tuberculosis treatment results in a reduction of drug sensitive and increase in multidrug-resistant tuberculosis. Furthermore, use of second line drugs results in a decrease of the multidrug-resistant and increase of extensively drug resistant tuberculosis as most cases of multidrug resistant tuberculosis occur as a result of inappropriate, misuse or mismanaged treatment. Both the analytic results and numerical simulations suggest that quarantine of extensively drug resistant TB cases in addition to treatment of other forms of TB may be able to reduce the spread of the epidemic in poor resource-settings.