Multiple-drug resistant tuberculosis (MDR-TB) arises mostly due to improper use of antibiotics and the failure of infected patients to strictly comply with their treatment regimen. An increase in tuberculosis morbidity, accompanied by an appearance of MDR-TB, has been documented since the early 1990s (for instance, in Estonia). The development and spread of MDR-TB has become a serious problem for the success of anti-TB control and elimination programs.
 
In this talk, a dynamical model for MDR-TB with exogenous re-infection will be presented. The model, which monitors the dynamics of both the drug-sensitive and drug-resistant TB strains, takes the general SEIT (Susceptible-Exposed-Infectious-Treated) from. Qualitative analysis of the model enables the determination of important epidemiological thresholds, such as the basic reprodution number. Further, it is shown that the model undergoes the phenomenon of backward bifurcation, which may characterize the dynamics of the model.  One of the main findings of this study is that once MDR-TB appears in a population, it can establish itself regardless of the presence of drug-sensitive TB in the population (although the former is derived from the latter). Numerical simulations confirm our theoretical analysis.

This is a joint work with A. Gumel (University of Manitoba).