Modelling the Transitional Dynamics of Mycobacterium Tuberculosis Strain
The World Health Organization’s targets of eliminating Tuberculosis (TB) by 2050 is challenged by the emergence and spread of drug resistance TB. However, the traditional mechanism of resistance is that of acquired resistance, whereby the mycobacterium Tuberculosis (MTB) strain develops mutations under selective pressure of insufficient drug therapy. These mutations have the tendency of changing the drug target protein, restricting the bacteria to the anti-TB agent. We propose a discrete state markov chain model with three disease states: Drug Susceptible (DS), Multi Drug Resistant (MDR) and Extra Drug Resistant (XDR) to further study the transitional dynamics of the MTB strain. The study made use of a retrospective data on resistant pattern to first line and second line anti TB drugs. The structural properties of the model established life expectancies of DS and MDR strains as well as the probability of first resistance of the DS strain. Key estimates were assessed by the bootstrapping procedure which converged in estimates to the actual data. If the experiment were repeated infinitely many times, in 95 out of 100, the interval 2.782 x 10-7 to 0.018 will contain the true probability of first mutation of the DS strain. A key contribution of this study is the revealing therapeutic cycle of the treatment regime of the TB disease based on the TB progression data which saw the period after the 20th cycle of the treatment being prominent in some key strain dynamics. These findings may also help explain further the pharmacodynamic properties of the "first line" anti-Tuberculosis drugs for enhance TB treatment.
Journal of Medical and Biomedical Sciences (2016) 5(2), 13-23