Modelling of a drug resistant tuberculosis for the contribution of resistance and relapse in Xinjiang, China

Tuberculosis has been prevalent in Xinjiang with severe drug resistance situation. It is unclear that which Mycobacterium tuberculosis (M.tb) infections (drug sensitive or drug resistant) most affected the tuberculosis incidence, how to identify the relative contribution of primary and acquisition resistance attributable to drug resistant tuberculosis incidence and relapse percentage in drug sensitive M.tb infection in Xinjiang. In this paper, a dynamical transmission model of drug resistant tuberculosis with fast/slow progression (both in drug sensitive and drug resistant M.tb transmission) and relapse is addressed by incorporating acquisition resistance and primary resistance. Theoretically, it is proved that the disease free equilibrium is globally asymptotically stable when the basic reproduction number $ \mathcal{R}_0\leq1 $, whereas the disease is uniformly persistent, and there exists at least one endemic equilibrium if $ \mathcal{R}_0>1 $. The model is fitted to the newly monthly tuberculosis cases infected by drug sensitive and drug resistant M.tb from 2017 to 2018 in Xinjiang by carrying out Markov chain Monte Carlo algorithm, and it is identified that the contribution percentages of drug sensitive and drug resistant M.tb infections separately reach 80.07% and 19.93% among incident cases of tuberculosis, which illustrates that drug sensitive M.tb transmission is a predominant cause of tuberculosis prevalence in Xinjiang during 2017-18. Moreover, it is estimated that primary rather than acquisition resistance accounts for 74.88% of all incident drug resistant tuberculosis, and the mean relapse percentage is approximately 0.5% but increasing month by month in 2017-18. Our results suggest that early diagnosis and screening (including new tests and drug regimens) and thorough treatment of drug sensitive tuberculosis are the more effective measures in controlling tuberculosis transmission in Xinjiang.