Investigating the evolutionary dynamics of second-line Mycobacterium tuberculosis drug resistance in Tanzania using hypercubic modelling and the Baum–Welch algorithm

Mycobacterium tuberculosis (MTB) continues to pose a significant threat to public health, particularly with the emergence of drug-resistant strains. Research shows that first-line anti-tuberculosis drugs are increasingly failing, and second-line drugs are also showing resistance. This study investigates the evolutionary dynamics of second-line drugs used against MTB, specifically Bedaquiline, Delamanid, Linezolid, Clofazimine, and Levofloxacin. Data were collected from the Tanzania National Institute of Medical Research (NIMR) at the Central Tuberculosis Reference Laborator Muhimbili Centre (CTRL). The data were analysed using a 5-hypercubic model, with parameters estimated using the Baum–Welch algorithm. The findings show that the most probable drug-resistant acquisition, independent of other drugs analysed, is Bedaquiline with a probability of 0.8660 and Levofloxacin with a probability of 0.134. The evolutionary pattern begins with Bedaquiline, followed by Levofloxacin, then Clofazimine, and finally either Linezolid or Delamanid, each with an equal probability of occurring. This highlights the evolutionary patterns of drug resistance, providing insights that can inform health experts and policymakers in developing evidence-based, effective interventions to combat this growing public health challenge. • Resistance of Mycobacterium tuberculosis to second-line drugs is growing. • The study examines resistance paths among Bedaquiline, Delamanid, Linezolid, Clofazimine, and Levofloxacin. • A 5-hypercubic model was used to analyse evolutionary drug resistance patterns. • The Baum-Welch algorithm estimated model parameters for public health insights. • Most likely paths: { } → B D Q → L F X → C F Z → L Z D → D L M or { } → B D Q → L F X → C F Z → D L M → L Z D