Dynamic analysis of a two-strain tuberculosis model with imperfect treatment on complex networks

Tuberculosis (TB) is a common human infection that is often fatal if left untreated. If not treated appropriately, it may not only lead to relapse but also to the development of drug-resistant TB. The increase in drug resistance has become a major obstacle to the treatment of TB, significantly increasing the burden of disease. Moreover, the probability of contact varies from person to person. Complex networks are a useful tool for addressing the impact of exposure heterogeneity on the dynamics of disease transmission. To this end, this paper investigates a two-strain TB model with imperfect treatment on complex networks, where the two strains are drug-sensitive and drug-resistant strains. We first derive the basic reproduction numbers and introduce the invasion reproduction numbers for each strain, which are key thresholds for studying the competition and coexistence of two strains. Then, under certain conditions, the global asymptotic stability of disease-free equilibrium, drug-resistant equilibrium, and coexistence equilibrium is demonstrated. The persistence of the model is also shown. In particular, we note that two strains coexist even if the drug-resistant strain has a lower basic reproduction number. Most strikingly, the drug-resistant strain persists even when its basic reproduction number is less than 1. Finally, we enrich our research findings numerically. It is worth mentioning that sensitivity analyses support that the transmission rate of the drug-sensitive strain has the greatest impact on TB prevalence. Thus, this reveals that reducing contact between infected and uninfected people is the most important public health intervention, taking precedence over treatment and reduction of relapses.