A synthesized model of tuberculosis transmission featuring treatment abandonment

In this paper, we propose and justify a synthesized version of the tuberculosis transmission model featuring treatment abandonment. In contrast to other models that account for the treatment abandonment, our model has only four state variables or classes (susceptible, latent, infectious, and treated), while people abandoning treatment are not gathered into an additional class. The proposed model retains the core properties that are highly desirable in epidemiological modeling. Namely, the disease transmission dynamics is characterized by the basic reproduction number R0, a threshold value that determines the number of possible steady states and their stability properties. It is shown that the disease-free equilibrium is globally asymptotically stable (GAS) only if R0 < 1, while a strictly positive endemic equilibrium exists and is GAS only if R0 > 1. Analysis of the dependence of R0 on the treatment abandonment rate shows that a reduction of the treatment abandonment rate has a positive effect on the disease incidence and results in avoiding disease-related fatalities.