Using mathematical modeling to understand the effect of treatment efficacy of two-strain model of tuberculosis

Source abstract

This study focuses on the spread of tuberculosis, a contagious disease caused by Mycobacterium tuberculosis, with a special emphasis on the consequences of drug sensitivity and drug-resistant patients. Tuberculosis treatment normally lasts 6-8 months for newly infected persons, but can extend up to 2.5 years for patients with multidrug resistance. Despite the greater effort put in place to eradicate tuberculosis (TB), it has remained a major global health challenge, particularly in low- and middle-income countries This study presents a mathematical model of tuberculosis transmission patterns in both drug-sensitive and drug-resistant cases. We studied seven (7) compartments: susceptible, latently afflicted with DS-TB, latently infected with DR-TB, infectious with DS-TB, infectious with DR-TB, recovered with DS-TB, and recovered with DR-TB, and mathematically simulated natural growth, population interactions, and treatment effects. Disease-free equilibrium (DFE) and endemic equilibrium (EE) were identified. We determined the basic reproduction number which can be used to manage disease transmission dynamics, and thus established the requirements for local and global disease-free equilibrium stability using the Routh-Hurwitz criterion and the Lasalle-Lyapunov function, respectively. The examination of the stability of the disease-free equilibrium revealed that tuberculosis can be eradicated by reducing the rate of recovery of infected individuals with DS-TB and DR-TB, as well as the rate of natural death. The model's numerical analysis shows that tuberculosis will be eradicated in patients with both DS-TB and DR-TB if efforts to reduce DS-TB and DR-TB transmission rates are increased by continued treatment efficacy.