Mathematical modelling of tuberculosis disease spread with multidrug resistance effects

Tuberculosis (TB) is an infectious disease caused by Mycobacterium tuberculosis, which affects the lungs and other organs. In East Java, there were 87,048 TB cases, and only 53% of regions achieved the 90% treatment success target. A major challenge in TB control is drug resistance, including Multidrug-Resistant Tuberculosis (MDR-TB). Prevention is implemented through BCG vaccination, while treatment is administered using anti-tuberculosis drugs. This research models the spread of tuberculosis in East Java using two models, SVEITR (without resistance) and SVEITResR (with resistance), to analyse the pattern of disease spread based on data obtained from the East Java Provincial Health Office. The basic reproductive number (R0) is calculated using the next-generation method, and stability analysis is conducted at the Disease-Free Equilibrium (DFE) and Endemic Equilibrium (EE) to test the asymptotic stability of disease transmission The analysis of the SVEITResR mathematical model (R0=1.0987) shows it has a lower basic reproduction number than the SVEITR model (R0= 1.3007.). Both models indicate that the spread of tuberculosis in the East Java region has the potential to cause an outbreak. Numerical simulations using the fourth-order Runge-Kutta method project a significant decrease in the number of exposed individuals after 2024, while the number of infected individuals is expected to increase until 2025 before reaching a stable condition thereafter. Vaccination and first and second-line treatment effectively reduce exposure to infection and increase cure rates over time.