Numerical Solution of SIR Model with Time Delay for Transmission of Tuberculosis Disease

Despite Malaysia's efforts to combat tuberculosis (TB) through strategies like early detection, effective treatment, and public awareness campaigns, the disease remains a significant health challenge, especially in specific regions and among vulnerable populations. The Susceptible-Infected-Recovered (SIR) model is a valuable tool for comprehending TB transmission dynamics, particularly the interactions between susceptible, infected, and recovered individuals; however, accurately modeling TB transmission involves addressing the critical factor of time delay, which includes the recovery period and the duration for an infected person to transition to the recovered state, essential for capturing the true dynamics of TB spread. This study analyzes the effect of recovery time delay on the SIR model using Fifth - Order Runge-Kutta (RK5) method, solving a system of delay differential equations (DDEs). The results demonstrate that the SIR model with recovery time delay exhibits distinct patterns for the period of recovery. The findings highlight the influence of time delay on the dynamics of the SIR model for TB in Malaysia, particularly in the growth of the infected population and prolonging the recovery of individuals.