Tuberculosis Reactivation and Reinfection Dynamics Modeling with Delay Differential Equations

Tuberculosis (TB) remains a major public health challenge due to its complex transmission dynamics, which are influenced by reactivation of latent infection, reinfection of recovered individuals, and time delays in disease progression. This study provides a differential delay equations model to investigate TB disease stability. This method offers a more reasonable representation of TB transmission by including reactivation and reinfection as well as time delays in incubation, recovery, and immunodeficiency. The findings underline the important part time delays play in determining TB disease dynamics. Longer incubation periods extend the latent phase, increasing undetected transmission; treatment delays extension infectious periods leading to more secondary infections and immunodeficiency delays increase the risk of reinfection and reactivation, affecting long-term disease persistence. Numerical simulations show that high reactivation rates extension infection cycles, amplify disease fluctuations, and delay stabilization, even when the basic reproduction number and the effective reproduction number indicate infection elimination. It increases the sensitivity of other parameters by increasing feedback loops. Conversely, low reactivation rates facilitate swift transitions to equilibrium and decrease endemicity. They decrease the sensitivity of additional parameters and constrain feedback effects. The findings indicate that reactivation, reinfection, and time delays are critical factors in the persistence and control of tuberculosis.