Exploring a Mathematical Model with Saturated Treatment for the Co-dynamics of Tuberculosis and Diabetes

In this research, we present a deterministic epidemiological mathematical model that delves into the intricate dynamics of the co-existence of tuberculosis and diabetes. Our comprehensive analysis explores the interplay and the influence of diabetes on tuberculosis incidence within a human population segregated into diabetic and non-diabetic subgroups. The model incorporates saturated incidence rates and treatment regimens for latent tuberculosis infections, offering insights into their impact on tuberculosis control. Theoretical findings reveal the emergence of a phenomenon known as backward bifurcation, attributed to exogenous reinfection and saturated treatment. Additionally, our study employs both local and global sensitivity analyses to identify pivotal parameters crucial to the spread of tuberculosis within the population. This investigation contributes valuable insights to the understanding of the complex relationship between tuberculosis and diabetes, offering a foundation for more effective disease control strategies. 2020 MSC classification: 34A34, 92D30, 92B05, 65H10.