Mathematical Analysis of Repeated BCG Administration in Type 1 Diabetes: Improved Macrophage Response and Prolonged β-Cell Viability

This study develops an extended mathematical model to investigate innate immune dynamics in Type 1 Diabetes (T1D), focusing on the interplay between pro-inflammatory M1 macrophages, anti-inflammatory M2 macrophages, and pancreatic β-cells, which was shown in H.Hamam (2023). This model incorporates the immunomodulatory effect of Bacillus Calmette-Guérin (BCG) vaccination by representing each dose as a pulse-like input, implemented through a finite-duration Heaviside function, together with first-order elimination to describe the decay of the vaccine within the system. Simulation results after a single BCG pulse show a temporary decrease in M2 levels, followed by an increase in M2 macrophages, leading to a transient rise in β-cell levels. However, a key mechanism of this study is that repeated BCG doses generate a much clearer and more sustained improvement in β-cell levels compared to a single dose. Multiple-dose protocols produce more sustained reductions in inflammatory pressure, resulting in extended periods of β-cell preservation. Given uncertainties in several parameter values, a local sensitivity analysis was performed. The results show that parameters governing M2-mediated activation of β-cells