Can IL-10 Inhibitor Therapy Alongside MDT Enhance Leprosy Treatment? A Comprehensive Mathematical Study

Leprosy is characterized by complex biological and cellular interactions, driven primarily by the interplay between Th${}_1$ and Th${}_2$ cells. In this study, we develop a deterministic mathematical model to investigate the interactions among healthy and infected Schwann cells, M. leprae bacteria, and Th${}_1$–Th${}_2$ immune responses. The positivity and boundedness of the proposed five-dimensional system are established, and the disease persistence condition is characterized in terms of the basic reproduction number (${\mathcal{R}}_0$). The existence conditions for the endemic equilibrium are derived, while the global asymptotic stability of the endemic state is established through the construction of an appropriate Lyapunov function. To evaluate the robustness of the proposed model, parameter sensitivity with respect to ${\mathcal{R}}_0$ is investigated using Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficient sensitivity analysis. Furthermore, Monte Carlo uncertainty analysis (UA) is incorporated to account for the inherent uncertainty in the system, whereas a Sobol-based global sensitivity analysis quantifies the contribution of individual model parameters to the overall uncertainty. To further validate the dynamical behavior of the proposed system numerically, Lyapunov exponents are computed using the Benettin (renormalization) algorithm. The impact of combined multidrug therapy (MDT) and IL-10 inhibitor therapy is subsequently investigated within an optimal control framework, and the corresponding optimal treatment strategies are derived using Pontryagin’s maximum principle. Numerical simulations demonstrate that suppressing the Th${}_2$-mediated weakening of the host immune response through IL-10 inhibitor therapy provides superior long-term control of leprosy. The proposed treatment strategy therefore identifies IL-10 inhibitor therapy as a promising adjunct immunomodulatory intervention alongside MDT for enhancing protective cellular immunity against M. leprae in a cost-effective manner.