Mathematical Modelling to Exhibit the Influence of Latently Infected Schwann Cells in Leprosy: An Optimal Control-Based Study

Investigation of latency phase and it’s impact in leprosy remains a long-term debate for clinical and experimental scientists. In our research work, we have explicitly introduced the class of latently infected Schwann cells into the mathematical modeling framework along with susceptible Schwann cells, actively infected Schwann cells and M. leprae bacteria to explore the disease dynamics more accurately. Besides performing the stability analysis of the disease-free and endemic equilibriums, we have investigated the optimal control-induced system incorporating two drug therapies, Clofazimine and Dapsone using Pontryagin minimum principle. Optimal therapy shows much optimistic results as it correlates the tenure and drug dose of combined therapy more closely to the real world clinical data-based scenario. Numerical simulations are performed to validate all of our analytic outcomes using Matlab 2016a.