Critical observation of WHO recommended multidrug therapy on the disease leprosy through mathematical study

Leprosy is a skin disease and it is characterized by a disorder of the peripheral nervous system which occurs due to the infection of Schwann cells. In this research article, we have formulated a four-dimensional ODE-based mathematical model which consists of the densities of healthy Schwann cells, infected Schwann cells, M. leprae bacteria, and the concentration of multidrug therapy (MDT). This work primarily aims on exploring the dynamical changes and interrelations of the system cell populations during the disease progression. Also, evaluating a critical value of the drug efficacy rate of MDT remains our key focus in this article so that a safe drug dose regimen for leprosy can be framed more effectively and realistically. We have examined the stability scenario of different equilibria and the occurrence of Hopf-bifurcation for the densities of our system cell populations with respect to the drug efficacy rate of MDT to gain insight on the precise impact of the efficiency rate on both the infected Schwann cell and the bacterial populations. Also, a necessary transversality condition for the occurrence of the bifurcation has been established. Our analytical and numerical investigations in this research work precisely explores that the process of demyelination, nerve regeneration, and infection of the healthy Schwann cells are the three most crucial factors in the leprosy pathogenesis and to control the M. leprae-induced infection of Schwann cells successfully, a more flexible version of MDT regime with efficacy rate varying in the range η∈(0.025,0.059) for 100-120 days in PB cases and 300 days in MB cases obtained in this research article should be applied. All of our analytical outcomes have been verified through numerical simulations and compared with some existing clinical findings.