  Leprosy (Hansen's disease) is an infectious, neglected tropical disease
caused by the Mycobacterium Leprae (M. Leprae). Each year there are
approximately 2,02,189 new cases are detected globally. In the year 2017 more
than half million people were disabled due to leprosy and almost 50000 new
cases are added every year world wide. In leprosy, lepra reactions are the
major cause for nerve damage leading to disability. Early detection of lepra
reactions through study of biomarkers have important role in prevention of
subsequent disabilities. To our knowledge there seems to be very limited
literature available on within-host modeling at cellular level involving the
crucial biomarkers and the possible optimal drug regimen for leprosy disease
and lepra reactions. Motivated by these observations, in this study, we have
proposed and analyzed a three dimensional mathematical model to capture the
dynamics of susceptible schwann cells, infected schwann cells and the bacterial
load based on the pathogenesis of leprosy. We estimated the parameters from
various clinical papers to make the model more practical. The sensitivity of
couple of parameters was evaluated through PRCC method to find out the single
most influential parameter and also combination of two most influential
parameters was studied using SRCC method. The sensitivity of other remaining
parameters was evaluated using Sobol's index. We then have framed and studied
an optimal control problem considering the different medication involved in the
Multi Drug Therapy (MDT) as control variables. We further studied this optimal
control problem along with both MDT and steroid interventions. The finding from
this novel and comprehensive study will help the clinicians and public health
researchers involved in the process of elimination and eradication of leprosy.
