Mycobacterium leprae is a bacteria that causes the disease Leprosy (Hansen's
disease), which is a neglected tropical disease. More than 200000 cases are
being reported per year world wide. This disease leads to a chronic stage known
as Lepra reaction that majorly causes nerve damage of peripheral nervous system
leading to loss of organs. The early detection of this Lepra reaction through
the level of bio-markers can prevent this reaction occurring and the further
disabilities. Motivated by this, we frame a mathematical model considering the
pathogenesis of leprosy and the chemical pathways involved in Lepra reactions.
The model incorporates the dynamics of the susceptible schwann cells, infected
schwann cells and the bacterial load and the concentration levels of the bio
markers IFNβΞ³, TNFβΞ±, ILβ10, ILβ12, ILβ15 and ILβ17. We
consider a nine compartment optimal control problem considering the drugs used
in Multi Drug Therapy (MDT) as controls. We validate the model using 2D - heat
plots. We study the correlation between the bio-markers levels and drugs in MDT
and propose an optimal drug regimen through these optimal control studies. We
use the Newton's Gradient Method for the optimal control studies