A Study of Qualitative Correlations Between CrucialBio-markers and the Optimal Drug Regimen of Type-I LepraReaction: A Deterministic Approach

Abstract

Mycobacterium leprae is a bacteria that causes the disease Leprosy (Hansen’s disease), whichis 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 damageof peripheral nervous system leading to loss of organs. The early detection of this Lepra reactionthrough 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 andthe chemical pathways involved in Lepra reactions. The model incorporates the dynamics of thesusceptible schwann cells, infected schwann cells and the bacterial load and the concentrationlevels of the bio markers IF N − γ, T N F − α, IL − 10, IL − 12, IL − 15 and IL − 17. We considera 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 correlationbetween the bio-markers levels and drugs in MDT and propose a optimal drug regimen throughthese optimal control studies. We use the Newton’s Gradient Method for the optimal control studies.