Role of macrophage in the disease dynamics of cutaneous Leishmaniasis: a delay induced mathematical study

Abstract

Leishmaniasis is endemic in 88 countries throughout Africa, Asia, Europe, and North and South America. It is a vector borne zoonosis with important animal reservoirs and has a two stage life cycle-within animal vector and mammalian host. In this research article, a mathematical model is considered to analyze the disease dynamics of Leishmaniasis consisting susceptible (uninfected) macrophage cell, early stage infected (promastogotes) macrophage cell, late stage infected (amastigotes) macrophage cell and parasite population. The focus is to study the progression of the disease caused by pathogen within mammalian cycle. To study the model in broader aspect, a time delay is introduced into the system as there is a time lag in the interaction between uninfected macrophage cell and parasite population and spread of the disease. Theoretical analysis and numerical simulations reveals that, the delay induced system exhibits changes in the progression pattern of infected and uninfected macrophage cell and parasite population. Control effect i.e. drug dosing can minimize the phagocytic state of macrophages and suppress the state change from promastigotes into amastigotes inside macrophages. Moreover delay induced control give better result than proposed model with control as healthy macrophage cell population reaches more stable nature. Optimal control theory facilitates a cost effective drug dose strategy that increases the healthy macrophage cell population, whereas decreases rest of the population.