Implementation of suitable optimal control strategy through introspection of different delay induced mathematical models for leprosy: A comparative study

Abstract

Involving intracellular delay into a mathematical model and investigating the delayed systems by incorporating optimal control is of great importance to study the cell‐to‐cell interactions of the disease leprosy. Keeping this in mind, we have proposed two different variants of delay‐induced mathematical models with time delay in the process of proliferation of Mycobacterium leprae bacteria from the infected cells and a similar delay to indicate the time‐lag both in the proliferation of M. leprae bacteria and the infection of healthy cells after getting attached with the bacterium. In this research article, we have performed a comparative study between these two delayed systems equipped with optimal control therapeutic approach to determine which one acts better to unravel the complexities of the transmission and dissemination of leprosy into a human body as far as scheduling a perfect drug dose regime depending on this analysis remains our main priority. Our investigations suggest that adopting optimal control strategy consisting of combined drug therapy eliminates the oscillatory behavior of the delayed systems completely. Existence of optimal control solutions are demonstrated in detail. To achieve the optimal control profiles of the drug therapies and to obtain the optimality systems, Pontryagin's Minimum principle with delay in state are employed for our controlled systems. Furthermore, the analytical as well as the numerical outcomes obtained in this research article indicate that the delayed bacterial proliferation and M. leprae‐induced infection model equipped with optimal control policy performs more realistically and accurately in the form of a safe and cost‐effective double‐drug therapeutic regimen. All the mathematical results are verified numerically and the numerical results are compared with some recent clinical data in our article as well.