Application of an Optimal Control Therapeutic Approach for the Memory-Regulated Infection Mechanism of Leprosy through Caputo–Fabrizio Fractional Derivative

Xianbing Cao, Salil Ghosh, Sourav Rana, Homagnic Bose and Priti Kumar Roy ()
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Xianbing Cao: School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China
Salil Ghosh: Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, India
Sourav Rana: Department of Statistics, Visva-Bharati University, Santiniketan 731235, West Bengal, India
Homagnic Bose: Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, India
Priti Kumar Roy: Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, India

Mathematics, 2023, vol. 11, issue 17, 1-26

Abstract: Leprosy (Hansen’s disease) is an infectious, neglected tropical skin disease caused by the bacterium Mycobacterium leprae ( M. leprae ). It is crucial to note that the dynamic behavior of any living microorganism such as M. leprae not only depends on the conditions of its current state (e.g., substrate concentration, medium condition, etc.) but also on those of its previous states. In this article, we have developed a three-dimensional mathematical model involving concentrations of healthy Schwann cells, infected Schwann cells, and M. leprae bacteria in order to predict the dynamic changes in the cells during the disease dissemination process; additionally, we investigated the effect of memory on system cell populations, especially on the M. leprae bacterial population, by analyzing the Caputo–Fabrizio fractionalized version of the model. Most importantly, we developed and investigated a fractionalized optimal-control-induced system comprising the combined drug dose therapy of Ofloxacin and Dapsone intended to achieve a more realistic treatment regime for leprosy. The main goal of our research article is to compare this fractional-order system with the corresponding integer-order model and also to distinguish the rich dynamics exhibited by the optimal-control-induced system based on different values of the fractional order ζ ∈ ( 0 , 1 ) . All of the analytical results are validated through proper numerical simulations and are compared with some real clinical data.

Keywords: leprosy; mathematical modelling; optimal control; memory effect; Caputo–Fabrizio fractionalized system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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