Application of an Optimal Control Therapeutic Approach for the Memory-Regulated Infection Mechanism of Leprosy through Caputo–Fabrizio Fractional Derivative
Leprosy (Hansen’s disease) is an infectious, neglected tropical skin disease caused by the bacterium <i>Mycobacterium leprae</i> (<i>M. leprae</i>). It is crucial to note that the dynamic behavior of any living microorganism such as <i>M. leprae</i> not only depen...
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MDPI AG
2023-08-01
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| author | Xianbing Cao Salil Ghosh Sourav Rana Homagnic Bose Priti Kumar Roy |
| author_facet | Xianbing Cao Salil Ghosh Sourav Rana Homagnic Bose Priti Kumar Roy |
| author_sort | Xianbing Cao |
| collection | DOAJ |
| description | Leprosy (Hansen’s disease) is an infectious, neglected tropical skin disease caused by the bacterium <i>Mycobacterium leprae</i> (<i>M. leprae</i>). It is crucial to note that the dynamic behavior of any living microorganism such as <i>M. leprae</i> 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 <i>M. leprae</i> 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 <i>M. leprae</i> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ζ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>. All of the analytical results are validated through proper numerical simulations and are compared with some real clinical data. |
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| last_indexed | 2024-03-10T23:18:19Z |
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| spelling | doaj.art-5095691b37b14048a64d2f71244c71d92023-11-19T08:30:00ZengMDPI AGMathematics2227-73902023-08-011117363010.3390/math11173630Application of an Optimal Control Therapeutic Approach for the Memory-Regulated Infection Mechanism of Leprosy through Caputo–Fabrizio Fractional DerivativeXianbing Cao0Salil Ghosh1Sourav Rana2Homagnic Bose3Priti Kumar Roy4School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, ChinaCentre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, IndiaDepartment of Statistics, Visva-Bharati University, Santiniketan 731235, West Bengal, IndiaCentre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, IndiaCentre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, IndiaLeprosy (Hansen’s disease) is an infectious, neglected tropical skin disease caused by the bacterium <i>Mycobacterium leprae</i> (<i>M. leprae</i>). It is crucial to note that the dynamic behavior of any living microorganism such as <i>M. leprae</i> 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 <i>M. leprae</i> 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 <i>M. leprae</i> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ζ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>. All of the analytical results are validated through proper numerical simulations and are compared with some real clinical data.https://www.mdpi.com/2227-7390/11/17/3630leprosymathematical modellingoptimal controlmemory effectCaputo–Fabrizio fractionalized system |
| spellingShingle | Xianbing Cao Salil Ghosh Sourav Rana Homagnic Bose Priti Kumar Roy Application of an Optimal Control Therapeutic Approach for the Memory-Regulated Infection Mechanism of Leprosy through Caputo–Fabrizio Fractional Derivative Mathematics leprosy mathematical modelling optimal control memory effect Caputo–Fabrizio fractionalized system |
| title | Application of an Optimal Control Therapeutic Approach for the Memory-Regulated Infection Mechanism of Leprosy through Caputo–Fabrizio Fractional Derivative |
| title_full | Application of an Optimal Control Therapeutic Approach for the Memory-Regulated Infection Mechanism of Leprosy through Caputo–Fabrizio Fractional Derivative |
| title_fullStr | Application of an Optimal Control Therapeutic Approach for the Memory-Regulated Infection Mechanism of Leprosy through Caputo–Fabrizio Fractional Derivative |
| title_full_unstemmed | Application of an Optimal Control Therapeutic Approach for the Memory-Regulated Infection Mechanism of Leprosy through Caputo–Fabrizio Fractional Derivative |
| title_short | Application of an Optimal Control Therapeutic Approach for the Memory-Regulated Infection Mechanism of Leprosy through Caputo–Fabrizio Fractional Derivative |
| title_sort | application of an optimal control therapeutic approach for the memory regulated infection mechanism of leprosy through caputo fabrizio fractional derivative |
| topic | leprosy mathematical modelling optimal control memory effect Caputo–Fabrizio fractionalized system |
| url | https://www.mdpi.com/2227-7390/11/17/3630 |
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