A gradient-based time-delay optimization algorithm for evaluating control strategies in a fractional-order infectious disease model

Mathematical models have played a crucial role in developing strategies to control various diseases by identifying effective interventions. However, balancing different interventions to develop an optimal cost-effective strategy remains a significant challenge. In this study, the eight-compartmental...

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Published in:Computers in biology and medicine Vol. 196; no. Pt C; p. 110864
Main Authors: Ghosh, Indranil, Cheong, Huey Tyng, Teo, Kok Lay
Format: Journal Article
Language:English
Published: United States Elsevier Ltd 01.09.2025
Subjects:
Adams–Bashforth scheme
Algorithms
Caputo–Fabrizio derivative
Communicable Diseases - economics
Communicable Diseases - epidemiology
Fractional optimal control problem
Gradient-based optimization algorithm
Humans
Internal Medicine
Models, Biological
Other
SIDARTHE model
Time-delay
Adams–Bashforth scheme
Time-delay
SIDARTHE model
Caputo–Fabrizio derivative
Fractional optimal control problem
Gradient-based optimization algorithm
ISSN:0010-4825, 1879-0534, 1879-0534
Online Access:Get full text
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Summary:Mathematical models have played a crucial role in developing strategies to control various diseases by identifying effective interventions. However, balancing different interventions to develop an optimal cost-effective strategy remains a significant challenge. In this study, the eight-compartmental SIDARTHE model is refined with realistic cost and control functions. Four control interventions are undertaken to provide insights into the model. We combined the Adams–Bashforth method and the composite trapezoidal rule to design an innovative gradient-based time-delay optimization algorithm. To the best of our knowledge, this is the first study to perform cost optimization for parameter changes over different time periods in the field of fractional-order infectious disease modeling. The implementation of control interventions results in a cost reduction of approximately 35.61% compared to the initial cost when no control is used. This cost optimization effectively demonstrates the financial benefits of implementing control interventions in the model. Furthermore, this study highlights the progress achieved by implementing the Caputo–Fabrizio fractional derivatives, which provides a closer match with real-case disease incidence data from Italy, especially for fractional order of 0.7. This clearly shows the influence of the memory properties of the fractional operator. The numerical results obtained provide valuable insight into the benefits of implementing control interventions. Future research and practice can build on this foundation to enhance treatment strategies using our time-delay optimization algorithm. •A discrete-time time-delay optimization algorithm is proposed.•Optimizing cost over parameter changes in fractional-order disease modeling.•Four control strategies imposed with a cost function and dynamical system.•The algorithm optimized the cost approximately up to 35.61%.
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ISSN:0010-4825
1879-0534
1879-0534
DOI:10.1016/j.compbiomed.2025.110864