Ghosh, Indranil (2025) Optimal control of fractional-order infectious disease models using gradient-based time-delay optimisation algorithm. Doctoral thesis, Sunway University.
Full text not available from this repository.Abstract
Fractional calculus extends differentiation and integration to noninteger orders, allowing more accurate simulation of systems with memory. This provides a unified way to model biological systems, including infectious diseases that exhibit memory effects. Mathematical models of infectious diseases with control strategies are often too complex to be solved analytically. Fractional derivatives, such as the Caputo derivative, satisfy classical conditions but suffer from singularities that lead to slow convergence and reduced robustness when modelling complex phenomena. To overcome these issues, this research aims to mathematically model and simulate infectious diseases using the fractional-order differential equations consisting of the nonsingular and nonlocal Caputo–Fabrizio (CF) and Atangana–Baleanu–Caputo (ABC) fractional derivatives. Furthermore, this study aims to implement various optimal control strategies for three-compartment (SIR) and eight-compartment (SIDARTHE) epidemiological models. Subsequently, the Toufik–Atangana numerical scheme is modified by combining the trapezoidal scheme and the fractional Euler scheme. The effectiveness of the modified scheme is demonstrated by error comparison with the exact solution. Through skilful discretisation of the fractional-order dynamical system using the Adams–Bashforth and the modified Toufik–Atangana numerical schemes, and the composite trapezoidal rules for cost and constraint functions, the optimal control problem is approximated as an optimal control problem governed by a discrete-time dynamical system with one, two, and multiple time delays. The gradient formulae of the cost and constraint functions are derived with respect to the decision variables. On this basis, a unified gradient-based optimisation algorithm is developed. This optimisation algorithm is then used to solve several fractional optimal control problems for which their exact solutions are available. Moreover, it is also applied to the fractional optimal control problems of the SIR and SIDARTHE models. The effectiveness of the proposed schemes is demonstrated by comparing numerical solutions of the CF and ABC fractional operator models with the exact solutions. The results show that it has higher accuracy than existing methods. Furthermore, this study highlights the progress achieved in the implementation of the CF derivative, obtaining results that are closer to the actual disease incidence data in Italy. The improvement is particularly noticeable at the fractional order of 0.7 in the SIDARTHE model. This clearly shows the influence of the memory properties of the fractional derivative. In addition, the study conducts cost optimisation for parameter changes over different time periods. The results are compared to the costs without control. Using the multiple-time-delay method, the cost optimisation for the SIR model achieves a maximum reduction of up to 53.46%. For the SIDARTHE model, the cost optimisation using the two-time-delay method results in a reduction of approximately 64.74%. The obtained numerical results provide valuable insight into the benefits of implementing control interventions
| Item Type: | Thesis (Doctoral) |
|---|---|
| Uncontrolled Keywords: | fractional differential equation; numerical methods; gradient-based time-delay optimisation algorithm; fractional optimal control problem; infectious disease models |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Sunway University > School of Mathematical Sciences |
| Depositing User: | Ms Yong Yee Chan |
| Date Deposited: | 26 Jul 2026 05:03 |
| Last Modified: | 26 Jul 2026 05:14 |
| URI: | http://repository.sunway.edu.my/id/eprint/3549 |
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