Complex dynamics of a fractional-order epidemic system integrating with fractional-order optimal control and PRCC analysis
Abstract
Classical ODE-based compartmental models have laid the groundwork for epidemic modeling; however, they do not account for behavioral changes throughout an outbreak. This research introduces a three-compartmental fractional-order model that encapsulates this constraint via the memory effect. The biological viability of existence and the uniqueness of the solution of the proposed model have been assessed. Consequently, we have proved the positivity and ultimate boundedness of the system solutions. Utilizing the next-generation matrix framework, the threshold parameter, R 0 , is derived. The asymptotic study of the model reveals its ‘threshold behavior’, undergoing a transcritical bifurcation at β = β ∗ . The model is augmented to include treatment and media controls by establishing an optimal control framework concentrated on reducing the overall cost and number of infections. The existence and uniqueness of the optimal control solution are proved. Model parameters are ranked via global sensitivity analysis using PRCC to identify the most influential ones. This method ranks each variable based on its sensitivity. An economic analysis of potential combinations of control strategies has been conducted to identify the optimal strategy for disease management. The analytical conclusions are validated by numerical simulations in MATLAB.
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BibTeX
@article{sahoo2026complex,
title = {{Complex dynamics of a fractional-order epidemic system integrating with fractional-order optimal control and PRCC analysis}},
author = {Kulamani Sahoo and Snehasis Barman and Anup Kumar Barman and Tapan Kumar Kar and Sarada Mohapatra and David Bassir and Ghanshyam Tejani},
journal = {Results in Control and Optimization},
year = {2026},
month = oct,
doi = {10.1016/j.rico.2026.100851},
url = {https://hal.science/hal-05820440v1},
note = {CC BY-NC-ND},
}
RIS
TY - JOUR
TI - Complex dynamics of a fractional-order epidemic system integrating with fractional-order optimal control and PRCC analysis
AU - Kulamani Sahoo
AU - Snehasis Barman
AU - Anup Kumar Barman
AU - Tapan Kumar Kar
AU - Sarada Mohapatra
AU - David Bassir
AU - Ghanshyam Tejani
PY - 2026
DA - 2026/10/20
JO - Results in Control and Optimization
DO - 10.1016/j.rico.2026.100851
UR - https://hal.science/hal-05820440v1
AB - Classical ODE-based compartmental models have laid the groundwork for epidemic modeling; however, they do not account for behavioral changes throughout an outbreak. This research introduces a three-compartmental fractional-order model that encapsulates this constraint via the memory effect. The biological viability of existence and the uniqueness of the solution of the proposed model have been assessed. Consequently, we have proved the positivity and ultimate boundedness of the system solutions. Utilizing the next-generation matrix framework, the threshold parameter, R 0 , is derived. The asymptotic study of the model reveals its ‘threshold behavior’, undergoing a transcritical bifurcation at β = β ∗ . The model is augmented to include treatment and media controls by establishing an optimal control framework concentrated on reducing the overall cost and number of infections. The existence and uniqueness of the optimal control solution are proved. Model parameters are ranked via global sensitivity analysis using PRCC to identify the most influential ones. This method ranks each variable based on its sensitivity. An economic analysis of potential combinations of control strategies has been conducted to identify the optimal strategy for disease management. The analytical conclusions are validated by numerical simulations in MATLAB.
SN - 2666-7207
ER -