A computational fractional order model for optimal control of wearable healthcare monitoring devices for maternal health

Abstract

The post-COVID-19 landscape has propelled the global telemedicine sector to a projected valuation of USD 91.2 billion by 2022, with a remarkable compounded annual growth rate (CAGR) of 18.6% from 2023 to 2030. This paper introduces an analytical wearable healthcare monitoring device (WHMD) designed for the timely detection and seamless transmission of crucial health vitals to telemedical cloud agents. The fractional order modeling approach is employed to delineate the efficacy of the WHMD in pregnancy-related contexts. The Caputo fractional calculus framework is harnessed to show the device potential in capturing and communicating vital health data to medical experts precisely at the cloud layer. Our formulation establishes the fractional order model's positivity, existence, and uniqueness, substantiating its mathematical validity. The investigation comprises two major equilibrium points: the disease-free equilibrium and the equilibrium accounting for disease presence, both interconnected with the WHMD. The paper explores the impact of integrating the WHMD during pregnancy cycles. Analytical findings show that the basic reproduction number remains below unity, showing the WHMD efficacy in mitigating health complications. Furthermore, the fractional multi-stage differential transform method (FMSDTM) facilitates optimal control scenarios involving WHMD utilisation among pregnant patients. The proposed approach exhibits robustness and conclusively elucidates the dynamic potential of WHMD in supporting maternal health and disease control throughout pregnancy. This paper significantly contributes to the evolving landscape of analytical wearable healthcare research, highlighting the critical role of WHMDs in safeguarding maternal well-being and mitigating disease risks in edge reconfigurable health architectures.