Mathematical modeling of childhood infectious diseases using fractional derivatives and control strategies
Year: 2026
Type: article
Abstract: Globally, childhood infectious diseases present persistent public health challenges, especially in underserved regions with constrained access to healthcare and vaccinations. Aiming to encapsulate the memory-dependent and hereditary aspects of childhood disease dynamics, this work presents a new fractional-order epidemiological framework using the Caputo-Fabrizio derivative. It incorporates two dynamic control strategies-vaccination and isolation/treatment-to represent realistic intervention measures. Through the Laplace-Adomian Decomposition Method, we achieved analytical solutions and numerical solutions were found using Euler's numerical scheme. The epidemical threshold parameter is derived and the impact of key parameters on it is investigated. The no-infection scenario and persistent infection steady states are determined, and evaluation of stability both locally and globally are carried out for the endemic steady state. To further explore, our system’s dynamic behavior, the stability of the model solution is analyzed using the Sumudu transform, which is well-suited for fractional models with non-singular kernels such as the CF operator. Fundamental properties of the model-existence, uniqueness, positivity, and boundedness- are rigorously proven. Pontryagin’s optimality criterion are utilized for applying Control optimization theory for deriving the Hamiltonian system and determining optimal control strategies that minimize infection levels and intervention costs while maximizing recovery rates. Computational outcomes corroborate the theoretical predictions, illustrating that the integrated control strategy effectively mitigate childhood disease outbreaks.
Language: English
Field: Medicine
Domain: Health Sciences
Open Access status: gold
Estimated APC paid: $1,470
OpenAlex ID: W7131105071