A Fractional Calculus Approach to Pneumonia Transmission: Fractional-Order Dynamics of Pneumonia, with Intervention Assessment, and Epidemiological Data Fitting - Softcover

Inhaltsangabe

This book investigates the transmission dynamics of pneumonia using a fractional-order mathematical modeling framework that incorporates multiple intervention strategies such as vaccination, treatment, reinfection, and environmental control. The model applies three types of fractional differential operators Caputo, Caputo-Fabrizio, and Atangana-Baleanu-to capture memory effects in the spread of the disease. Theoretical analysis confirms the existence and uniqueness of the model solutions using fixed-point theory. To validate the model, it was fitted to monthly pneumonia hospitalization data for children aged 0-14 years in England from January 2021 to March 2024. Model parameters were estimated through least-squares optimization, and the results showed strong agreement between the simulated outcomes and the real data. Numerical simulations revealed that increasing the fractional order slows the rate of disease transmission, reduces the peak number of infections, and extends the duration of outbreaks, reflecting the memory characteristics of fractional systems.

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