Pneumonia remains a major global health burden, especially
among children under five and the elderly, and is a leading cause of death in
many low- and middle-income countries. In this paper, we formulate a novel
fractional pneumonia model utilising the generalized Atangana–Baleanu (GAB)
derivative. Pneumonia remains a global health threat, particularly in regions
with limited medical infrastructure. We extend the traditional integer-order
compartmental model into a fractional framework to capture the hereditary
properties and memory effects of disease transmission. We establish the
existence and uniqueness of solutions for all compartments (Vaccinated V,
Susceptible S, Carrier C, Infected I, and Recovered R) using fixed-point
theory. This mathematical foundation ensures the biological feasibility of our
memory-dependent model, which has significant implications for understanding
persistent transmission patterns in pneumonia epidemiology. A numerical scheme
based on Newton polynomial interpolation is derived. Finally, we discuss the
comparative dynamics of the model relative to data trends for Iowa and
Mississippi, demonstrating that fractional-order derivatives provide superior
flexibility in fitting localised epidemic spikes compared to traditional
models. Our key finding shows that regions with higher vaccination efficacy
experience significantly flattened epidemic curves, highlighting the critical
importance of vaccination coverage in pneumonia control strategies.
Author(s) Details
Khan Sana Rahman
Department of Applied Science, Everest College of Engineering and
Technology, Chhatrapati Sambhajinagar, Maharashtra, India.
Please see the book here :- https://doi.org/10.9734/bpi/nhstc/v8/7117
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