@article{Alhazmi2025, 
author = {Muflih Alhazmi and Safa M. Mirgani and Abdullah Alahmari and Sayed Saber},
title = {Application of LAPM and ABM methods to a fractional SCIR model of pneumonia diseases},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {11},
pages = {25667-25707},
keywords = {pneumococcal pneumonia, fractional-order model, stability analysis, nonlocal memory effects, numerical simulations, SCIR model},
url = {https://www.sciopen.com/article/10.3934/math.20251137},
doi = {10.3934/math.20251137},
abstract = {We develop a fractional SCIR (susceptible-carrier-infected-recovered) model for pneumococcal pneumonia using Caputo derivatives of order    0  <  ϱ  ≤  1 to capture memory effects from long carriage, waning immunity, and reinfection. The force of infection explicitly accounts for carriers' transmissibility. Using a next-generation approach, we derive the basic reproduction number              R        0   and prove the global asymptotic stability of the disease-free equilibrium when              R        0    <  1 and of the endemic equilibrium when              R        0    >  1 via Lyapunov functionals and a fractional LaSalle principle. Numerically, we combine the Laplace-Adomian-Padé method (LAPM) with a fractional Adams-Bashforth-Moulton scheme (ABM) to capture memory-driven transients. A sensitivity analysis identifies transmission intensity and routing into carriage as the dominant epidemic drivers, while treatment and mortality exert mitigating effects. A control extension yields a closed-form, control-adjusted              R        0  ; a minimal vaccination threshold; and an optimal control problem solved numerically. Finally, we outline a calibration workflow linking the model-predicted incidence to surveillance data, permitting a statistical estimation of the fractional order. Altogether, incorporating carriers and fractional memory modifies the thresholds and persistence conditions, producing dynamics that are more consistent with pneumococcal epidemiology.}
}