Fractional-order modeling and numerical simulation of diphtheria transmission in Rohingya refugee settlements using the fractional Adams-Bashforth-Moulton method

Fractional order derivatives have become increasingly significant in mathematical modeling of infectious disease dynamics due to their ability to capture memory and hereditary properties of biological processes. In this study, we adopt and analyze a fractional order Susceptible-Latent-Infectious-Recovered (SLIR) model to investigate the spread of diphtheria among the Rohingya refugee population in Bangladesh. The model incorporates the Caputo definition of the fractional derivative and is solved numerically using the Fractional Adams-Bashforth-Moulton method (FABMM). Model parameters, including disease transmission and recovery rates, are estimated using available epidemiological data. The impact of varying the fractional order and other key parameters on the progression and control of the outbreak is explored through comprehensive numerical simulations. Graphical representations of daily and cumulative case trajectories for different fractional orders are presented, highlighting the effectiveness of fractional modeling in forecasting and controlling outbreaks. The results suggest that fractional order models provide more flexible and realistic predictions compared to classical integer-order approaches. These findings can aid the Bangladeshi government and humanitarian organizations in developing effective disaster response and public health strategies for preventing and managing diphtheria outbreaks.

کلیدواژه ها:

Mathematical modeling ، Epidemiology ، Fractional calculus ، Caputo sense ، FABMM