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Investigation of Buruli Ulcer and Cholera Mathematical Model Through Fractional Order Derivative Using Deep Neural Network |
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PP: 297-321 |
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doi:10.18576/pfda/120205
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Author(s) |
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Mohammed A. El-Shorbagy,
Adnan Sami,
Mati ur Rahman,
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Abstract |
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| Here, we present a comprehensive investigation of a complex epidemiological model incorporating power-law, exponential, and Mittag–Leffler kernels governed by the fractal–fractional Caputo (FFC) derivative. The model describes the dynamics of disease transmission and progression through multiple interacting compartments, including susceptible humans Sh, infected and recovered subgroups Ib,Ic,Rb,Rc,Rbc, and the interaction with environmental or vector-based reservoirs B and secondary susceptible/infected populations Sν , Iν . The FFC operator FFC Dτ ,κ is employed in each governing equation to capture the memory and hereditary effects inherent in biological systems. Key epidemiological processes, such as primary and secondary infections, cross-infection rates, recovery, and reinfection mechanisms, are explicitly incorporated. Both analytical and numerical techniques are utilized to examine the qualitative behavior and stability of the solutions within the FFC framework. A semi-analytical solution for the Buruli ulcer and cholera model is obtained using the Adams–Bashforth method. Numerical simulations are performed in MATLAB for both integer and non-integer orders within the interval (0,1). The simulation results demonstrate solution stability and single-point convergence, with a significant enhancement in stability observed for lower non-integer orders. Furthermore, the simulations are extended using a deep neural network approach for the considered model. Two hidden layers are employed, using hyperbolic tangent and linear activation functions, respectively. The dataset is divided into training, testing, and validation phases. Overall, the findings highlight the effectiveness and adaptability of fractal–fractional calculus in modeling complex temporal dynamics and provide deeper insights into disease management strategies in memory-dependent epidemiological environments. |
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