TY - EJOU
AU - Faiz, Zeshan
AU - Ahmed, Iftikhar
AU - Baleanu, Dumitru
AU - Javeed, Shumaila
TI - A Novel Fractional Dengue Transmission Model in the Presence of Wolbachia Using Stochastic Based Artificial Neural Network
T2 - Computer Modeling in Engineering \& Sciences
PY - 2024
VL - 139
IS - 2
SN - 1526-1506
AB - The purpose of this research work is to investigate the numerical solutions of the fractional dengue transmission
model (FDTM) in the presence of Wolbachia using the stochastic-based Levenberg-Marquardt neural network
(LM-NN) technique. The fractional dengue transmission model (FDTM) consists of 12 compartments. The human
population is divided into four compartments; susceptible humans (*S*_{h}), exposed humans (*E*_{h}), infectious humans
(*I*_{h}), and recovered humans (*R*_{h}). Wolbachia-infected and Wolbachia-uninfected mosquito population is also
divided into four compartments: aquatic (eggs, larvae, pupae), susceptible, exposed, and infectious. We investigated
three different cases of vertical transmission probability (*η*), namely when Wolbachia-free mosquitoes persist only
(*η* = 0.6), when both types of mosquitoes persist (*η* = 0.8), and when Wolbachia-carrying mosquitoes persist only
(*η* = 1). The objective of this study is to investigate the effectiveness ofWolbachia in reducing dengue and presenting
the numerical results by using the stochastic structure LM-NN approach with 10 hidden layers of neurons for three
different cases of the fractional order derivatives (*α *= 0.4, 0.6, 0.8). LM-NN approach includes a training, validation,
and testing procedure to minimize the mean square error (MSE) values using the reference dataset (obtained by
solving the model using the Adams-Bashforth-Moulton method (ABM). The distribution of data is 80% data for
training, 10% for validation, and, 10% for testing purpose) results. A comprehensive investigation is accessible to
observe the competence, precision, capacity, and efficiency of the suggested LM-NN approach by executing the
MSE, state transitions findings, and regression analysis. The effectiveness of the LM-NN approach for solving the
FDTM is demonstrated by the overlap of the findings with trustworthy measures, which achieves a precision of up
to 10^{−4}.
KW - Wolbachia; dengue; neural network; vertical transmission; mean square error; Levenberg-Marquardt
DO - 10.32604/cmes.2023.029879