@Article{cmes.2023.029879,
AUTHOR = {Zeshan Faiz, Iftikhar Ahmed, Dumitru Baleanu, Shumaila Javeed},
TITLE = {A Novel Fractional Dengue Transmission Model in the Presence of Wolbachia Using Stochastic Based Artificial Neural Network},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {139},
YEAR = {2024},
NUMBER = {2},
PAGES = {1217--1238},
URL = {http://www.techscience.com/CMES/v139n2/55312},
ISSN = {1526-1506},
ABSTRACT = {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 (<i>S<sub>h</sub></i>), exposed humans (<i>E<sub>h</sub></i>), infectious humans
(<i>I<sub>h</sub></i>), and recovered humans (<i>R<sub>h</sub></i>). 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 (<i>η</i>), namely when Wolbachia-free mosquitoes persist only
(<i>η</i> = 0.6), when both types of mosquitoes persist (<i>η</i> = 0.8), and when Wolbachia-carrying mosquitoes persist only
(<i>η</i> = 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 (<i>α </i>= 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<sup>−4</sup>.},
DOI = {10.32604/cmes.2023.029879}
}