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 (Sh), exposed humans (Eh), infectious humans (Ih), and recovered humans (Rh). 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 whenWolbachia-free mosquitoes persist only (η = 0.6), when both types ofmosquitoes persist (η = 0.8), and whenWolbachia-carrying mosquitoes persist only (η=1). The objective of this study is to investigate the effectiveness of Wolbachia 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 © 2024 Tech Science Press. All rights reserved.
