Fractional order modeling and solution of West Nile virus epidemic model in presence of Wolbachia.

This study investigates a deterministic mathematical model to analyze the dynamics of West Nile Virus (WNV) in the presence of Wolbachia-infected mosquitoes as a biocontrol strategy to reduce West Nile virus transmission. The model comprises twelve compartments, including four compartments for bird populations, four compartments for Wolbachia-free and four compartments for Wolbachia-infected mosquito populations. An artificial neural network (ANN) trained with the Levenberg-Marquardt (LM) algorithm is employed to solve the resulting complex nonlinear system. Using Caputo fractional derivatives, reference datasets for the model are generated numerically using the Adams-Bashforth-Moulton method. The ANN-LM framework partitions the data into training (70%), validation (15%), and testing (15%) subsets. Three scenarios of vertical transmission probabilities (η) of Wolbachia are evaluated: persistence of Wolbachia-free mosquitoes only (η = 0.6), coexistence of both type of mosquitoes (η = 0.8), and persistence of Wolbachia-infected mosquitoes only (η = 1). The model is further tested under fractional orders (α = 0.7, 0.8, 0.9). Simulations reveal that the Wolbachia dominant scenario (η = 1) combined with α = 0.9 reduces WNV prevalence in bird hosts by over 65%, confirming the bacterium's efficacy in blocking transmission. The ANN-LM method achieves high accuracy, with correlation coefficients exceeding 0.99, mean square errors as low as 1.6×10-3, and absolute errors consistently below 10-4. The plots for regression analysis and error histograms further validate the model's robustness. These findings highlight the potential of Wolbachia-based biocontrol strategies and neural network optimization in enhancing the precision and computational efficiency of fractional-order epidemiological models.