Optimizing vertical transmission control: A hybrid neural network approach with <i>Wolbachia</i> for Zika virus

In this study, we investigate cutting-edge control strategies designed to address the global health threat posed by the Zika virus. Our exploration utilizes an advanced numerical approach, the artificial neural network (ANN), complemented by the hybrid efficiency of global and local search schemes. The research delves into the distinctive properties of Wolbachia, a bacterium, assessing its potential to hinder virus transmission and regulate the population of Ades aegypti mosquitoes, the primary carriers of the Zika virus. The study employs a rigorous mathematical framework, categorizing individuals into distinct compartments such as newborns, adults, Wolbachia-uninfected mosquitoes, and Wolbachia-infected mosquitoes. We pinpoint the disease-free equilibrium (DFE) and compute the basic reproductive number [Formula: see text]. Through extensive simulations, we scrutinize the model’s stability by manipulating critical parameters, including biting rates [Formula: see text], mosquito death rates [Formula: see text], and pregnancy delays [Formula: see text]. Importantly, our model incorporates the dynamics of Zika transmission and its correlation with microcephaly, both with and without the presence of Wolbachia. To numerically handle the dynamic model, we introduce a computational procedure, visually illustrating how the presence of Wolbachia significantly impacts infected classes, leading to a reduction in new cases and an improvement in overall model stability. We propose the utilization of the global optimization genetic algorithm (GA) and local search interior point algorithm (IPA) to solve the model. We devised an error-based objective function for the differential model, which was then optimized using the hybrid computational efficiency of GA-IPA. The validation of our proposed computational method, ANNPs-GA-IPA, involved a comprehensive comparison of the results obtained against reference solutions, affirming the accuracy and reliability of our approach.