The purpose of this work is to present the numerical solutions of the nonlinear mathematical Leptospirosis disease (LD) model using the computational performances of the artificial neural networks (ANNs) along with the optimization procedures based on the global search genetic algorithm (GA) and local search active-set algorithm (ASA) scheme, i.e., ANNs-GA-ASA. LD is a zoonotic disease that is occurring in the whole world, obtained by rodents that become the reason of death in the people. The LD model based on the susceptible-infected-recovered, i.e., SIR, is used to solve the mechanisms of disease spread. The optimization of an error-based fitness function, which is constructed through the differential mathematical system using the hybrid computing proficiencies of the ANNs-GA-ASA for solving the LD model. The stochastic ANNs-GA-ASA procedures are applied to the LD model to authenticate the precision, exactness, reliability and competence of the ANNs-GA-ASA. The obtained results using the ANNs-GA-ASA of the LD model will be compared using the Runge–Kutta scheme, which authenticate the importance of the ANNs-GA-ASA. Furthermore, statistical analysis through different actions for the LD model approve the convergence and precision of the ANNs-GA-ASA.