This study indicates the design of swarming procedure based on the stochastic framework of artificial neural networks (ANNs) along with the particle swarm optimization (PSO) and sequential quadratic programming (SQP) for the Leptospirosis disease model (LDM). LDM is zoonotic disease, which broadly occurs in each continent of the world. LDM is dependent upon three classes and the numerical solutions are presented by using the procedures of ANNs-PSO-SQP. The construction of a merit function is provided based on the LDM and then optimized by using the PSO-SQP. The proposed ANNs-PSO-SQP scheme is used to LDM to indorse the exactness, precision, trustworthiness, and aptitude of the ANNs-PSO-SQP. The obtained ANNs-PSO-SQP of the LDM compared with the Adams method, which confirm the significance of the proposed ANNs-PSO-SQP. The neuron analysis based on the larger and smaller neurons will be provided to authenticate the correctness of the ANNs-PSO-SQP for solving the LDM. Moreover, statistical representations based on different operators will be provided to check the reliability of the ANNs-PSO-SQP for solving the LDM.