The purpose of the current work is to solve the SIR nonlinear model based on dengue fever using a stochastic numerical computing scheme together with the artificial neural networks (ANNs) optimized by a well-known global genetic algorithm (GA) and local refinements of sequential quadratic programming (SQP), i.e., ANN-GA-SQM. The optimization of an error based merit function is performed by using the concepts of differential model along with the initial conditions to solve the SIR nonlinear model based dengue fever. The stochastic ANN-GA-SQM capability to solve the SIR nonlinear model based dengue fever is scrutinized to examine the correctness, precision, efficiency and constancy of the ANN-GA-SQM. The obtained numerical results of the SIR nonlinear model based dengue fever via ANN-GA-SQP are compared with the Adams results that authenticate the significance of the ANN-GA-SQM. Furthermore, statistical deliberations using the ‘semi interquartile range’, ‘mean absolute deviation’ and ‘Theil's inequality coefficient’ have been implemented to authenticate the convergence and precision of the designed ANN-GA-SQM.