The present study introduces a novel design of Morlet wavelet neural network (MWNN) models to solve a class of a nonlinear nervous stomach system represented with governing ODEs systems via three categories, tension, food and medicine, i.e., TFM model. The comprehensive detail of each category is designated together with the sleep factor, food rate, tension rate, medicine factor and death rate are also provided. The computational structure of MWNNs along with the global search ability of genetic algorithm (GA) and local search competence of active-set algorithms (ASAs), i.e., MWNN-GA-ASAs is applied to solve the TFM model. The optimization of an error function, for nonlinear TFM model and its related boundary conditions, is performed using the hybrid heuristics of GA-ASAs. The performance of the obtained outcomes through MWNN-GA-ASAs for solving the nonlinear TFM model is compared with the results of state of the article numerical computing paradigm via Adams methods to validate the precision of the MWNN-GA-ASAs. Moreover, statistical assessments studies for 50 independent trials with 10 neuron-based networks further authenticate the efficacy, reliability and consistent convergence of the proposed MWNN-GA-ASAs.