The aim of this work is to introduce a stochastic solver based on the Levenberg-Marquardt backpropagation neural networks (LMBNNs) for the nonlinear host-vector-predator model. The nonlinear host-vector-predator model is dependent upon five classes, susceptible/infected populations of host plant, susceptible/infected vectors population, and population of predator. The numerical performances through the LMBNN solver are observed for three different types of the nonlinear host-vector-predator model using the authentication, testing, sample data, and training. The proportions of these data are chosen as a larger part, i.e., 80% for training and 10% for validation and testing, respectively. The nonlinear host-vector-predator model is numerically treated through the LMBNNs, and comparative investigations have been performed using the reference solutions. The obtained results of the model are presented using the LMBNNs to reduce the mean square error (MSE). For the competence, exactness, consistency, and efficacy of the LMBNNs, the numerical results using the proportional measures through the MSE, error histograms (EHs), and regression/correlation are performed.