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The current study is related to solve a nonlinear vector-borne disease with a lifelong immunity model (VDLIM) by designing a computational stochastic framework using the strength of artificial Levenberg-Marquardt backpropagation neural network (ALMBNN). The detail of the nonlinear VDLIM is provided along with its five classes. The numerical performances of the results have been presented using the ALMBNN by taking three different cases to solve the nonlinear VDLIM using the training, sample data, testing and authentication. The selection of the statics is selected as 80% for training, while the data for both testing and validations is applied 10%. The results of the nonlinear VDLIM are performed using the ALMBNN and the correctness of the scheme is observed to compare the results with the reference solutions. The calculated performance of the results to solve the nonlinear VDLIM is applied for the reduction of the mean square error. In order to check the competence, efficacy, exactness and reliability of the ALMBNN, the numerical investigations using the proportional procedures based on the MSE, correlation, regression and error histograms are presented.

This study is relevant to present the numerical form of the nonlinear dengue fever SIR system are presented using the artificial neural networks along with the Levenberg-Marquardt backpropagation technique, i.e. ANNs-LMB. The procedures of ANNs-LMB are applied with three different sample data scales based on testing, training and authentication. The statistics to solve three cases of the nonlinear dengue fever based on susceptible, infected and recovered system are selected with 75%, 15% and 10% for training, validation and testing, respectively. To find the numerical results of the nonlinear dengue fever system, the reference dataset is designed on the basis of Adams scheme for the numerical solution. The numerical results based on the nonlinear dengue fever system are obtained through the ANNs-LMB to reduce the mean square error. In order to check the exactness, reliability, effectiveness and competence of the proposed ANNs-LMB, the numerical outcomes are proficient to the proportional measures using the topographies of the fitness attained in mean squared error sense, correlation, error histograms and regression.

In this research, the well-known non-linear Lane–Emden–Fowler LEF equations are approximated by developing a nature-inspired stochastic computational intelligence algorithm. A trial solution of the model is formulated as an artificial feed-forward neural network model containing unknown adjustable parameters. From the LEF equation and its initial conditions, an energy function is constructed that is used in the algorithm for the optimisation of the networks in an unsupervised way. The proposed scheme is tested successfully by applying it on various test cases of initial value problems of LEF equations. The reliability and effectiveness of the scheme are validated through comprehensive statistical analysis. The obtained numerical results are in a good agreement with their corresponding exact solutions, which confirms the enhancement made by the proposed approach.

In this paper, an efficient procedure based on the neural networks methodology is presented for the solution of the fuel ignition model in one dimension. The neural networks were optimised with the particle swarm optimisation algorithm hybridised with sequential quadratic programming. The accuracy and convergence of the scheme are analysed by Monte Carlo simulations and their statistical analyses for three test cases of the problem represented by Bratu-type equations. It was found that the hybrid approach converges in all cases, and can solve the problem with higher accuracy and reliability than most of the methodologies used so far to solve this problem.