Stochastic Framework for Solving the Prey-Predator Delay Differential Model of Holling Type-Ⅲ

The current research aims to implement the numerical resultsfor the Holling third kind of functional response delay differential modelutilizing a stochastic framework based on Levenberg-Marquardt backpropagationneural networks (LVMBPNNs). The nonlinear model depends uponthree dynamics, prey, predator, and the impact of the recent past. Threedifferent cases based on the delay differential system with the Holling 3^(rd) type of the functional response have been used to solve through the proposedLVMBPNNs solver. The statistic computing framework is provided byselecting 12%, 11%, and 77% for training, testing, and verification. Thirteennumbers of neurons have been used based on the input, hidden, and outputlayers structure for solving the delay differential model with the Holling 3rdtype of functional response. The correctness of the proposed stochastic schemeis observed by using the comparison performances of the proposed and referencedata-based Adam numerical results. The authentication and precision ofthe proposed solver are approved by analyzing the state transitions, regressionperformances, correlation actions, mean square error, and error histograms.

Swarming Computational Techniques for the Influenza Disease System

The current study relates to designing a swarming computational paradigm to solve the influenza disease system(IDS).The nonlinear system’s mathematical form depends upon four classes:susceptible individuals,infected people,recovered individuals and cross-immune people.The solutions of the IDS are provided by using the artificial neural networks(ANNs)together with the swarming computational paradigm-based particle swarmoptimization(PSO)and interior-point scheme(IPA)that are the global and local search approaches.The ANNs-PSO-IPA has never been applied to solve the IDS.Instead a merit function in the sense of mean square error is constructed using the differential form of each class of the IDS and then optimized by the PSOIPA.The correctness and accuracy of the scheme are observed to perform the comparative analysis of the obtained IDS results with the Adams solutions(reference solutions).An absolute error in suitable measures shows the precision of the proposed ANNs procedures and the optimization efficiency of the PSOIPA.Furthermore,the reliability and competence of the proposed computing method are enhanced through the statistical performances.