On nonlinear ordinary differential system for infectious disease: A neuro-swarming intelligence scheme

It is believed that nonlinear ordinary differential systems are essential for epidemic modeling because they can narrate the complex and unpredictable aspects of the spread of infectious diseases. Therefore, one can use nonlinear differential systems to propose control measures for the spread of diseases, and it remains a challenging task for researchers to obtain the best solution for such nonlinear systems. The present article offers the best solution remedy for nonlinear differential systems. To be more specific, to address the nonlinear dynamics of the spread of COVID-19, we propose an intelligent computational framework based on single-layer feed-forward artificial neural networks (FF-ANNs) and the optimization techniques of global and local search approaches. The SEIR-NDC model is solved by using a global-local search strategy called PSONM, which combines Particle Swarm Optimization (PSO) and the Nelder-Mead Simplex (NM). The differential nonlinear mathematical model based on SEIR-NDC and initial conditions is used in the hybrid PSONM combination to optimize an error-based fitness function. Ten neurons are used to demonstrate the numerical performance of the SEIR-NDC nonlinear model using ANN methods in conjunction with PSO-SQP. The correctness of the developed scheme is testified through the comparative analysis of the reference solution and the obtained outcomes. The absolute error performances are reported within appropriate ranges for every class of the SEIR-NDC model. It is found that the AE lies in the range 10–14 and 10–17. The statistical analysis is presented to verify the developed scheme's stability, convergence, and robustness. The statistical measures, i.e., mean square error falls between 10–8 and 10–13, while the mean absolute deviation falls between 10–8 and 10–11. We believe that the outcomes of the present analysis will be a helping hand in encountering nonlinear differential systems that are subject to practical applications.