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The current study provides the solutions of the mathematical model based on the coronavirus including the effects of vaccination and quarantine. The numerical stochastic process relying on Levenberg-Marquardt backpropagation technique (L-MB) neural networks (NN), i.e., L-MBNNs, is presented to solve the model. The entire dynamics of the proposed model depends upon the human population, which is represented by N and is further divided into multiple subgroups. The detail of these subgroups is presented in the form of susceptible population (S), exposed population (E), and infected people (I). Likewise, Q represents the quarantined and R shows the recovered or deceased individuals. Those who have been immunized are symbolized by V. All these categories make the model SEIQRV, that is based on a system of nonlinear differential equations. The statistics that is used to provide the numerical solutions of the SEIQRV model is 76% for training, 10% for testing and 14% for authorization. The correctness of the L-MBNNs is tested by using the comparison of the proposed and reference solutions (Adam method). The statistical representations are provided in order to check the reliability, competence and validity of L-MBNNs using the procedures of error histograms (EH), state transitions (ST), regression and correlation. [ABSTRACT FROM AUTHOR]

In this paper, we study on the numerical solution of fractional nonlinear system of equations representing the one-dimensional Cauchy problem arising in thermoelasticity. The proposed technique is graceful amalgamations of Laplace transform technique with q -homotopy analysis scheme and fractional derivative defined with Atangana–Baleanu (AB) operator. The fixed-point hypothesis is considered in order to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. In order to illustrate and validate the efficiency of the future technique, we consider three different cases and analyzed the projected model in terms of fractional order. Moreover, the physical behavior of the obtained solution has been captured in terms of plots for diverse fractional order, and the numerical simulation is demonstrated to ensure the exactness. The obtained results elucidate that the proposed scheme is easy to implement, highly methodical as well as accurate to analyze the behavior of coupled nonlinear differential equations of arbitrary order arisen in the connected areas of science and engineering. [ABSTRACT FROM AUTHOR]