A fractional order numerical study for the influenza disease mathematical model

Abstract

The motive of these investigations is to present the numerical performances of the fractional order mathematical influenza disease model (FO-MIDM) by designing the computational framework based on the stochastic Levenberg-Marquardt backpropagation neural networks (LMBNNs). The fractional order derivatives have been used to get more accurate performances of the MIDM as compared to the integer order. The MIDM is divided into four subcategories, (i) susceptible S(q), (ii) infected I(q), (iii) recovered R(q) and (iv) cross-immune people C(q). Three different cases based FO derivatives have been numerically presented by using the MIDM. The achieved results based on the MIDM have been presented by using the computing stochastic structure LMBNNs through the process of training, confirmation and testing to decrease the mean square error (MSE) values using the reference (data-based) results. To observe the competence, precision, capability and aptitude of the proposed computing structure LMBNNs, a comprehensive investigation is accessible by performing the correlation, MSE, error histograms, information of state transitions and regression analysis. The worth of LMBNNs procedure is validated through the overlapping of the results with good measures up to the accuracy of 5 to 7 decimals for solving the MIDM.