Using Artificial Deep Neural Network Analysis for the Investigation of Fractional Order Pine Wilt Disease Mathematical Model

In this study, the transmission dynamics of a fractional order host-vector mathematical model of pine wilt disease is investigated. The Atangana-Baleanu fractional order derivative is applied instead of classical order derivative for incorporating nonlocal and memory effects in the system through fractional parameter. The considered model is rigorously studied for existence and uniqueness, in addition with Ulam-Hyers stability, providing a strong theoretical base for the model. A brief discussion on the disease free equilibrium and endemic equilibrium points is presented using basic reproduction number [Formula: see text] of the system. Furthermore, an efficient numerical method is applied to obtain the approximate solution of the proposed system. The graphical results show that, the fractional parameter [Formula: see text] has the significant impact on the disease dynamics. When the value of [Formula: see text] is decreases then the memory is getting stronger, hence past history effect the present transmission dynamics and when the value of [Formula: see text] increases [Formula: see text] the memory become weaker and the fractional model tends to its integer order counterpart. The plots of all variables affirms the significant effect of fractional parameter in the system dynamics. Using the important concept of artificial intelligence based deep neural networks, some important thresholds like mean squared error and root mean squared error as well as the regression coefficients are analyzed. The absolute error between the numerical results and those predicted by deep neural networks are compared. For the mentioned computational purposes, the Levenberg-Marquardt algorithm and Matlab 2023 are used. Graphical illustrations with performance analysis for test, validation, train and all data are displayed.