USING ARTIFICIAL DEEP NEURAL NETWORK ANALYSIS FOR THE INVESTIGATION OF FRACTIONAL-ORDER PINE WILT DISEASE MATHEMATICAL MODEL
Fractals, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1142/s0218348x27400147
- Dergi Adı: Fractals
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Compendex, INSPEC, zbMATH, Academic Search Ultimate (EBSCO), Engineering Source (EBSCO), Technology Collection (ProQuest)
- Anahtar Kelimeler: Deep Neural Networks, Fractional-Order Model, Host’s Vector Dynamics, Levenberg–Marquardt Algorithm, Numerical Simulation, Pine Wilt Disease, Qualitative Analysis
- İstanbul Gelişim Üniversitesi Adresli: Evet
Özet
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 non-local 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 R0 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 ρ has a significant impact on the disease dynamics. When the value of ρ decreases, then the memory gets stronger, hence past history affects the present transmission dynamics and when the value of ρ increases (ρ → 1), the memory becomes weaker and the fractional model tends to its integer-order counterpart. The plots of all variables affirm the significant effect of fractional parameter in the system dynamics. By 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 is 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.