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Journal of Environmental Accounting and Management 14(2) (2026) 179--191 | DOI:10.5890/JEAM.2026.06.004

Yeliz Karaca$^1$, Mati ur Rahman$^2$, Saira Tabassum$^3$, Dumitru Baleanu$^4$

$^1$ Department of Mathematics and Department of Neurology, University of Massachusetts Chan Medical School (UMASS), 55 Lake Avenue North, Worcester, MA 01655, USA

$^2$ Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia

$^3$ Department of Applied Sciences, National Textile University, Faisalabad 37610, Pakistan

$^4$ Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

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Abstract

The subtle patterns within complex datasets can be captured through computational mathematical modeling by resorting to various algorithmic mechanisms toward the solution of complex problems. Deep Neural Networks (DNNs) are poised as feedforward networks owing to the data flow from the input layer direction toward that of the output layer with no change in layer connections. The complexity and heterogeneity of infectious diseases, as a public health concern, lies in the vitality to stop their spread timely. Accordingly, this study introduces a mathematical model incorporating vaccination to analyze the dynamics of lumpy skin disease (LSD) with the fractional Caputo operator. The model comprises five compartments representing susceptible, vaccinated, exposed, infected and recovered classes. First, the problem's qualitative study is addressed, building on existing results and deriving a unique solution by fixed-point theory application. For the semi-analytical solution of the LSD model, the generalized Adams-Bashforth Moulton method is used. The simulation results, considering different initial data, illustrate that the model's solution is stable, converging to a single point. Notably, lower fractional orders demonstrate better stability outcomes. Further, the model is analyzed by the DNN method application for which two hidden layers are taken, the first as the tanh activation function and the other activation function as linear. The dataset concerning fractional order is split into three categories as training, testing and validation. The novel proposed scheme, namely Fractional Epi-DNNs, manifests consistency through the fractional-based epidemic compartmental models accompanied by DNN-based artificial intelligence techniques, which are powerful to analyze the fractional dynamics' intricacies to manage and simulate the spread of LSD by tackling complex data-intensive circumstances.

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