Integrating Novel Deep Neural Networks on the Analysis of Fractional  Epidemiological Models in both Populations with Disease Infection

Sana Ullah Saqib; Muhammad Wajahat Anjum; Ali Hasan; M. Hakam Ali Qasmi

doi:10.48165/jmmfc.2024.1207

Authors

Sana Ullah Saqib Department of Applied Mathematics, National Chung Hsing University, Taichung, Taiwan.
Muhammad Wajahat Anjum Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan.
Ali Hasan Department of Mathematics and Statistics, The University of Lahore, Lahore 54590, Pakistan.
M. Hakam Ali Qasmi Department of Applied Mathematics and Statistics, IST, Islamabad.

DOI:

https://doi.org/10.48165/jmmfc.2024.1207

Keywords:

Deep Neural Networks (DNNs), Supervised Learning, Fractional Epidemical Model., Intelligent computing, bio informatics. Infectious diseases.

Abstract

Deep Neural Networks (DNNs) have become one of the most significant tools utilized in analyzing complicated systems, surpassing the ability to comprehend complexities. The study provides the advantage of DNNs' interest to improve the analysis of intricate patterns and produce insightful findings. It is crucial to comprehend the dynamics of infectious disease spread in ecological systems, especially when it comes from predator to prey, because of its significance for a variety of real-world situations. In complicated regulation environments, the size range of prey and predator populations is influenced by the complicated interactions between infections and predator-prey relationships. The analysis of fractional epidemiological models in both populations with disease infection (FEM-BPDI) is performed through the novel application of artificial intelligence, particularly Deep Neural Networks (DNNs). Datasets for Deep Neural Networks are generated using the fde12 solver. Training, testing, and validation phases are applied to the DNNs models to acquire solutions for the FEM-BPDI under different epidemiological scenarios. Several statistical metrics, such as mean-squared error analyses, auto correlation of error (ACE), correlation input and error (CIE), error histogram visualizations, and expected regression measurements, are used to show the efficiency that DNNs are at solving the FEM-BPDI. The model's stability and resilience in forecasting disease dynamics are highlighted by a low Mean Squared Error (MSE) that is obtained. Also, the small or negligible Absolute error provides more evidence of the suggested technique's efficacy. This study highlights the critical role that AI-powered Deep Neural Networks play in improving the comprehension and forecasting of fractional epidemiological models in the context of dual population dynamics, providing invaluable insight into the dynamics of disease transmission and ecosystem control.

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