This research addresses the challenge of three types of non-uniform site percolation on a non-regular Bethe lattice (TNRBL) with its epidemiological implications. By utilizing a non-regular Bethe lattice (NRBL), we explore the estimation of vital percolating variables such as cluster size distribution (CSD), critical connection probability (CCP), percolation probability of connected sites (PP), and average cluster size (ACS). We apply the generating function (GF) and the generalized recursive method (GRM) to gain insights into these variables. The study demonstrates that spanning non-uniform dynamic percolation through the fitted model probabilities enhances the efficiency of intervention strategies, potentially revolutionizing disease control. The findings revealed that, for inhomogeneous site non-uniform percolation on the proposed model, a higher fraction of connection and distribution probabilities enhances the intensity of the percolation process. This increase subsequently leads to a significant enlargement of the mean degree of the system during the percolation process. The shape profiles of the findings are illustrated to observe their behavior across varying parameter choices. Furthermore, we investigated the novel coronavirus 2019 (COVID-19) diffusion pattern utilizing the proposed dynamically altered parameters and identified various variables (courtesy of groups) for disease control methods. We acknowledge that the research being carried out is substantial, that its findings are intended to generate enthusiasm, and that scientists anticipate employing several percolation methods to conduct it. In addition, the research not only adds to the development of more accurate control plans for future global health crises, but it also offers up new avenues for the improvement of models that anticipate epidemics. This study lays the door for an improved comprehension of the complex dynamics of epidemics, and it provides a platform for future studies to investigate a variety of intervention techniques.
Citation: Muhammad Imran Shahid. Advanced modeling approach to percolation on lattices: analysis of complex systems and their implications[J]. Big Data and Information Analytics, 2026, 10: 130-157. doi: 10.3934/bdia.2026007
This research addresses the challenge of three types of non-uniform site percolation on a non-regular Bethe lattice (TNRBL) with its epidemiological implications. By utilizing a non-regular Bethe lattice (NRBL), we explore the estimation of vital percolating variables such as cluster size distribution (CSD), critical connection probability (CCP), percolation probability of connected sites (PP), and average cluster size (ACS). We apply the generating function (GF) and the generalized recursive method (GRM) to gain insights into these variables. The study demonstrates that spanning non-uniform dynamic percolation through the fitted model probabilities enhances the efficiency of intervention strategies, potentially revolutionizing disease control. The findings revealed that, for inhomogeneous site non-uniform percolation on the proposed model, a higher fraction of connection and distribution probabilities enhances the intensity of the percolation process. This increase subsequently leads to a significant enlargement of the mean degree of the system during the percolation process. The shape profiles of the findings are illustrated to observe their behavior across varying parameter choices. Furthermore, we investigated the novel coronavirus 2019 (COVID-19) diffusion pattern utilizing the proposed dynamically altered parameters and identified various variables (courtesy of groups) for disease control methods. We acknowledge that the research being carried out is substantial, that its findings are intended to generate enthusiasm, and that scientists anticipate employing several percolation methods to conduct it. In addition, the research not only adds to the development of more accurate control plans for future global health crises, but it also offers up new avenues for the improvement of models that anticipate epidemics. This study lays the door for an improved comprehension of the complex dynamics of epidemics, and it provides a platform for future studies to investigate a variety of intervention techniques.
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Muhammad Imran Shahid. Advanced modeling approach to percolation on lattices: analysis of complex systems and their implications[J]. Big Data and Information Analytics, 2026, 10: 130-157. doi: 10.3934/bdia.2026007
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