The epidemiological aspects of the viral dynamic of the SARS-CoV-2 have become increasingly crucial due to major questions and uncertainties around the unaddressed issues of how corpse burial or the disposal of contaminated waste impacts nearby soil and groundwater. Here, a theoretical framework base on a meshless algorithm using the moving least squares (MLS) shape functions is adopted for solving the time-fractional model of the viral diffusion in and across three different environments including water, tissue, and soil. Our computations predict that by considering the $\alpha$ (order of fractional derivative) best fit to experimental data, the virus has a traveling distance of $1mm$ in water after 22, regardless of the source of contamination (e.g., from tissue or soil). The outcomes and extrapolations of our study are fundamental for providing valuable benchmarks for future experimentation on this topic and ultimately for the accurate description of viral spread across different environments. In addition to COVID-19 relief efforts, our methodology can be adapted for a wide range of applications such as studying virus ecology and genomic reservoirs in freshwater and marine environments.

Keywords: Coronavirus; Fractional diffusion equation; Moving least squares (MLS) shape functions; SARS-CoV-2; Viral dynamics; Virus diffusion coefficients.

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