A mathematical model for precise predicting microbial propagation based on solving variable-order fractional diffusion equation

Continued mortality from Covid-19 disease and environmental considerations resulting from the cemetery, landfill, wastewater treatment plants, and mass personal protective equipment (PPE) disposal sites demonstrate the importance of carefully studying how microorganisms spread in and across the soil, surface water, and groundwater. In this research, fractional diffusion equation for different functions has been solved using fractional derivative form with variable-order (VO) to predict the diffusion of the SARS-CoV-2 virus. Comparison of the obtained results with the available experimental data and mathematical calculations shows that the use of VO form can predict the viral behavior more accurately. The main advantage of considering a VO fractional derivatives instead of a constant-order fractional derivative or classical derivative is accurately predicting the behavior of propagation of microorganisms over large time and dimensional scales. In addition, to the specified SARS-CoV-2 virus, the method presented in this study will be able to investigate the diffusion pattern of all environmental pollutants at the nanoscale/microscale, including carcinogenic compounds, such as biogenic amines in aqueous and porous media. The obtained results manifest a high accuracy of mathematical approach which provides helpful information to urban and health planners/managers worldwide to manage other possible outbreaks.

Automated summary

In this research, a fractional diffusion equation with variable-order (VO) was used to predict the diffusion of the SARS-CoV-2 virus. The use of VO form resulted in more accurate predictions of viral behavior compared to constant-order fractional derivatives. The method also has the advantage of accurately predicting the propagation behavior of microorganisms over large time and dimensional scales. Additionally, it can be applied to investigate the diffusion patterns of other environmental pollutants at the nanoscale/microscale.