Mathematical Modelling of the Spatial Epidemiology of COVID-19 with Different Diffusion Coefficients

Abstract

This paper addresses the discrepancy between model findings and field data obtained and how it is minimized using the binning smoothing techniques: means, medians, and boundaries. Employing both the quantitative and the qualitative methods to examine the complex pattern involved in COVID-19 transmission dynamics reveals model variation and provides a boundary signature for the potential of the disease’s future spread across the country. To better understand the main underlying factor responsible for the epidemiology of COVID-19 infection in Ghana, the continuous inflow of foreigners, both with and without the disease, was incorporated into the classical Susceptible-Exposed-Quarantined-Recovered SEIQR model, which revealed the spread of the COVID-19 by these foreigners. Also, the diffusion model provided therein gives a threshold condition for the spatial spread of the COVID-19 infection in Ghana. Following the introduction of a new method for the construction of the Lyapunov function for global stability of the nonlinear system of ODEs was observed, overcoming the problem of guessing for the Lyapunov function.