Spatiotemporal Analysis of the Spread of the COVID-19 Epidemic in Chile Using a Percolation Model

Percolation describes the critical behaviour of spatial cells that progressively change their state until they compromise an entire given space. Once a threshold proportion is reached, a large continuous cell is formed that allows the space to be compromised in a continuous trajectory. This model has been used for the spatial progress of infectious disease epidemics. We propose a logistic model of space-time progression that allows an estimation of the time at which the percolation threshold is reached. In this study, we analysed the space-time progression of the COVID-19 epidemic through Chile. We first describe the process, apply the logistic model, and simulate the process on a long grid of square cells that imitates the Chilean situation. We found that, in practice, the percolation occurred when 81.63% of the communes were infected. The logistic model had an excellent fit (R² = 0.967). The grid model revealed that when less than 65% of the cells were infected, no percolation events occurred. The percolation model is applicable to the spatial progression of epidemics in Chile and is an example of directed percolation. It is useful to show that at least 65% of the communes need to be infected for the entire country to be affected. Alternatively, keeping 35% of the communes free of infection would prevent the spread of an epidemic. The logistic model of the spatial spread of an epidemic allows an estimation of the time when the threshold would be reached, which constitutes a window during which mitigation or control measures can be implemented.