  Over the past two decades there has been a number of global outbreaks of
viral diseases. This has accelerated the efforts to model and forecast the
disease spreading, in order to find ways to confine the spreading regionally
and between regions. Towards this we have devised a model of geographical
spreading of viral infections due to human spatial mobility and adapted it to
the latest COVID-19 pandemic. In this the region to be modelled is overlaid
with a two-dimensional grid weighted with the population density defined cells,
in each of which a compartmental SEIRS system of delay difference equations
simulate the local dynamics (microdynamics) of the disease. The infections
between cells are stochastic and allow for the geographical spreading of the
virus over the two-dimensional space (macrodynamics). This approach allows to
separate the parameters related to the biological aspects of the disease from
the ones that represent the spatial contagious behaviour through different
kinds of mobility of people acting as virus carriers. These provide sufficient
information to trace the evolution of the pandemic in different situations. In
particular we have applied this approach to three in many ways different
countries, Mexico, Finland and Iceland and found that the model is capable of
reproducing and predicting the stochastic global path of the pandemic. This
study sheds light on how the diverse cultural and socioeconomic aspects of a
country influence the evolution of the epidemics and also the efficacy of
social distancing and other confinement measures.
