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We have studied the dynamic evolution of the Covid-19 pandemic in Argentina. The marked heterogeneity in population density and the very extensive geography of the country becomes a challenge itself. Standard compartment models fail when they are implemented in the Argentina case. We extended a previous successful model to describe the geographical spread of the AH1N1 influenza epidemic of 2009 in two essential ways: we added a stochastic local mobility mechanism, and we introduced a new compartment in order to take into account the isolation of infected asymptomatic detected people. Two fundamental parameters drive the dynamics: the time elapsed between contagious and isolation of infected individuals ($$\alpha$$ α ) and the ratio of people isolated over the total infected ones (p). The evolution is more sensitive to the $$p-$$ p - parameter. The model not only reproduces the real data but also predicts the second wave before the former vanishes. This effect is intrinsic of extensive countries with heterogeneous population density and interconnection.The model presented has proven to be a reliable predictor of the effects of public policies as, for instance, the unavoidable vaccination campaigns starting at present in the world an particularly in Argentina.

Many COVID-19 vaccines are proving to be highly effective to prevent severe disease and to diminish infections. Their uneven geographical distribution favors the appearance of new variants of concern, as the highly transmissible Delta variant, affecting particularly non-vaccinated people. It is important to device reliable models to analyze the spread of the different variants. A key factor is to consider the effects of vaccination as well as other measures used to contain the pandemic like social behaviour. The stochastic geographical model presented here, fulfills these requirements. It is based on an extended compartmental model that includes various strains and vaccination strategies, allowing to study the emergence and dynamics of the new COVID-19 variants. The model conveniently separates the parameters related to the disease from the ones related to social behavior and mobility restrictions. We applied the model to the United Kingdom by using available data to fit the recurrence of the currently prevalent variants. Our computer simulations allow to describe the appearance of periodic waves and the features that determine the prevalence of certain variants. They also provide useful predictions to help planning future vaccination boosters. We stress that the model could be applied to any other country of interest.

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