Periodic epidemic outbursts explained by local saturation of clusters (preprint)

Adding the notion of spatial locality to the susceptible-infected-removed (or SIR) model, allows to capture local saturation of an epidemic. The resulting minimum model of an epidemic, consisting of five ordinary differential equations with constant model coefficients, reproduces slowly decaying periodic outbursts, as observed in the COVID-19 or Spanish flu epidemic. It is shown that if immunity decays, even slowly, the model yields a fully periodic dynamics.

Clustering, diffusion and evolution of COVID19 infections during lock-down (preprint)

Epidemics such as the spreading of COVID19-virus are highly non linear, and therefore difficult to predict. In the present pandemy as time evolves, it appears more and more clearly that a clustered dynamics is a key element of description. This means that the disease rapidly evolves within spatially localized networks, that diffuse and eventually create new clusters. We improve upon the simplest possible compartmental model, the SIR model, by adding an additional compartment associated with the clustered individuals. The so-obtained SBIR model compares satisfactorily with results on the pandemic propagation in a number of European countries, during and immediately after lock-down. Especially, the decay exponent of the number of new cases after the first peak of the epidemic, is observed to be very similar for countries in which a strict lock-down is applied. We derive an analytical expression for the value of this exponent, relating it to the initial exponential growth phase of the epidemic and to the time-scale of cluster-diffusion.