An algebraic formula, deep learning and a novel SEIR-type model for the COVID-19 pandemic.

The most extensively used mathematical models in epidemiology are the susceptible-exposed-infectious-recovered (SEIR) type models with constant coefficients. For the first wave of the COVID-19 epidemic, such models predict that at large times equilibrium is reached . However, epidemiological data from Europe suggest that this approach is .

A Model for Reinfections and the Transition of Epidemics.

Reinfections of infected individuals during a viral epidemic contribute to the continuation of the infection for longer periods of time. In an epidemic, contagion starts with an infection wave, initially growing exponentially fast until it reaches a maximum number of infections, following which it wanes towards an equilibrium state of zero infections, assuming that no new variants have emerged. If reinfections are allowed, multiple such infection waves might occur, and the asymptotic equilibrium state is one in which infection rates are not negligible.

A comprehensive spatial-temporal infection model.

Motivated by analogies between the spread of infections and of chemical processes, we develop a model that accounts for infection and transport where infected populations correspond to chemical species. Areal densities emerge as the key variables, thus capturing the effect of spatial density. We derive expressions for the kinetics of the infection rates, and for the important parameter , that include areal density and its spatial distribution.

Drying in porous media with gravity-stabilized fronts: experimental results.

In a recent paper [Yiotis et al., Phys. Rev.