Hydrogels are materials widely used in countless applications, particularly in the biomedical, pharmaceutical, and nutraceutical fields, because of their biocompatibility and their mechanical and transport properties. Several approaches are known to evaluate their properties, but only a few approaches are under development to mathematically describe their behaviour, in terms of how the materials answer to mechanical stimuli and how incorporated active substances are released. In this review, the main properties of hydrogels are summarized and the structure–property relationships are investigated (i.e. how the macromolecular structure influences the properties of macroscopic samples made of hydrogels). A selection criterion is proposed based on the comparison of three characteristic times: relaxation time, diffusion time, and process time. Then, the most common experimental methods to investigate the hydrogel properties are summarized, along with the state-of-the-art of mathematical modelling, with reference to the mechanical and transport properties of hydrogels, with particular attention to the viscoelastic and poroelastic behaviours. Last but not least, some case histories which can be classified as viscoelastic, poroelastic, or poroviscoelastic behaviours are presented.

The COVID-19 disease is rapidly spreading in whole globe, affecting millions of people and pushing governments to take drastic measures to contain the outbreaks. The understanding of the dynamics of the epidemic is of great interest for the governments and health authorities that are facing COVID-19 outbreaks. The scarce presence of epidemiologic data, due to the still ongoing outbreaks, makes prediction difficult and mainly based on heuristic (fitting) models. However, these models with non-physical based parameters, can only give limited insight in the evolution of the outbreaks. In this work a SIRD compartmental model was developed to describe and predict the evolution of the Chinese and Italian outbreaks. Exploiting the similarities of the measures taken by the governments to contain the virus and of the total population number of Hubei province and Italy, the model was tuned on the Chinese outbreak (almost extinguished) and by perturbation the Italian outbreak was describe and predicted.