A new approach to formulating mathematical models of increasing complexity to describe the dynamics of viral epidemics is proposed. Unifying the compartmental and stochastic approaches, it focuses on daily communicative activities of different groups of population (commuting, work, shopping, socializing) viewing them as the channels through which infection spreads. In order to describe these activities, we introduce a map of social interactions characterizing the structure of the population to which the model is applied and the patterns of behaviour typical to the social groups it is made of. By employing the mathematics of difference equations, the new approach makes it possible to incorporate the clinical picture of a particular viral infection and the complications it causes directly, in the way this picture is reported by medical professionals. As an illustration of the new approach, we consider the simplest model formulated in its framework and apply it to the ongoing pandemic of SARS-CoV-2 (COVID-19), using the UK as a representative country, to assess the impact of non-pharmaceutical measures of social distancing imposed to control its course. Although the purpose of this application is merely to illustrate the approach which is open to further development, the simplest model nevertheless allows one to make some predictions and an a posteriori assessment of the measures already taken.

The dataset consists of (i) the numerical code implementing the algorithm described in detail in the manuscript, (ii) the raw data for COVID-19 in four countries used for comparing theory and observational data and (iii) the relevant theoretical curves obtained using the code and used in the figures presented in the manuscript.

The code implements the algorithm described in the manuscript and the values it uses are given in the manuscript.