Percolation across households in mechanistic models of non-pharmaceutical interventions in SARS-CoV-2 disease dynamics

Since the emergence of the novel coronavirus disease, mathematical modelling has become an important tool for planning strategies to combat the pandemic by supporting decision-making and public policies, as well as allowing an assessment of the effect of different intervention scenarios. A proliferation of compartmental models was observed in the mathematical modelling community, aiming to understand and make predictions regarding the spread of COVID-19. Such approach has its own advantages and challenges: while compartmental models are suitable to simulate large populations, the underlying well-mixed population assumption might be problematic when considering non-pharmaceutical interventions (NPIs) which strongly affect the connectivity between individuals in the population. Here we propose a correction to an extended age-structured SEIR framework with dynamic transmission modelled using contact matrices for different settings in Brazil. By assuming that the mitigation strategies for COVID-19 affect the connections between different households, network percolation theory predicts that the connectivity across all households decreases drastically above a certain threshold of removed connections. We incorporated this emergent effect at population level by modulating the home contact matrices through a percolation correction function, with the few remaining parameters fitted to to hospitalisation and mortality data from the city of Sao Paulo. We found significant support for the model with implemented percolation effect using the Akaike Information Criteria (AIC). Besides better agreement to data, this improvement also allows for a more reliable assessment of the impact of NPIs on the epidemiological dynamics.