Interplay of social distancing and border restrictions for pandemics via the epidemic renormalisation group framework

Abstract

One of the biggest threats to humanity are pandemics. In our global society they can rage around the world with an immense toll in terms of human, economic and social impact. Forecasting the spreading of a pandemic is, therefore, paramount in helping governments to enforce a number of social and economic measures, apt at curbing the pandemic and dealing with its aftermath. We demonstrate that the epidemic renormalisation group approach to pandemics provides an effective and simple way to investigate the dynamics of disease transmission and spreading across different regions of the world. The framework also allows for reliable projections on the impact of travel limitations and social distancing measures on global epidemic spread. We test and calibrate it on reported COVID-19 cases while unveiling the mechanism that governs the delay in the relative peaks of newly infected cases among different regions of the globe. We discover that social distancing measures are more effective than travel limitations across borders in delaying the epidemic peak. We further provide the link to compartmental models such as the time-honoured SIR-like models. We also show how to generalise the framework to account for the interactions across several regions of the world, replacing or complementing large scale simulations.

Figure 1

Infected cases per million in the sum of the two regions, as a function of k and for two choices of the region population.

Figure 2

Left panels: Peak timing for region-1 (dashed) and region-2 (solid) for ${\gamma }_1=0.4$ (top) and ${\gamma }_1=0.75$ (bottom), and different values for ${\gamma }_2$. Right panels: Delay in the epidemic peak in region-2 for fixed $k/n_{m2}={10}^{-4}$, as a function of the week $t_{\text{cl}}$ when the borders are closed (after which $k=0$). The top panel corresponds to $b_2=\infty$ (no initial cases), while the bottom one to $b_2=200$. The vertical line marks the time of the peak for region-1.

Figure 3

Infected $\mathcal{I}(t)$ and recovered R(t) cases per million for the US compared to the data. We used $ϵ=0.09$.

Figure 4

Values of $\tilde{\gamma }$ in the SIR model as a function of $\gamma$ in the eRG approach, for 3 values of $ϵ$.

Figure 5

Comparison between the infected cases in Italy and Denmark (left plot) and in the European Union and United States (right plot) and the fits in our two-region eRG model.

Figure 6

Simulation of an epidemic diffusion in a sample of European countries (see text) starting from a “seed region”, in black. In the top row, the $\gamma$ coefficients for the European countries are fixed to random values; in the bottom row, they are all fixed to ${\gamma }_i=1$. The result shows the importance of social distancing measures within each region with respect to the diffusion due to travel.