Survey-Based Calibration of the One-Community and Two-Community Social Network Models Used for Testing Singapore's Resilience to Pandemic Lockdown

TL;DR

Quantifies social resilience by calibrating Jin-Girvan-Newman–style dynamic social networks to Singapore's pandemic experience. It develops one- and two-community variants and calibrates them with a large phone-contact survey (N=2,057) to infer contact-generation and deletion rates, plus inter- and intra-community interaction structure. The best-fit one-community model yields $r_0 \approx 0.01$, $r_1 \approx 0.002$, and $\gamma \approx 0.005$, predicting a 1–2 month recovery after lockdown, with inter/intra parameters $\alpha \approx 0.305$ and $\beta \approx 0.582$. The study discusses heterogeneity, non-stationarity, and finite-size considerations, and offers a practical framework for data-driven calibration of social resilience models.

Abstract

A resilient society is one capable of withstanding and thereafter recovering quickly from large shocks. Brought to the fore by the COVID-19 pandemic of 2020--2022, this social resilience is nevertheless difficult to quantify. In this paper, we measured how quickly the Singapore society recovered from the pandemic, by first modeling it as a dynamic social network governed by three processes: (1) random link addition between strangers; (2) social link addition between individuals with a friend in common; and (3) random link deletion . To calibrate this model, we carried out a survey of a representative sample of $N = 2,057$ residents and non-residents in Singapore between Jul and Sep 2022 to measure the numbers of random and social contacts gained over a fixed duration, as well as the number of contacts lost over the same duration, using phone contacts as proxy for social contacts. Lockdown simulations using the model that fits the survey results best suggest that Singapore would recover from such a disruption after 1--2 months.

Figures (9)

• Figure 1: Timeline of intervention measures implemented by the Singapore Government during the COVID-19 pandemic and the relative timing of the survey performed for this study. These were introduced in phases with varying levels of restrictions: (1) Circuit Breaker (1 Apr-1 Jun 2020); (2) Reopening Phase 1 (2-18 Jun 2020); (3) Reopening Phase 2 (19 Jun-27 Dec 2020); (4) Reopening Phase 3 (28 Dec 2020-7 May 2021); (5) Reopening Phase 2 (8-16 May 2021); (6) Phase 2 Heightened Alert (16 May-13 Jun 2021); (7) Phase 3 Heightened Alert (14 Jun-21 Jul 2021); (8) Phase 2 Heightened Alert (22 Jul-9 Aug 2021); (10) Preparatory Stage of Transition (10 Aug-26 Sep 2021); (11) Phase 2 Heightened Alert (27 Sep-21 Nov 2021); (12) Transition Phase (22 Nov 2021-25 Apr 2022). From 26 Apr 2022 onwards, Singapore was declared a COVID-19 resilient nation, because it was believed that herd immunity has been achieved by the nation-wide vaccination program. Also indicated in this figure is the first COVID-19 case on 23 Jan 2020, the approximate pandemic periods caused by the alpha, delta, and omicron strains, as well as the start and end of our survey. Finally, we also show in gray the six-month period that would contribute to the response of the first survey participant, and the six-month period that would contribute to the response of the last survey participant.
• Figure 2: Flow diagram illustrating the time evolution of phone contacts during the six-month time period covered by the survey. A variable without a prime represents the total number of contacts; a variable with a single prime represents the number of contacts that survived from the prior time period; and a variable with a double prime represents contacts that were newly acquired, either randomly or socially during the time period. $\Gamma_1$ represents the number of contacts lost during the first three-month time period, while $\Gamma_2$ represents the number of contacts lost during the second three-month time period.
• Figure 3: The complete distribution of age from Question A2 of our survey. The Singapore Department of Statistics maintains a database of the number of residents by age, from 0 years of age to 89 years of age, and the histogram of this demographics data for 2023 is smoother than what we show here. This is because for statistical analyses, the Singapore Department of Statistics recommends the use of five-year age groups as part of their National Statistical Standards. As we can see in Table \ref{['tab:distributions']}, Qualtrics selects survey participants based on these age groups, and therefore they do not control the proportions down to the actual age. The Qualtrics survey also does not include participants below 21 years of age, because the standards of ethics approval to include minors are much higher.
• Figure 4: Heat map of the distribution of the contact's ages obtained from Question B11a. In this figure, the horizontal axis is the participant's age (from Question A2), while the vertical axis is the contact's age (from Question B11a). In this plot, we see strong evidence for a participant is more likely to be connected to someone close to his/her own age, to his/her parents 20-30 years older, to his/her children 20-30 years younger.
• Figure 5: Relationship between the mJGN model parameters $r_0$, $r_1$, $\gamma$, the extensive number of attempts $\tilde{\mathcal{R}}_0$, $\tilde{\mathcal{R}}_1$, $\tilde{\mathcal{G}}$ sampled from Poisson distributions with means $r_0 N$, $r_1 N_m$, $\gamma N_e$, the extensive actual counts $\mathcal{R}_0$, $\mathcal{R}_1$, $\mathcal{G}$ and intensive counts per node $R_0$, $R_1$, and $\Gamma$. The first two sets of counts are over all nodes, for a single time step, whereas the last set of counts are over a time period, for a single node.