Social Networks in times of economic meltdown

From homogeneous mixing to data‑driven networks /

COVID‑19 made it clear that epidemics—and their economic fallout—are not just about “how infectious” a pathogen is, but who meets whom, where, and when. Classical SIR models assume homogeneous mixing: each individual has equal probability to meet any other. In reality, contact and mobility are structured in networks: households, workplaces, schools, transport routes, and digital platforms.

Work like Charting the Next Pandemic and the GLEAM framework showed before COVID‑19 that realistic epidemic forecasting needs explicit networks of mobility and contacts, where disease dynamics (SIR/SEIR) run on graphs built from data. COVID‑era studies went further: they used time‑resolved contact surveys, high‑resolution mobility data, and temporal network methods to fit and forecast outbreaks and to quantify the impact of policy.

This post zooms in on three data‑supported arguments that illustrate how temporal mixing patterns and strong long ties (SLs) can be modeled with SIR‑type dynamics to predict future pandemics and their societal consequences. [Each argument can be demonstrated with public data and a simple chart]

/ Contact mixing and the effective reproduction number $R_t$Rt

Changes in the mean number of daily contacts in the population closely track changes in the effective reproduction number $R_t$Rt; simple SIR models with time‑varying contact rates can capture this relationship.

The CoMix social contact survey followed households across Europe from early 2020, repeatedly asking participants to report all in‑person contacts on the previous day. For the UK and other countries, the CoMix team publishes:

• time series of the mean number of contacts per person, and
• corresponding estimates of $R_t$Rt, derived by combining these contact patterns with infectiousness profiles.

In network terms, each time point gives a snapshot of a temporal contact network summarized by its average degree $⟨k(t)⟩$⟨k(t)⟩. In a simple SIR‑on‑network model, the transmission rate can be written as$$\beta (t)=\tau ⟨k(t)⟩,$$β(t)=τ⟨k(t)⟩,

where $\tau$τ is the per‑contact transmission probability. Together with recovery rate $\gamma$γ, this gives$$R_t\approx \frac{\beta (t)}{\gamma }=\frac{\tau }{\gamma }⟨k(t)⟩\mathrm{.}$$Rt≈γβ(t)=γτ⟨k(t)⟩.

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Community mobility indices are effective proxies for time‑varying transmission rates in SIR‑type models; drops in mobility precede and predict reductions in case growth.

Google’s COVID‑19 Community Mobility Reports provide daily, anonymized, aggregate percentage changes in visits to workplaces, retail, transit stations, parks, and other categories, relative to a pre‑pandemic baseline. Our World in Data republishes these series in an accessible form, alongside confirmed case counts and other epidemiological indicators.

Several studies, such as an analysis for India, show that reductions in mobility (especially in transit and workplaces) are significantly correlated with reductions in disease severity indicators, including incidence and case growth. At national level, mobility drops of 40–80% during lockdown correspond to marked slowdowns in epidemic growth; as mobility rebounds in the “unlock” phases, case growth resumes.

In a metapopulation or SIR framework, one can treat mobility as a temporal network density measure and write

$$\beta (t)={\beta }_{0}f(M(t)),$$β(t)=β0f(M(t)),

where $M(t)$M(t) is a mobility index (e.g., workplace visits), and $f$f is typically increasing (more movement → more effective contacts).

[This justifies using mobility as a time‑varying network input to SIR models. Instead of a static contact rate, the epidemic is modeled on a temporal network whose effective density is inferred from mobility]

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Structured mixing (who meets) shapes which groups are hit /

Age‑structured contact matrices—who mixes with whom—are critical to predicting how epidemics (and therefore their economic consequences) are distributed across demographic groups.

The CoMix project and related efforts provide age‑structured contact matrices: for each pair of age groups $(i,j)$(i,j), the average number of daily contacts from group $i$i to group $j$j is estimated, and matrices are published over time. These matrices differ dramatically between pre‑COVID and lockdown phases and between settings (home, work, school, other).

In an age‑structured SIR model, the force of infection on age group $i$i at time $t$t is$${\lambda }_i(t)=\sum _j{\beta }_{ij}(t)\frac{I_j(t)}{N_j},$$

λi(t)=j∑βij(t)NjIj(t), with ${\beta }_{ij}(t)\propto C_{ij}(t)$βij(t)∝Cij(t), where $C_{ij}(t)$Cij(t) is the contact matrix entry (mean contacts from $i$i to $j$j). Policies like school closures and shielding of older adults correspond to modifying specific blocks of this matrix.

/ [TBC]