Spatial scales of COVID-19 transmission in Mexico (preprint)

During outbreaks of emerging infectious diseases, internationally connected cities often experience large and early outbreaks, while rural regions follow after some delay. This hierarchical structure of disease spread is influenced primarily by the multiscale structure of human mobility. However, during the COVID-19 epidemic, public health responses typically did not take into consideration the explicit spatial structure of human mobility when designing non-pharmaceutical interventions (NPIs). NPIs were applied primarily at national or regional scales. Here we use weekly anonymized and aggregated human mobility data and spatially highly resolved data on COVID-19 cases, deaths and hospitalizations at the municipality level in Mexico to investigate how behavioural changes in response to the pandemic have altered the spatial scales of transmission and interventions during its first wave (March - June 2020). We find that the epidemic dynamics in Mexico were initially driven by SARS-CoV-2 exports from Mexico State and Mexico City, where early outbreaks occurred. The mobility network shifted after the implementation of interventions in late March 2020, and the mobility network communities became more disjointed while epidemics in these communities became increasingly synchronised. Our results provide actionable and dynamic insights into how to use network science and epidemiological modelling to inform the spatial scale at which interventions are most impactful in mitigating the spread of COVID-19 and infectious diseases in general.

The unintended consequences of inconsistent pandemic control policies (preprint)

Controlling the spread of COVID-19 - even after a licensed vaccine is available - requires the effective use of non-pharmaceutical interventions: physical distancing, limits on group sizes, mask wearing, etc. To date, such interventions have neither been uniformly nor systematically implemented in most countries. For example, even when under strict stay-at-home orders, numerous jurisdictions granted exceptions and/or were in close proximity to locations with entirely different regulations in place. Here, we investigate the impact of such geographic inconsistencies in epidemic control policies by coupling search and mobility data to a simple mathematical model of SARS-COV2 transmission. Our results show that while stay-at-home orders decrease contacts in most areas of the US, some specific activities and venues often see an increase in attendance. Indeed, over the month of March 2020, between 10 and 30% of churches in the US saw increases in attendance; even as the total number of visits to churches declined nationally. This heterogeneity, where certain venues see substantial increases in attendance while others close, suggests that closure can cause individuals to find an open venue, even if that requires longer-distance travel. And, indeed, the average distance travelled to churches in the US rose by 13% over the same period. Strikingly, our model reveals that across a broad range of model parameters, partial measures can often be worse than none at all where individuals not complying with policies by traveling to neighboring areas can create epidemics when the outbreak would otherwise have been controlled. Taken together, our data analysis and modelling results highlight the potential unintended consequences of inconsistent epidemic control policies and stress the importance of balancing the societal needs of a population with the risk of an outbreak growing into a large epidemic.

They stumble that run fast: the economic and COVID-19 transmission impacts of reopening industries in the US (preprint)

COVID-19 has laid bare the United States economically and epidemiologically. Decisions must be made as how and when to reopen industries. Here we quantify economic and health risk tradeoffs of reopening by industry for each state in the US. To estimate total economic impact, we summed income loss due to unemployment and profit loss. We assess transmission risk by: (1) workplace size, (2) human interactions, (3) inability to work from home, and (4) industry size. We found that the industry with the highest estimated economic impact from COVID-19 was manufacturing in 40 states; the industry with the largest transmission risk index was accommodation and food services in 41 states, and the industry with the highest economic impact per unit of transmission risk, interpreted as the value of reopening, was manufacturing in 37 states. Researchers and decision makers must work together to consider both health and economics when making tough decisions.

Stochasticity and heterogeneity in the transmission dynamics of SARS-CoV-2 (preprint)

SARS-CoV-2 causing COVID-19 disease has moved rapidly around the globe, infecting millions and killing hundreds of thousands. The basic reproduction number, which has been widely used and misused to characterize the transmissibility of the virus, hides the fact that transmission is stochastic, is dominated by a small number of individuals, and is driven by super-spreading events (SSEs). The distinct transmission features, such as high stochasticity under low prevalence, and the central role played by SSEs on transmission dynamics, should not be overlooked. Many explosive SSEs have occurred in indoor settings stoking the pandemic and shaping its spread, such as long-term care facilities, prisons, meat-packing plants, fish factories, cruise ships, family gatherings, parties and night clubs. These SSEs demonstrate the urgent need to understand routes of transmission, while posing an opportunity that outbreak can be effectively contained with targeted interventions to eliminate SSEs. Here, we describe the potential types of SSEs, how they influence transmission, and give recommendations for control of SARS-CoV-2.

The role of directionality, heterogeneity and correlations in epidemic risk and spread (preprint)

Most models of epidemic spread, including many designed specifically for COVID-19, implicitly assume that social networks are undirected, i.e., that the infection is equally likely to spread in either direction whenever a contact occurs. In particular, this assumption implies that the individuals most likely to spread the disease are also the most likely to receive it from others. Here, we review results from the theory of random directed graphs which show that many important quantities, including the reproductive number and the epidemic size, depend sensitively on the joint distribution of in- and out-degrees ("risk" and "spread"), including their heterogeneity and the correlation between them. By considering joint distributions of various kinds we elucidate why some types of heterogeneity cause a deviation from the standard Kermack-McKendrick analysis of SIR models, i.e., so called mass-action models where contacts are homogeneous and random, and some do not. We also show that some structured SIR models informed by complex contact patterns among types of individuals (age or activity) are simply mixtures of Poisson processes and tend not to deviate significantly from the simplest mass-action model. Finally, we point out some possible policy implications of this directed structure, both for contact tracing strategy and for interventions designed to prevent superspreading events. In particular, directed networks have a forward and backward version of the classic "friendship paradox" -- forward links tend to lead to individuals with high risk, while backward links lead to individuals with high spread -- such that a combination of both forward and backward contact tracing is necessary to find superspreading events and prevent future cascades of infection.

Beyond R0: the importance of contact tracing when predicting epidemics (preprint)

The basic reproductive number --- R0 --- is one of the most common and most commonly misapplied numbers in public health. Although often used to compare outbreaks and forecast pandemic risk, this single number belies the complexity that two different pathogens can exhibit, even when they have the same R0. Here, we show how to predict outbreak size using estimates of the distribution of secondary infections, leveraging both its average R0 and the underlying heterogeneity. To do so, we reformulate and extend a classic result from random network theory~\cite{Newman2001} that relies on contact tracing data to simultaneously determine the first moment (R0) and the higher moments (representing the heterogeneity) in the distribution of secondary infections. Further, we show the different ways in which this framework can be implemented in the data-scarce reality of emerging pathogens. Lastly, we demonstrate that without data on the heterogeneity in secondary infections for emerging infectious diseases like COVID-19, the uncertainty in outbreak size ranges dramatically. %, in the case of COVID-19 from 10-70\% of susceptible individuals. Taken together, our work highlights the critical need for contact tracing during emerging infectious disease outbreaks and the need to look beyond R0 when predicting epidemic size.

Beyond $R_0$: Heterogeneity in secondary infections and probabilistic epidemic forecasting (preprint)

The basic reproductive number -- $R_0$ -- is one of the most common and most commonly misapplied numbers in public health. Although often used to compare outbreaks and forecast pandemic risk, this single number belies the complexity that two different pathogens can exhibit, even when they have the same $R_0$. Here, we show how to predict outbreak size using estimates of the distribution of secondary infections, leveraging both its average $R_0$ and the underlying heterogeneity. To do so, we reformulate and extend a classic result from random network theory that relies on contact tracing data to simultaneously determine the first moment ($R_0$) and the higher moments (representing the heterogeneity) in the distribution of secondary infections. Further, we show the different ways in which this framework can be implemented in the data-scarce reality of emerging pathogens. Lastly, we demonstrate that without data on the heterogeneity in secondary infections for emerging infectious diseases like COVID-19, the uncertainty in outbreak size ranges dramatically. Taken together, our work highlights the critical need for contact tracing during emerging infectious disease outbreaks and the need to look beyond $R_0$ when predicting epidemic size.