This post is the 4th of several devoted to addressing the complex challenges of modelling the coronavirus as a public health issue. It is also about clarifying for a wider audience how and why such modelling is important, as well as the value and power of complex systems thinking and computational modelling for public health policy.
The focus of the first post was to explain how models influence public health policy and why some models are better at modelling COVID-19 than others, given the challenge of complexity. The post ended asking the question: So, what does an effective model look like? (CLICK HERE for the first post) In response I said I would review two of the models getting the most attention. Before turning to these models, however, the second post reviewed, from a complex systems perspective, what a public health model of infectious disease looks like in the first place. (CLICK HERE for the second post) The 3rd post reviewed the first of our two models: the simulation model by Ferguson and colleagues at Imperial College London (CLICK HERE for the third post).
The current post will review the utility of complex network modelling for infectious diseases and, more specifically, the model by Vespignani and colleagues at Northeastern University in the States.
The failure to embrace public health
In most western countries — particularly those located in the global north — the narrative of modern medicine is rather consistent: our medical problems are our own, each of us, including their cause and cure. If someone is depressed, we see it’s a psychological problem; if someone is overweight, it is a personal eating issue; and if someone regularly catches the flu it as a problem with their immune system.
Public health experts, epidemiologists, health sociologists, medical anthropologists and social workers have rather consistently challenged this idea, arguing instead that, contrary to the picture painted by western medicine, our health is not anywhere near as personal and private as we tend to think it.
And the argument has been reasonably convincing. Nuances aside, the intertwined histories of population and public health throughout the world are ultimately a story of significant accomplishment. As proof, a short list is sufficient: clean drinking water, sanitation, food safety, air quality, vaccines and preventable diseases, tobacco control, family planning and so forth. And these accomplishments have extended themselves well into the globalized era in which we presently live through the monumental efforts of such globally- focused organisations as the World Health Organization.
Still, despite these accomplishments and tremendous successes, population and public health in the 21st century faces a crisis of understanding. And the major culprits, it appears (in addition to more localized factors) are the same economic, political, cultural, and technological forces of globalization that have, in many ways, purportedly made the world a better place. In short, we’ve enjoyed the benefits of public health without embracing its most important point:
The message is this: the causes and cures of our health are largely a public matter, and in complex and nuanced ways that we regularly (and perhaps purposely) fail to understand. Equally important — from the negative impact poverty has on wellbeing to ensuring citizens equitable access to healthcare — these causes and cures are primarily social determinants and social solutions.
THE HIDDEN INFLUENCE OF SOCIAL NETWORKS
Perhaps one of the most important studies to demonstrate to western medicine the importance of public health was the game-changing 2007 study by Christakis and Fowler — The Spread of Obesity in a Large Social Network Over 32 Yearspublished in the New England Journal of Medicine. The network scientist, Albert-László Barabási, who wrote a commentary when the study was published, in which he clarifies why this study was so important. He states:
A recent study reported that among people who carried a single copy of the high- risk allele for the FTO gene, which is associated with fat mass and obesity, the risk of obesity increased by 30%. The risk of obesity increased by 67% among people who carried two alleles, and on average they gained 3.0 kg (6.6 lb) or more.1 Given that approximately one sixth of the population of European descent is homozygous for this allele, this link between the FTO gene and obesity appears to be one of the strongest genotype–phenotype associations detected by modern genome-screening techniques” (p. 404).
But here is Barabási’s key point:
That obesity has a genetic component is not surprising: researchers have long known that it often runs in families. In this issue of the Journal, Christakis and Fowler suggest that friends have an even more important effect on a person’s risk of obesity than genes do.
In short, when it comes to health issues such as obesity, our social networks are a more important cause and cure. Our health is impacted significantly by the networks with which we interact, which include not only families, friends and partners, but also co-workers, acquaintances and the networks of people we randomly interact with in public. Even more difficult to grasp — and this is one of the most important insights that Christakis and Fowler showed — is that our health is also significantly impacted by the networks with which our networks interact and so on and so forth. And, it is this important insight regarding the role that social networks play in our health that makes the study of social networks is so powerful. Barabási explains it like this:
The authors reconstructed a social network showing the ties between friends, neighbors, spouses, and family members among participants of the Framingham Heart Study, making use of the fact that the participants had been asked to name their friends to facilitate follow-up in the study. The authors observed that when two persons perceived each other as friends, if one friend became obese during a given time interval, the other friend’s chances of following suit increased by 171%. Among pairs of adult siblings, if one sibling became obese, the chance that the other would become obese increased by 40%. The results of this study also indicate that obesity is clustered in communities. For example, the risk that the friend of a friend of an obese person would be obese was about 20% higher in the observed network than in a random network; this effect vanished only by the fourth degree of separation.
In other words, as Christakis and Fowler suggest, the impact that others have on our health is not just an issue of ‘birds of a feather flocking together’. Instead, it appears that health is a social contagion. It spreads across our social networks. The health of our social networks impacts and is deeply intertwined with our individual health. And we, in turn, influence the health of the networks of which we are a part.
For more on this study and its social network, watch this video. And for more on the role networks play in health, watch this Ted Talk by Christakis.
How social networks impact COVID-19
While such an insight by Christakis and Fowler was a game-changer, the next challenge — which network scientists working in fields such as public health and infectious disease modelling have spent the last decade or more trying to understand — is how exactly how these social networks impact health, as well as what a health versus unhealthy social network looks like. Case in point is COVID-19 and the complex network model by Vespignani and colleagues at Northeastern University in the States. Before we proceed to that study, a few key network terms need to be defined.
As with our review of microsimulation and modelling in general in my previous posts, we cannot get into the details of social networks sufficiently in a post. We can, however, review some key concepts and, for those interested, a few online sources for learning more, sufficient to understand what network scientists are trying to understand about the role social networks play in the spread of the coronavirus.
Here is a quick list of key terms – which can be found in (Newman, 2003) – that network
Vertex or a node: A fundamental unit of a network represented usually by a dot.
Edge or a link: A line connecting vertices.
Directed or undirected edges: An edge is directed is if it runs only in one direction (such as in a one-way road between two points), and undirected if it runs in both directions (Newman 2003, p. 173). A network in which all edges are directed is referred to as a directed network or graph.
Neighborhood of a node i in a graph is simply defined as the set of all nodes that the node i is connected to. The usual convention is to assume that i is not connected to itself i.e., avoid loops.
Degree: The number of connections (edges) a vertex has. For a directed network, one wants to know the direction of those connections. Those connections going out are called ’out-degree,’ and those coming in are called ’in-degree.’
Component: The component to which a vertex belongs is the set of all vertices that can be reached from that vertex using existing edges in the network. ’For a directed graph, there is an in-component and an out-component, which are the sets of vertices from which the vertex can be reached and which can be reached from it,’ respectively (Newman 2003, p. 173).
Geodesic path: The geodesic path refers to shortest route in the network from one vertex to another.
Diameter: ’is the length of the longest geodesic path in a network’ (Newman 2003, p. 173).
Of the numerous writings on networks currently available – for example, (Albert and Barabasi, 2002, Barabasi, 2003) – two authors stand head and shoulders above the rest (at least for us), mainly for the quality of their critical insights into network analysis, which is important, as well as the clarity and accessibility of their writing. Those two authors are Mark Newman and John Scott. Newman is highly useful because he is trained as a physicist and is one of the top scholars in the field of complex networks; in turn, Scott is a sociologist and one of the leading scholars in social networks. One of the best online books is Introduction to Social Network Methods by Robert A. Hanneman and Mark Riddle.
The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak
Now that we have a basic sense of some of the key concepts of network science, we can turn to the Network study on travel restrictions by Alessandro Vespignani and international colleagues through the Network Science Institute at Northeastern University.(As with my review of the Imperial model inBlog Post 3, I will quote from their work and then, in green font, make some comments for clarification)
THEY STATE: Motivated by the rapid spread of COVID-19 in Mainland China, we use a global metapopulation disease transmission model to project the impact of travel limitations on the national and international spread of the epidemic. The model is calibrated based on internationally reported cases and shows that at the start of the travel ban from Wuhan on 23 January 2020, most Chinese cities had already received many infected travelers.”
SOME SPECIFICS ABOUT THEIR MODEL
THEY STATE: To model the international spread of the COVID-19 out-break we use the Global Epidemic and Mobility Model (GLEAM), an individual-based, stochastic, and spatial epidemic model.
Castellani comment: As you may recall from Post 3, I explained what stochastic models are. Here they are using a similar approach, as its value is it allows for real-world randomness and messiness to enter the modelling process. Also, similar to the Imperial model, it is individual-based and spatial.
THEY STATE: GLEAM uses a metapopulation network approach integrated with real-world data where the world is divided into sub-populations centered around major transportation hubs (usually airports). The subpopulations are connected by the flux of individuals traveling daily among them. The model includes over 3,200 sub-populations in roughly 200 different countries and territories. The airline transportation data consider daily origin-destination traffic flows from the Official Aviation Guide (OAG) and IATA databases (updated in 2019), while ground mobility flows are de-rived by the analysis and modeling of data collected from the statistics offices for 30 countries on 5 continents. Mobility variations in Mainland China were derived from Baidu Location-Based Services (LBS).
Castellani comment: Here is where the network model is different from the Imperial model. In the network model, network data is used, specifically transportation data. These data are key because then the progression of COVID-19 could be modelled along these networks. If you click on the image to the right –>, it will allow you to run an infectious disease model on a social network. To run the model hit SETUP and then GO.
THEY STATE: Within each sub-population, the human-to-human transmission of COVID-19 is modeled using a compartmental representation of the disease where individuals can occupy one of the following states: Susceptible (S), Latent (L), Infectious (I) and Removed (R). Susceptible individuals can acquire the virus through contacts with individuals in the infectious compartment, and become latent, meaning they are infected but cannot transmit the infection yet.
Castellani comment: Similar to the Imperial model, which I dicussed in Post 3, this network model follows the basic SEIR model (susceptible, exposed, infected and recovered).
So, what did they learn?
THEY STATE:The analysis of the COVID-19 outbreak and the modeling assessment of the effects of travel limitations could be instrumental to national and international agencies for public health response planning.We show that by 23 January 2020, the epidemic had already spread to other cities within Main-land China. The travel quarantine around Wuhan has only modestly delayed the epidemic spread to other areas of Main-land China. This is in agreement with separate studies on the diffusion of the SARS-CoV-2 virus in Mainland China.
THEY STATE: The model indicates that while the Wuhan travel ban was initially effective at reducing international case importations, the number of cases observed outside Mainland China will resume its growth after 2-3 weeks from cases that originated elsewhere.
THEY STATE: Furthermore, the modeling study shows that additional travel limitations up to 90% of the traffic have a modest effect unless paired with public health interventions and behavioral changes that achieve a considerable reduction in the disease transmissibility.
Castellani comment: While some of their predictions require update (as new data has become available, which is why testing and information is so important!) their general insight has proven useful, as it has been corroborated by other models and the data — namely, social distancing, testing, and governmentally led public health interventions to mitigate and suppress the spread of COVID-19.
THEY STATE: The model also indicates that even in the presence of the strong travel restrictions in place to and from Mainland China since 23 January 2020, a large number of individuals exposed to the SARS-CoV-2 have been traveling internationally without being detected.Moving forward we expect that travel restrictions to COVID-19 affected areas will have modest effects, and that transmission-reduction interventions will provide the greatest benefit to mitigate the epidemic.
As this study has hopefully demonstrated, network model are a useful addition to the other approaches being employed to understand the coronavirus. Network models are primarily valuable because they allow us to see the specific routes by which disease travels through a population or, more specifically, a community. In the case of the current study, they could follow the disease along major transportation routes.