Coronavirus: A Serious Need for Analyzing Connections

Coronavirus: A Serious Need for Analyzing Connections

Graph Analytics may be invaluable to help prevent epidemics.

On February 24, James Hamblin published an article in The Atlantic with the attention-grabbing headline, “You’re Likely to Get the Coronavirus.” In it, he compares the current COVID-19 epidemic with previous events: H5N1 Avian Flu, SARS, and MERS. Each of these was much more fatal to humans. Fortunately, they were also more confined in their spread, keeping the total fatalities to fewer than 1000 persons each. On the other hand, many public health scientists are pessimistic about keeping COVID-19 tightly confined, in part because it is less virulent. One scientist expects it will eventually be like the cold or the flu — a seasonal malady which is global and kills a certain number of persons every year.

Here is the reasoning: persons infected with COVID-19 are slow to show symptoms; they can be contagious without knowing it. Therefore, infected persons will continue normal activity for a while and will infect many others. Conversely, persons who had SARS felt sick, stopped moving about, and in many cases died, ending further infection from them. 

Viral Propagation

This discussion about the dynamics of infection — viral propagation — called to mind mathematical models that I had read about in my grad school days when I first started to study graph analytics and network dynamics. One paper that has stuck with me is Maximizing the spread of influence through a social network, by David Kempe and Jon Kleinberg. They described two categories of propagation mechanism — linear threshold, where a target is activated when enough of its neighbors are activated, and independent cascade, where each activated person has a certain probability of activating each of its neighbors. The independent cascade model seems to fit COVID-19 better.

The Johns Hopkins Center for Systems Science and Engineering is maintaining a global map of COVID-19 cases, visually depicting the vital statistics by location, down to the city when possible. When I see where the disease has reached North America, I see a high correlation to the major international airports, because of course air passengers were the means by which the virus crossed the oceans.

Screenshot from Johns Hopkins CSSE Coronavirus-19 map, taken on February 26, 2020.

Modeling the Spread of COVID-19

Where is all of this leading? We could build a simple graph-based model to model the spread of an infectious disease like COVID-19.

1. Recently I presented some webinars on graph algorithms that used the global commercial flight routes as a dataset. Use this graph or a similar one to model the high-level COVID-19 propagation pathways.

2. Using the Independent Cascade model, describe the basic dynamics. Take into account the factors mentioned in the Atlantic article and others that seem relevant:
         1. likelihood of being infected by a neighbor
         2. simple probabilistic and timestep (Markov) model for the states of an infected person, such as
                        – Number of air passengers per day on each route.
                        – Likelihood of being contagious, with delay and duration times
                        – Likelihood of feeling unwell, with delay and duration times
                        – Likelihood of dying, the delay times

Is this an amateurish approach? Sure. But it might at least be a good educational tool to explain how and why different diseases propagate differently.

For serious work, you would want to couple this with models of land-based propagation. Here is where it gets much more complex because there is a much higher degree of human interaction. Epidemiologists have existing techniques for these studies, and no doubt some of them are using graph modeling already. The graph could model both geolocation data as well as more abstract things such as steps in a screening and quarantine program. Researchers in the biological sciences are also already using graphs to model metabolic processes and pathways and using subgraph similarity in the search for effective treatments. Bioscientists have driven many of the advances in network analytics. Graph analytics is also providing richer data to train deep learning applications, finding patterns and solutions that humans overlook.

Connecting Ideas

Our colleagues at TigerGraph’s sales office in China have granted the local authorities a license to use TigerGraph Enterprise Edition for the duration of the crisis. At the main TigerGraph offices in the U.S., we’re planning how we can likewise assist in the race against COVID-19. We already offer free versions, on the cloud or to install on your own.

This is an opportunity for people from different fields and backgrounds to collaborate on a common concern. We’re setting up a special forum at https://community.tigergraph.com/c/project-impact/covid-19. If you have ideas and questions about using graph models and analytics or are looking for collaborators, we invite you to join us there.

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