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Network Models and Superspreaders
Network Models and Superspreaders
Superspreaders
Superspreaders
Following the 20/80 rule, 1 in 5 people are superspreaders that transmit infections to far more people than the majority do. Superspreaders can be people who come into contact with a high volume of people. It is impossible to predict or confirm who will be a superspreader. For COVID-19, majority of young people do not show symptoms even if they are infected, but they could carry on with their lives transmitting the virus everywhere. Some people get infected with stronger strains of COVID-19 than others, and other people travel a lot more than others. Here are some attributes that classify potential superspreaders: degree, closeness, and activity potential (NCBI).
One example of a superspreader for SARS-CoV-2 is a 61 year old woman who reportedly spread the virus to over 30 people at the Shincheonji Church of Jesus the Temple of the Tabernacle in South Korea in late February. Here are some other examples of superspreaders in society:
Social: Someone who has mono and does not show signs or any of the symptoms goes to a party, kisses someone else and continues to go out and kiss people for the following few nights will potentially give mono to a high volume of people because of the large amount of people he/she is kissing while infected with the disease.
Food: Someone infected with a disease could be working in a restaurant and subsequently cook/serve the food of all of the customers dining in as well as ordering for take out.
Transportation: If throughout a work week multiple infected cases all had ridden the subway, it is possible a daily commuter of the subway is the superspreader as he/she would be infecting significantly more people than the average person. The following figure and table are from the National Center of Biotechnology and illustrates how easy a super-spreader could infect such a high volume of people over such a limited time.
Source: World Health Organization Regional Office for the Western Pacific 2005
Network Contagion Models
Network Contagion Models
SIR/SEIR Models can be networked models as well. Each node in the network would be an individual, and an edge between individuals would represent a social connection that a disease can be transmitted over. Nodes that are connected to people who are infected would be the exposed or susceptible people who could eventually get infected and make the nodes they are connected to also exposed or susceptible. The networked version of the model is dynamic as people recover or continue to get infected. COVID-19 is spreadable through the people individuals interact with, which is why it is important to think about a networked epidemiological model to understand the dynamics of the virus.
In this network, we see at time t = 0 that the red node “0” becomes an infected individual. At t = 1, node 2 and 3 become susceptible to the disease since they are socially connected, and by t = 2 node 2 and 3 are infected as well. At t = 3 we see that the neighboring nodes of infected individuals become susceptible. If this dynamic network continues to grow and more and more individual nodes become susceptible due to their infected neighbors, then the disease will spread.
The following drawing fits the model of high school friend groups. If the red lines represent a group of friends and two of them are dating, then when they break up, one of them will inevitably seek a relationship with a blue dot in a different group because it is uncommon to date multiple people in a friend group. That is how it is exemplified with spreading across clusters.
Furthermore, the way that a network associated with an outbreak looks depends on the type of outbreak and the way that it is transmitted. The network below illuminates how STDs can spread by mapping out sexual relationships.
Source: A sexual network associated with an STD outbreak. Sexually Transmitted Infections, Potterat et al. doi:10.1136/sti.78.suppl_1.i152
Source:https://www.ncbi.nlm.nih.gov/pubmed/22639701?dopt=abstract&otool=fhcrclib Potter GE, Handcock MS, Longini IM, Halloran ME. 2012. Estimating within-school contact networks to understand influenza transmission. Annals of Applied Statistics. 6(1): 1-26; doi: 10.1214/11-AOAS505
Unlike STDs though, influenza can spread by merely contact which makes it more likely to spread through the network.
The networks shown to the left show that friendship networks, contact networks, and transmission networks are all different. Despite this, the different networks all impact each other.
Below are examples of networks within schools that show the power of network connectivity and social distancing:
Typical groups and person-to-person links for model teenager. The teenager (T1) belongs to a household (fully connected network, mean link contact frequency 6/day), an extended family or neighborhood (fully connected network, mean link contact frequency 1/day), and 6 school classes (ring network with connections to 2 other teenagers on each side as shown in black; purple links denote connections of other teenagers within the class; mean link contact frequency 1/day). Two random networks are also imposed, 1 within the age group (teenager random, average of 3 links/teenager, mean link contact frequency of 1/day), and 1 across all age groups (overall random average of 25 links/person [not all links shown], mean link contact frequency of 0.04/day)
Source: Targeted Social Distancing Designs for Pandemic Influenza, Robert J. Glass*Comments to Author , Laura M. Glass†, Walter E. Beyeler*, and H. Jason Min*Author affiliations: *Sandia National Laboratories, Albuquerque, New Mexico, USA; †Albuquerque Public High School, Albuquerque, New Mexico, USA https://wwwnc.cdc.gov/eid/article/12/11/06-0255-f4
Initial growth of an infectious contact network. Colored rectangles denote persons of designated age class, and colored arrows denote groups within which the infectious transmission takes place. In this example, from the adult initial seed (large purple rectangle), 2 household contacts (light purple arrows) bring influenza to the middle or high school (blue arrows) where it spreads to other teenagers. Teenagers then spread influenza to children in households who spread it to other children in the elementary schools. Children and teenagers form the backbone of the infectious contact network and are critical to its spread; infectious transmissions occur mostly in the household, neighborhood, and schools.
Source: Targeted Social Distancing Designs for Pandemic Influenza, Robert J. Glass*Comments to Author , Laura M. Glass†, Walter E. Beyeler*, and H. Jason Min*Author affiliations: *Sandia National Laboratories, Albuquerque, New Mexico, USA; †Albuquerque Public High School, Albuquerque, New Mexico, USA https://wwwnc.cdc.gov/eid/article/12/11/06-0255-f4
That’s why the CDC has recommended social distancing in response to COVID-19. Social distancing reduces network connectivity and thus slows the rate of transmission.
More on Networks
More on Networks
Networks help us understand what our underlying social structure is. This is because the way that people interact is different than the random mixing model. Unlike the random mixing model, most interactions and connections in real life are relatively structured (e.g. families, neighbors, classmates, co-workers, best freinds etc). Thus, most people don't cross paths with the population uniformily, and instead the path is more dependent on one's social life.
When we combine analysis of networks and SIR/SEIR models, we can have a better understanding of how diseases spread through societies and create smarter policies and behavior changes to address pandemics.
Networks help explain second order effects. The second order effect is why social distancing measures entail only interacting with people from your household, as opposed to merely avoiding crowded spaces and continuing to spend time with various friends one-on-one. If somebody infected goes to another household and infects them - if nobody from said household interacts with other people, then the spread will be contained. However, if two members from said household left the house separately and each saw one friend separatley, then the disease will have spread to at least 4 homes. If those homes have multiple people who aren't social distancing diligently either, then the disease spreads to even more homes.
Networks can also help us with contact tracing which can help inform decision making. This taught us that we should especially avoid immunocompromised and elderly people.
It's not just the number of contacts we have, it's who we contact and how many contacts they have. Below are some suggested behavours (clarified with high school tropes):
Reduce the number of people you contact (embrace being a loner)
Steer clear of people with lots of contacts (avoid the popular kid with a big friend group)
Avoid groups with different connections (ignore your "floater" friends who are part of multiple friend groups)
Don't be a superspreader (cut out on assembly meetings)
Network models can help us to reason and act.
Websites and Media
Websites and Media
https://blogs.unimelb.edu.au/sciencecommunication/2012/09/25/its-a-small-world-after-all/
https://www.bbc.com/news/health-51447143
https://en.wikipedia.org/wiki/Basic_reproduction_number
https://www.cis.upenn.edu/~mkearns/teaching/NetworkedLife/contagion13.pdf
Academic papers of relevance:
Academic papers of relevance:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4047528/
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4047528/
https://www.nature.com/articles/srep01905?message-global%3Dremove
https://www.journals.uchicago.edu/doi/pdfplus/10.1086/386272
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5333634/
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6303749/
Sources:
Sources:
A sexual network associated with an STD outbreak. Sexually Transmitted Infections, Potterat et al. doi:10.1136/sti.78.suppl_1.i152
https://www.ncbi.nlm.nih.gov/pubmed/22639701?dopt=abstract&otool=fhcrclib Potter GE, Handcock MS, Longini IM, Halloran ME. 2012. Estimating within-school contact networks to understand influenza transmission. Annals of Applied Statistics. 6(1): 1-26; doi: 10.1214/11-AOAS505
Targeted Social Distancing Designs for Pandemic Influenza, Robert J. Glass*Comments to Author , Laura M. Glass†, Walter E. Beyeler*, and H. Jason Min*Author affiliations: *Sandia National Laboratories, Albuquerque, New Mexico, USA; †Albuquerque Public High School, Albuquerque, New Mexico, USA https://wwwnc.cdc.gov/eid/article/12/11/06-0255-f4
World Health Organization Regional Office for the Western Pacific 2005
Contributors: Maggie Maranz, Collette Patel, Heba Syed, and Michael Lin
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