Network Effects Lead to Unpredictable Disease Outbreaks
https://health.usnews.com/health-care/patient-advice/articles/2018-09-19/hand-foot-and-mouth-disease-is-spreading-again
This article is about a recent outbreak of the virus that causes hand, foot, and mouth disease which causes red oozing blisters to appear on one’s body. This outbreak gained national publicity when three MLB pitchers were sidelined with the disease. This disease, which usually only effects children under the age of 5, has become uncommonly prevalent on college campuses this fall. The dynamics of this spread can be thought of in terms of our recent lecture on epidemics.
We can consider the population of American college students to form a SIR graph in which each node (student) is labeled as either susceptible (S), infected (I), or removed (R) at each discrete time step. At each new time step, every infected student can pass on the disease with probability p to any of their k neighbors. The basic reproductive number R=p*k characterizes the propensity of the disease to spread through the entire graph. According to the article, the virus is easily spread between people through direct contact, especially when feces, mucus or saliva are involved. These substances can also linger on surfaces and remain infectious. This corresponds to our model having a relatively large value of p, so that infected nodes are very likely to pass on the disease. Appropriately, one of the prevention methods mentioned by the article was to practice good sanitation practices such as thoroughly washing hands after going to the bathroom, and wiping down surfaces such as tabletops and handrails. This action serves to lower the infection probability p in our model. A second factor explaining the recent outbreak of hand, foot, and mouth disease is the fact that college campuses are crowded with thousands of students in a relatively small area. This article suggests that the density of students on college campuses causes a large number of people to be at risk for infection even when there is only one “patient zero”. This corresponds to a larger value of k which represents the average number of susceptible nodes neighboring any given infected node in our model. Another prevention method mentioned by the article was to encourage students to stay home if they notice any open lesions or rashes on their body. This strategy reduces k by effectively removing the edges between an infected node and its neighbors until that particular node has been removed. These two methods both serve to reduce the reproductive number R. When this value falls below 1, the probability that the outbreak will die out approaches 1 as the number of time steps increases.
The question remains as to why this outbreak spontaneously emerged. One qualitative explanation is as follows. Propose that the United States is described by a Watts-Strogatz-like model where students at the same university have strong homophilic links, and students across universities form weak ties with some small probability c. As depicted in figure 21.7 of our textbook, for intermediate values of c (such as ~0.2) oscillations intermittently appear and then disappear. This is because the system achieves network-wide synchronization for some duration before falling back “out of sync” for reasons that are hard to quantify. This sudden outbreak of hand, mouth and foot disease could have occurred via a similar mechanism.