Vampire Bats and Social Distancing
This semester has presented new challenges, such as students agreeing to a Behavioral Compact in order to gain access to campus. Some measures for safety, like being in small groups and maintaining 6 feet, does not initially seem difficult but can enter some grey areas. For example, what do you do when a friend you don’t live with wants to join you for coffee? Should you really be walking next to each other on the sidewalk?
CNN’s article on vampire bats claims that some animals, even social ones, distance themselves from their network when they are sick or even just feeling ill. While the initial study was in a controlled lab environment, experimenters were interested in whether the results would hold up in the wild. This brings us to a tree in Belize where a colony of vampire bats reside. Th existing network was maintained to the best of the researchers’ abilities. The focus was on adult females because some males are residents while others didn’t necessarily live in that particular tree hollow. With a real disease, this does open additional areas to spread and it is possible that females, their young, and resident males form clusters that are dense, but this does not provide protection from infection as modeled by probability rather than a choice to adopt new technology. There is a positive payoff to having friends in that vampire bats groom each other and that has inherent health benefits. Could strong or many grooming partners protect against illness? The vampire bats were given a non-viral non-bacterial dose that evoked an immune system response equivalent to being sick. The other half in the control group were given a saline solution as placebo. Thus the focus was on vampire bat social engagement rather than the potency of a disease. Their interactions were then tracked by small, lightweight sensors glued to their bodies that activated each other when nearby.
One major finding was that sick vampire bats interacted with less bats regardless of health status meaning a lower k value. As a result, R-naught is lower which in turn allows the disease to be considered less dangerous. So the findings suggest that sick vampire bats isolate themselves which includes decreased grooming (a social activity that would likely increase risk of transmission) as well as a reduced number of contact calls (recognizable unique calls meant to alert an opportunity to share food). I chose a node during the treatment period and identified its edges to complete the following calculations and consider the basic branching model. I assumed that since a given healthy bat encounters a sick bat at probability 0.35, if the encounter occurs the disease is transmitted. The particular sick node had 7 edges, so I used a random number generator to determine whether each node it was connected to would become infected. Ro=pk=0.35*7=2.45 which is still a high value and quite dangerous. From this, I derived the herd immunity value 1-(1/2.45)=0.59. Since on average sick bats had 4 fewer links, the behaviorally unadjusted value would be much higher at 0.35*11=3.85. I here is 1-(1/3.85)=0.74 which is a much larger portion of the population needing to be immune for the disease to die out. Vampire bats lower the number of expected cases by lowering k, p, or both. In terms of the number of bats a sick bat meets, this decreases as the sick bat moves around less or sleeps, distances itself, and forages alone. Sanitary measures such as not participating in paired grooming, not sharing food despite it being rivalrous property, and not sleeping in close proximity of others can lower the value of p so the disease will die out.
Another finding was that sick bats spent less time interacting with other bats by a difference of about 25 minutes. I considered this information with the SIR Model because individuals are contagious for a certain number of steps/time. The researchers considered the treatment time to be a 6 hour period after an initial 3 hours readapting to their roost. This can be interpreted as sick bats shortening their infectious stage and thus protecting susceptible bats. The drawing shows a possible scenario if infection lasted 1 less step on a created network (not from the study) to highlight the possible impact of being contagious for longer. Finally, sick bats interacted with fewer healthy, popular bats (bats that are centralized in the network and have many friends). I propose a possible asymmetric information equilibrium where sick bats have more knowledge (know that they feel sick) and interactions between healthy bats are valuable. Then a bat that seems lazy because it is resting may be a signal of sickness that signals this bat having lower value to healthy bats especially if they are popular. Then perhaps the sick behavior of resting as the body tries to recover decreases disease spread.
Researchers also revealed that bats living with sick bats distanced themselves too. This could be explained as a diffusion model in which all nodes (bats) initially reject the idea of not being healthy, but a starter node bat feels sick and switches to recognizing that they might not be healthy. Bats that live together have each other in common and possibly share friends, so when the threshold fraction of a given bat’s neighbors switch, they too will accept and maybe go on to social distance. The decision to distance also relates to the “Tragedy of the Commons” or in this case roosts. The overuse of this common property could result in many sick bats, which could destroy a home valued for its protection if parasites manipulate host behavior as posited in the study. What would it take for a college student to accept the possibility of being sick? Would students isolate themselves without societal pressure or enforced quarantine?
Sources:
Even vampire bats know to socially distance themselves when they get sick, study says – CNN
Common vampire bat contact calls attract past food-sharing partners – ScienceDirect