2018-07-30: Setting heterogeneous biting risk parameters
Just as I was wondering how to parameterize a biting risk distribution, I learned that Prashanth had recently digitized this plot from INDIE:
https://prod--cdn-iiif.elifesciences.org/lax:32625/elife-32625-fig2-v1.tif/full/1500,/0/default.jpg
In subplot (a), each bar represents an individual, and bar height represents a mosquito blood meal matched back to that individual at the indicated time of the season. On Prashanth’s recommendation I kept only the “peak biting” data for my analysis.
Here’s that digitized data, keeping only peak biting and rotating the axis:
Jaline’s description of the “change_biting_risk” function is that it doesn’t change the overall number of bites, just the distribution of those bites. Thus, we can describe “risk” as what proportion of overall bites any one individual receives, and redraw the above plot with a new y-axis (left, below). But the risk function expects a distribution in units of relative risk, so we can make this same plot again, taking the mean biting proportion (0.0196) as the “baseline” (right below):
Now we can convert this to a frequency distribution, to which we can fit some functional form:
Current distribution options in the biting risk function are uniform, Gaussian, and exponential, so exponential is clearly the best choice here. Unsurprisingly given that we have constructed this distribution to have mean=1, an exponential with lambda=1 gives the best fit (using fitdistr in R, log-likelihood of -51):
The part of all this I’m least comfortable with is the assumption that “mean risk” is the appropriate thing to use as the baseline. As a quick check, I tried using the median risk instead (0.0072), which yields much higher RR values and a best-fit exponential distribution with lambda=0.37 (log-likelihood=-102):
Given that the median-valued version is less interpretable and gives a worse fit, I went with the mean-value version for the heterogeneous biting simulations I ran over the weekend. Adding this functionality quite dramatically attenuated intervention impact, leaving much more residual transmission at a given intervention coverage than we’d been seeing previously.