> inflection points are where the curve 
> goes from increasing at an increasing 
> rate to increasing at a decreasing rate.

This is another facet of IPM that offers significant utility to farmers, but not beekeepers dealing with varroa. The only "increasing at a decreasing rate" I've ever heard mentioned is the reduced rate of reproduction associated with multiple mature reproductive females entering the same cells, and if the varroa infestation has gotten that bad, the colony has dim prospects.

"Reproduction of Varroa jacobsoni in cells of Apis mellifera containing one or more mother mites and the distribution of these cells". JAR 1995, 34, 187–196
http://dx.doi.org/10.1080/00218839.1995.11100904

Mondragon "Mortality of mite offspring: A major component of Varroa destructor resistance in a population of Africanized bees". Apidologie 2006, 37, 67–74.
http://dx.doi.org/10.1051/apido:2005053


One thing that I'd like to see is an attempt at a feed supplement that includes something to mess with the mites' mating pheromones, which these guys say could be as simple as making that pheromone ubiquitous in all brood cells.  (But if Newton had worked for the USDA, they would have ignored the implications of his discovery of the universal nature of gravity in terms of Kepler's first and second laws of planetary motions, and instead funded him only to do research on reducing the fall of apples, and the damage to their market value.) 

"The mating behavior of Varroa destructor is triggered by a female sex pheromone. / Identification and dose-dependent effects of components of the Varroa sex pheromone." Apidologie 44, 481-490
https://doi.org/10.1007/s13592-013-0198-5

Paywalled, but ain't the lock that ain't been picked:
https://drive.google.com/file/d/1wKWz2M9gs-x4dpl83NVMdOVjOnuK8APP/view?usp=sharing
https://tinyurl.com/fdxkmh2b

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