Ever since clicking ‘publish’ on my first post in the Great Models series, I didn’t feel right about it. I like to be original and interesting, however, I chose to write about the ‘mosquito theorem’ because it was a safe choice – because the work was foundational and because Ross’ achievements are highly and widely respected. I had named this blog post series Great Models and given the name, I felt compelled to chose work that was undeniably significant. In keeping with my blog mission, in the future I want to make the choices of Great Models more with respect to elegant model derivation for a given question, and not with respect to the gravity of the conclusions. The next model that I plan to discuss, I chose just because it’s fun. This will shatter my expectation that I have to choose only work that is already widely acclaimed.
Since that post, I started reading The Malaria Capers by Robert S. Desowitz. The dust jacket of the book states that despite the progress of 21st century science, malaria is more prevalent in tropical regions now than 50 years ago – and that truly the situation is worse because now a large number of mosquitoes are resistant to insecticides. The first part of the book was a story about how scientist’s determined the transmission route of kala azar (visceral leishmaniasis). An interesting aside is that kala azar appears to be a relatively new infectious disease, one that did not cause it’s first epidemic until 1824 (pp. 34).
To understand the spread of kala azar, the first problem for scientists was to identify the infectious agent. Initially, this was thought to be a hookworm because hookworm infections were common and sometimes found in patients that had died from kala azar. The infectious agent, in fact, was a protozoan first observed by Dr. William Boog Leishman. However, at the time it was quite some work to determine what the specks that Leishman had seen inside macrophages actually were. Initially, it was thought that these bodies could be trypanosomes.
The so-called Leishman-Donovan bodies were then put in a saline solution. This revealed a flagellated elongated life stage and this transformation implied an insect vector in the transmission of the black fever. Bed bugs were very common and unpopular at the time and so these arthropods were scientist’s first guess. To incriminate the bed bugs it was necessary to show that the protozoan could survive in these insect’s intestines and then moved to the salivary glands (where they could be transferred during biting) or that they were defacated and rubbed into the bite wound. This could not be demonstrated for bed bugs and instead it was determined that the silvery sandfly was the guilty party. The silvery sandfly first became a candidate vector when the range maps of this sandfly and kala azar epidemics were overlayed and found to be suspiciously related.
None of this story has much to do with modelling, but it highlights the challenge of making inferences in science when there are multiple plausible hypotheses and only incomplete knowledge. Would solving the kala azar problem be any simpler today?
With a more advanced taxonomic key for microbes and with modern day molecular techniques, it would be much easier to determine that the Leishman-Donovan bodies were not an organism that had ever been seen before, and to slot them into the tree-of-life as an animal-like protist. However, determining the insect vector might still be roughly as challenging now as it was in the 1900’s because the knowledge gains made in the areas of vector ecology and epidemiology over this period have been less dramatic.
Problems with multiple plausible hypotheses and incomplete information are a type of problem where modelling can make a great contribution. Here, the mathematical model is used to build a bridge between each hypothesis and the available evidence, to understand if any of the hypotheses are consistent with the limited information on hand, and even more so, to determine what additional characteristics and additional pieces of evidence must exist if each of these hypotheses are to be consistent. For example, modelling might be used to determine if the seasonal variation in kala azar is consistent with the seasonally driven vector population biology combined with the current best explanation of vector-human epidemiology. In fact, it was mentioned in the book that major kala azar epidemics occur on a 15-year cycle and, to me, that sounds like a great modelling problem for someone!