[A series of posts explaining a paper on the mathematical modeling of the spread of antiviral resistance. Links to other posts in the series by clicking tags, “Math model series” or “Antiviral model series” under Categories, left sidebar. Preliminary post here. Table of contents at end of this post.]
We conclude our section by section examination of the mathematical modeling paper by Lipsitch et al., published in PLoS Medicine. We have finally arrived at the final section, Discussion (starting on page 8 of the .pdf version). In the second post we said many scientists read only the Abstract, Introduction and Discussion sections of papers to see if they are sufficiently interested (or have enough specialist knowledge) to read the Methods and Results sections. This may shock you, as most people assume that when scientists read and cite a paper they have read the whole thing in detail. When it is in their own field, usually they have, but outside their own area of special knowledge there is neither the time nor ability to do this. And frankly, neither is it usually worth the effort. The scientific enterprise is a web of trust, credibility and credulity. The reputation and credentials of a scientist and his or her institution or laboratory, an unquestioned (and probably misplaced) faith in the peer review system, and simple necessity are the foundations of day to day practice. This is why allegations of scientific fraud are so deadly. But since we have been through the paper in detail, we don’t have to take the Discussion section on faith, except for one proviso. Online journals are now able to publish more and longer papers and to include details not possible when print space was limited. So this paper and many others now have online supplements with additional material, often important and valuable. We will find it necessary to refer to this as well, although we will not go through the mathematics because it uses methods that would require a graduate course to explain (although it’s not that complicated).
The first two paragraphs of the Discussion give the big picture, both the premise of the modeling effort and the overall result. It says the model confirms what common sense and other models have also shown, that a combination of an effective antiviral and non-drug measures, if applied sufficiently quickly and intensively, can reduce and stretch the duration of spread of epidemic influenza in a community. Increasing the duration allows additional time for preparation and eases the burden on health services. If resistance develops but the mutant is less genetically fit and transmits less effectively, then if measures are applied quickly, say within the first few thousand cases, spread can be aborted. This is the “Tamiflu blanket” scenario.
However the authors, and most expert observers, consider the required conditions improbable. There is currently not enough available Tamiflu nor the means to distribute it in a timely manner. The model examines two questions related to the ideal case: what happens when timely coverage of the population by antiviral use is much less than 40% of the population; and what happens if mutant resistant strains evolve that are just as fit or almost as fit as the sensitive strains? The model examines even very rare emergences of one mutant in 50,000 to 500,000 prophylaxed cases because we must assume assume that with mass antiviral use, tens or even hundreds of millions of people will be treated. Even rare occurrences would then happen with certainty. And since outbreaks will occur in many communities almost simultaneously, rare resistant mutants in one community can spread to others even when the others have been intensively treated with antivirals. In other words, you might conceivably have a local Tamiflu blanket but not a global one. The model shows that even for rare mutants will eventually spread rapidly and widely. So in this sense the model delivers bad news.
But there is less pessimistic news in the details, and it is summarized in paragraphs three and four of the Discussion. The third paragraph notes again that when antiviral and other measures are insufficient to stop spread completely (the likely case), the optimum benefit comes from intermediate use. Benefit does not ramp up continuously with population coverage. The authors argue for the reasonableness of this with a simple thought experiment. You are always better off using Tamiflu and less coverage is sometimes better than more coverage.
A second counter-intuitive (potential) outcome is revealed by the model. The more intense the non-drug interventions (e.g., social distancing), the higher the level of eventual resistance in the population. The reason relates to the speed with which the sensitive strain can spread in a population where transmissibility is high (less intervention), more sensitive spread occurring before a rarely emerging resistant strain can get going. Slowing the spread with non-drug interventions gives the needed time for the resistant strain to gain a foothold and start to spread before the sensitive strain has infected more people.
It is important to recognize that all of these results describe what might happen under very plausible conditions, not what would definitely happen in a pandemic. The model helps us understand why these things could happen and enlarges our intuition for the dynamics of influenza spread when antivirals are used on a population. In constructing this fairly simple model, a number of important assumptions had to be made. In the final posts we will ask to what extent these assumptions affect what we learn from the model.
Table of contents for posts in the series: