[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.]

This is the last in a long series attempting to explain a recent paper by Lipsitch et al. on mathematical modeling of the effects on influenza control of antiviral resistance, published in *PLoS Medicine* in January 2007. Modeling is a valuable technique but for most readers, even most scientists in the flu community, the model itself is a black box. We wanted to look into the box to see its contents. Along the way we have tried to convey the flavor of mathematical modeling and locate this tool among the many other tools available to scientists to understand influenza. For a summary of what we learn from this paper we can do no better than quote the authors (from their **Discussion** section, internal literature citations omitted):

The simple model used here enables evaluation in a general way of the potential impact of resistance on an influenza control program, to assess the relative contributions of different factors (parameters) contributing to the epidemic. It uses a simplified, exponentially distributed natural history; however, since most of the conclusions (except for those about the magnitude of delays) are about the final state of the population, and all terms in the equations can be nondimensionalized by dividing by the generation time, this simplification does not have a major effect on outcomes. This model does not account for saturation of contacts due to transmission within families and other small groups, and therefore predicts higher attack rates than more complex, agent-based models for a given value of R

_{0}.Given the simplifications inherent in any model and the large uncertainties about the properties of a potential pandemic strain and its resistant variants, we emphasize the qualitative predictions of the model . . . rather than the exact quantitative predictions.Important predictions that we believe to be robust to model structure are that (1) antiviral use will favor the spread of resistance even if such use rarely generates de novo [spontaneously arising] resistant strains; (2) despite the spread of resistance, prophylaxis and treatment can both delay and reduce the size of the epidemic; (3) nondrug interventions (if effective) and antiviral use – which will likely be used together in the response to a pandemic – generally have synergistic benefits, despite the fact that nondrug interventions may promote resistance; and (4) relatively minor differences in fitness cost may make large differences in outcomes, even when emergence probabilities are low (Figure 4). These results extend those of previous models, which showed (like our model) that the fitness cost of resistance strongly influences the ability of resistant strains to spread during an epidemic. [our emphasis]

Notice the bolded sentence:

Given the simplifications inherent in any model and the large uncertainties about the properties of a potential pandemic strain and its resistant variants, we emphasize the qualitative predictions of the model . . . rather than the exact quantitative predictions.

The Lipsitch team are accomplished modelers with a solid understanding of their subject matter. One of the (many) things I like about this paper is it does not over interpret the results but extracts what is useful and potentially important. Many scientific papers are made to bear more interpretative weight than they should in press reports, but authors are often complicit. (I think of this every time I see a paper on a new vaccine technology that “works in mice.”) Modeling requires a variety of skills foreign to biologists and biology is also foreign to many modelers. So it is not surprising some modelers have an exaggerated or false impression of how generalizable their work is. Fortunately there is a cadre of flu modelers both expert in modeling and their subject matter. The Lipsitch team are among them. There are a number of others.

We close, then, with the bottom line of the Lipsitch paper (literally, the last paragraph) about the role of antivirals in controlling influenza after taking the emergence of resistance into account:

Optimism about the benefits of antivirals in an influenza pandemic should be tempered by the knowledge that transmissible, pathogenic resistant strains are a real possibility and could reduce the benefits of antiviral use in pandemic control. Successful implementation of nondrug interventions to control resistance will, in most circumstances, amplify the benefits of antiviral use in controlling the pandemic, although such interventions may increase the proportion of resistant cases. Because the impact of resistance is relatively insensitive to the rate at which resistant strains emerge de novo in antiviral recipients, efforts to control influenza transmission overall may be of greater benefit than efforts to reduce the de novo rate of emergence of resistance. Despite these caveats, we do not believe that concerns about resistance should preclude the widespread deployment of antivirals as part of the response to a pandemic. If these drugs, used prophylactically or for treatment, are effective in reducing transmission of the next pandemic strain, they should provide benefits by reducing the number of infected patients and delaying transmission, even if resistant strains ultimately become widespread.

Whether you agree or not, we hope at least you now have some idea how this judgment was arrived at.

Table of contents for posts in the series:

The Introduction. What’s the paper about?

Sidebar: thinking mathematically

The rule book in equation form

Effects of treatment and prophylaxis on resistance

Effects of Tamiflu use and non drug interventions

Effects of fitness costs of resistance