Why model infectious disease?

People sometimes ask: What use are mathematical models of infectious disease? There are excellent works addressing this question in depth, including McKenzie, Garnett et al, and Grundmann and Hellriegel, among many others. They are all recommended reading and offer comprehensive answers from multiple perspectives. In the meantime, I offer a few observations.

Sir Ronald Ross, who discovered that mosquitoes carry the malaria parasite, viewed the modeling process as a way of thinking carefully about epidemiologic issues. The process of constructing a mathematical model, by its very nature, requires that careful, precise ideas are formulated as the model is built. The discipline of writing down and analyzing disease processes can sharpen and inform one's thinking. The history of mathematical modeling and the payoff for malaria research is illustrated beautifully in Smith et al.

The modeling process can also uncover gaps in our knowledge and understanding, often highlighting the need for additional research and expertise in order to realistically address particular issues. Thus, modeling can be a process for both facilitating multi- or cross-disciplinary collaborations and identifying needed observational or laboratory studies. Examples of models highlighting knowledge gaps for mosquito-borne infections can be seen in Reiner and Perkins et al. 

Importantly, models enable virtual experiments and studies, including ones that cannot be carried out easily, if at all, in the real world. Mathematical models are thus tools for analyzing what if scenarios, doing feasibility studies, and carrying out risk assessments. McKenzie illustrates these points clearly for the case of biodefense.

Models allow us to assess the impact of uncertainty, and variation in data, upon our ability to make decisions, as has been studied thoughtfully recently by Christley et al. Mathematical approaches exist and are commonly applied to models to deal with uncertainty in quantitative ways, as reviewed recently by Wu et al, and illustrated by Okais et al for the case of vaccination.

I also tend to think of models as mechanisms for summarizing, synthesizing, and communicating complex information. It never ceases to amaze me how much space in research papers is devoted to specifying a model (little space) relative to the amount of prose needed to explain the model, the data required to run it, and its output (much space). The clear, precise, and economical encapsulation of so much information, typically only a few lines of equations and table of parameter values, is very appealing. Mathematics is a much more precise language than the spoken or written word.  

Modeling has many uses beyond those touched upon here, some of which will, no doubt, be the topics of future blogs.