Modeling Infectious Diseases in Humans and Animals

  • Matt J. Keeling &
  • Pejman Rohani
Princeton University Press: 2007. 366 pp. $65, £38.95 9780691116174 | ISBN: 978-0-6911-1617-4

Infections produce further infections. The implications of this simple observation have long intrigued theoreticians and confounded empiricists. It implies nonlinear dynamics, to use the mathematical jargon, and this makes it difficult to be intuitive about what will happen next, especially if the intention is to intervene. Expert opinion is often not up to the task; we also need the insights provided by mathematical models. These are being widely used to help understand the epidemiology of infectious diseases and to design control programmes. Models can support, add to and sometimes even overturn prevailing wisdom — think of malaria, AIDS, measles or foot-and-mouth disease.

In 1991, Roy Anderson and Robert May published the hugely influential Infectious Diseases of Humans (Oxford University Press). The subject has since advanced significantly, and Modeling Infectious Diseases in Humans and Animals meets the need for a new synthesis. Authors Matt Keeling and Pejman Rohani are mathematicians by training who have made important and original contributions to epidemiology, so they are well qualified to deliver an authoritative, comprehensive and up-to-date review.

Their book contains a guide to different models and provides worked examples of the insights that models offer, and of specific applications to real-world problems. They cover an impressive range of mathematical approaches, from two-line coupled differential equations through event-based stochastic models to spatially explicit microsimulations, and many others. Their examples cover an equally wide range of infectious diseases, from measles in school children to sexually transmitted infections in koalas. In every case, there is a thoughtful description of the rationale for the model, the assumptions behind it, the types of question it can be used to address, how to implement it (helpfully supported by a website providing access to computer code), and what the model tells us.

With all of this to hand, is the reader fully equipped to become a modeller of infectious disease? Not quite. Modelling is more than a technical exercise. It also requires that the practitioner makes critical judgements at different stages of the process, notably design, parameterization, validation and prediction.

Model design is the first and most important step. Success depends on how well we pose the questions we want to answer, and how effectively we identify the essential biology and translate it into mathematical equations or computer code. Keeling and Rohani manage this effortlessly, but it is a difficult art to instil in others except by example. There are plenty of examples in their book that repay close attention: particularly the sections on seasonality and contact tracing.

The second step, and an active area in the field, is model parameterization. It is not a major theme of Modeling Infectious Diseases. It was once acceptable to run a projection through some data points and declare the model good enough. This is no longer the case. More powerful computers and software have increased the availability of sophisticated estimation techniques, often using bayesian methodologies.

The third step is validation — the extent to which we should believe, and sometimes act on, the output of a model. Keeling and Rohani take a mathematician's view of this. Their book is punctuated by concise summaries of the insights drawn from the models, presented as robust conclusions. These are helpful in communicating key results but empiricists will often, rightly, demand something more. Ideally, this should include testing model predictions against independent data.

Prediction is a difficult task that we routinely undertake, for example, when making a decision about implementing disease-control measures. Such decisions must always involve some kind of model, even if it is only a mental one. Mathematical models have two huge advantages. First, they are transparent — the inputs, assumptions and logic are available for inspection, criticism and change in a way that is rarely the case for expert opinion. Second, models can be used to explore, in silico, the expected impacts of many more different control options than could ever be trialled in practice. Often, models will be the best evidence we have for our decisions.

Keeling and Rohani advocate, as strongly as I do, the use of mathematical models to help design disease-control programmes and they devote the final chapter to this topic. They recognize that modelling is a partnership between modellers and empiricists, including experts in the disease system of interest, providers of epidemiological data and those responsible for disease control. For that reason, I hope that the readership of Modeling Infectious Diseases will extend beyond existing and new devotees of this challenging and exciting discipline. Most medics, vets and health workers will never write a mathematical model themselves, but it is increasingly important that they are familiar with the work of those that do.