Modeling Infectious Diseases in Humans and Animals
Matt J. Keeling & Pejman Rohani


Below is the text from reviews that have been published about Modeling Infectious Diseases.
Nature -- by Mark WoolhouseLancet Infectious Diseases -- by Sally Blower


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.

          Mark Woolhouse

Lancet Infectious Diseases

An informative textbook, Modeling infectious diseases  in humans and animals is written by a mathematician (Matt Keeling of the University of Warwick, Coventry, UK) and a physicist (Pejman Rohani of the University of Georgia, Athens, GA, USA). The authors assume in the reader a fairly sophisticated knowledge of mathematics and computational techniques, and the book is clearly aimed at advanced undergraduates or graduate students with a strong background in mathematics. A series of mathematical models, of increasing complexity, is clearly presented and the reader is taken through the appropriate mathematical analyses. A particularly nice feature of this book is that it includes web-based mathematical exercises.

The authors begin by describing simple epidemic models (focusing on the classic susceptible–infected–recovered model and its modifications) and then quickly progress to multi-pathogen/multi-host and temporally forced models, stochastic dynamics, and spatial models. Each chapter carefully explains the mathematical structure of a particular model (most of the models are based on a series of ordinary differential equations) and concludes with a few examples of the application of this type of model to a specific infectious disease of animals or human beings. Since the research of both authors is concerned with modelling childhood diseases, they have mainly selected examples from this area of modelling. Admittedly, this book is a textbook aimed at explaining some of the methodologies of modelling and does not intend to be a review of the literature of this field. However, I was disappointed that models of diseases of major medical importance such as HIV, tuberculosis, malaria, or hospital-acquired infections were not covered. Consequently, the reader is not made aware of the very large body of modelling literature that has focused on diseases that have great importance to public health.

The field of modelling infectious diseases is divided into two camps: those who believe that simple mathematical models are useful for understanding epidemiology and making predictions, and those who believe that complex models are necessary for making accurate predictions. Both simple and complex models have advantages and
disadvantages. Simple models are constructed on the basis of a few assumptions (that are usually made transparent) and a few parameter values. Generally, these models are thoroughly analysed both mathematically and numerically. Uncertainty analyses have been used to make predictions from simple models (ie, the predicted outcomes have error bars). Multivariate sensitivity analyses have been used to investigate the effect of all of the assumptions and ranges in parameter estimates on the predictions.
Simple models have therefore provided a great deal of insight into the dynamics and control of infectious diseases. However, if a model is over-simplified, important
processes can be omitted and the model will have limited usefulness. Complex models are built on the basis of many assumptions (that may not be explained and therefore can not be evaluated) and a multitude of unknown parameter values (that are often specified as single point estimates). Surprisingly, so far, complex epidemiological models have not been adequately analysed to determine the sensitivity of their results to assumptions and parameter values. These complex models have generally been used to simulate single scenarios to make predictions; these predictions could be highly inaccurate because of the many unknowns in the model. Therefore, paradoxically, although complex models may appear to be more realistic than simple models, their predictions can sometimes be less accurate and give a misleading sense of certainty.

Keeling and Rohani conclude that the future of infectious disease modelling should be to develop very complex models and use them as predictive tools. I agree,
in part, with their conclusion. However, I believe that it is always important to begin by constructing a simple model and then, if necessary, linking it with a complex model. The complex model should be built in a series of stages from the simple model and carefully explored at each stage by uncertainty and multivariate sensitivity analyses. This approach would enable the structure of the complex model to become more transparent, and the necessary degree of model complexity to be clearly assessed. To develop more useful models (whether they are simple or complex), modellers need to build close collaborations with infectious disease experts and biostatisticians. To construct more realistic models, modellers also need to use more sophisticated statistical techniques when fi tting models to data, and for parameterisation, validation, and verification.

Keeling and Rohani have produced an excellent textbook that will introduce mathematicians to the field of infectious disease modelling. Hopefully, after reading this book mathematicians will be motivated to build collaborations with infectious disease experts and biostatisticians.

            Sally Blower

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Matt Keeling      Pejman Rohani