Problems concerning both individual human health and the health of society at large are by nature inter-disciplinary. On the most basic level, knowledge about the biological workings of the body and psychological insight into human behaviour are crucial to understanding how best to cater for individual needs. And yet fundamentally human beings are also social animals, whose actions—having either positive or negative effects on health—are determined to a greater or lesser extent by the customs and fashions of other human beings with whom they interact. If one wishes to better understand human systems with a view to addressing health issues, it is therefore essential that expert judgments are made at all levels of description (individual behaviour, social context, and everything between); that is, judgements founded on co-operation between specialists working in a range of disciplines.

In essence, this book is a response to such a need. Drawing on a series of papers given at a recent conference hosted by the University of Durham's Tipping Points Project.¹ Chapters focus on modelling approaches to contemporary health and social problems—especially those considered a major burden to public services, such as smoking, binge drinking and heart disease—and include contributions from mathematicians, statisticians, health practitioners, psychologists, anthropologists and economists. A common theme throughout is the notion of ‘tipping’ behaviour within social and health systems, so that overall system properties can switch between markedly different states as a result of relatively modest or judiciously implemented interventions. For example, when considering the prevalence of cigarette smoking (a socially determined behaviour), it may be the case that small changes to exogenous factors (such as pricing and health warnings) can lead to large changes in the overall number of smokers. Should they exist, these kinds of ‘tipping points’ clearly have major implications for health policy, especially in terms of the way we assess a policy's associated risk and resilience. Yet ‘tipping behaviour’ itself is often sensitive to the way system models are set up or, indeed, the assumptions made when attempting to quantify system parameters. Even on the most basic level, therefore, one quickly recognises the need for inter-disciplinary consultation to establish the verisimilitude of assumptions and to determine realistic choices of parameter values. More broadly, one finds that some levels of description are not amenable to quantitative methods (which can become too cumbersome to offer genuine explanatory power), in which case qualitative approaches may be more suitable. In addition, one must recognise that human (health and social) systems are essentially ‘open’, so that modelling in one area of activity can have implications for modelling in others. Consequently, while the chapters in this volume cover a number of related modelling issues, we have found it expedient to divide content thematically into four parts, each of which are described in further detail below.

Arguably one of the most high profile contemporary health issues is smoking, and it is this topic which forms the focus of investigation in Part I through three chapters devoted to what we term The Smoking Epidemic. Clearly, one method for reducing the impact of smoking on health is to reduce actual numbers of smokers, and to this end, it is important to ask how socially determined behaviours (such as smoking) spread through populations in which there are competing social norms. The first two chapters in Part I address this question mathematically by adapting compartmental modelling approaches from epidemiology. Indeed, given that agents in social systems influence the activities of other agents with whom they interact (via imitation and coercion), there is a strong analogy between the transmission of behaviour patterns and infection by disease. However, unlike models for disease transmission, ‘infection’ can work in multiple directions; for example, a non-smoker can take up smoking if they choose to imitate the activities of current smokers, but so too can non-smokers coerce current smokers into abstention.

In Chapter 1, Bissell demonstrates how the inclusion of these kinds of multiple ‘infection’ incidence terms in a behaviour transmission model can lead to ‘tipping points’ in smoking dynamics, whereby small changes to system parameters can dramatically alter the expected prevalence of smoking. Nevertheless, while such a result may appear encouraging to those who would like to suppress smoking, it is important to acknowledge the model's limited predictive power in the face of uncertainties in parameter values. Consequently, Caiado examines the smoking model from a statistical perspective in Chapter 2, paying special attention to model uncertainty, and stochastic effects. Caiado notes that the model is sensitive to the effects of multiple incidence terms, justifying their inclusion in descriptions of behaviour transmission, but stresses the difficulty of obtaining reliable information about parameter choices, and hence the importance of collaborating with practitioners in other fields who are likely to have special insight into what features of the model are in need of improvement. Indeed, as Russell discusses in Chapter 3, one issue that warrants further investigation is the importance of gender differences in determining rates of smoking uptake. Russell describes how the incidence of smoking amongst women in the Northeast of England has been increasing at a time when overall smoking rates have been on the decline. This kind of anthropological insight suggests refinement of modelling activity to include gender-based effects, with possible implications for the emergence of social norms as predicted by such models, and the methods used by health practitioners to communicate ‘health messages’ amongst different groups of people.

The focus in Part II concerns more direct discussion of Mathematical Modelling in Healthcare and examines both how statistical models can be used to assess performance of cardiac surgeons and ‘real-time’ patient physiological status, and the use of applied mathematics in developing health diagnostics and improved medical devices. As Hickey et al. describe in Chapter 4, various circumstances in the United Kingdom (including Freedom of Information legislation) have led to numerous legal requirements surrounding the regulation of individual doctors, alongside a more general public appetite for access to transparent data, especially regarding cardiac surgery. And yet even when there exist ostensibly clear indicators of success, such as mortality data, monitoring performance is not straightforward. Historical records and ‘national averages’ are not necessarily good benchmarks for comparative analysis: developments in medical technique, alongside changes in patient demographic (such as an ageing population, or geographically varying levels of general health) mean that the risks of surgery are unlikely to stay constant either in time or place. In the face of such difficulties, the authors of Chapter 4 describe a number of approaches to dynamically assessing risk, which they compare in the context of current surgery data sets. By demonstrating the different ways in which models can lose calibration over time (with obvious implications for the way in which we interpret risk and evaluate quality of care), they argue that over reliance on a single risk-prediction model can be dangerous, and that there is a need to continually update models as data sets are expanded.

With these elements of risk evaluation in mind, Caiado et al. ask in Chapter 5 whether it is possible to monitor the ‘real-time’ physiological status of patience in intensive care, pointing out that most current scoring systems are ‘off-line’, cannot be customised for individual patients, and rely on arbitrary thresholds to trigger alarms. With a view to improving the reliability of monitoring processes, Caiado et al. propose a real-time Bayesian modelling approach based on dynamic adaptive scoring, one which can include subjective (i.e. patient-specific) information provided by hospital staff. They show that their approach can reduce the number of false alarms and argue that its flexibility may have other benefits; for example, real-time scoring could also provide ameans of optimising ward stay times, while reducing the chances of patient deterioration.

Chapters 4 and 5 are directly related to our ‘tipping point’ theme, because continuous performance evaluation may provide a means of staging ‘critical’ interventions in the activities of healthcare professionals. However, it is important to recognise that mathematical modelling can also be applied to healthcare at the biological level, a subject introduced by McKee & McGinty in Chapter 6. In particular, McKee & McGinty use three examples (drug-eluting stents, arterial blood flow, and the famous Clearblue pregnancy testing kit) to illustrate the part played by mathematical modelling in the development of medical technologies and diagnostic tools, especially when it comes to reducing design and production costs.

Issues surrounding monitoring, interventions, and medical technologies represent very much the treatment side of human health, and it is essential that one also considers the importance of social effects, especially given that social context helps to determine health-related behaviours (a topic already touched upon in Part I). Hence the emphasis placed on modelling Tipping Points in Social Dynamics in Part III, a section which consists of chapters on developing mathematical frameworks, the importance of cultural effects, and the human tendency to conform to social norms. A key question in this area is how social norms emerge at the macroscopic level as a consequence of microscopic processes governed by the behaviours of many individual human agents. In Chapter 7, Marsan et al. consider one possible approach to answering this question by outlining what they term system sociology, adapting ideas from kinetic theory to model agents as active particles whose interactions can be described using game theory. They argue that rare events (or ‘Black Swans’) can emerge naturally in such systems at the macro-scale because of reinforcement of qualitative trends at the micro-scale, and apply their approach to a simple model of social conflict. Though attempts to validate such models are very much in their infancy, the analogy between kinetic effects and micro-scale interactions is a promising avenue of future research into collective behaviour within social systems.

Another important question in this area is how culture and norms evolve in human populations, particularly the adoption of innovations in behaviour or technology. In Chapter 8, Bentley et al. investigate this problem from a neutral transmission perspective within the context of a spatially distributed population, placing their emphasis on trying to describe why certain practises are adopted and become prevalent even if these practises are not clearly superior to others similarly available (this is the sense in which the transmission is neutral—it is not subjected to selective pressure). Building on existing neutral models, Bentely et al. incorporate memory effects by allowing model agents to copy both contemporary and historical choices. Such a development is important because memory can result in ‘lost’ traits being reintroduced, thereby increasing the effective rate of innovation and—as the authors argue—act as an amplifier of cultural heterogeneity.

Of course, some cultural norms can bring tangible benefits to their adopters, and in these cases one would expect some form of gene–culture coevolution: an emerging subject of study introduced by Kendal and Walters in Chapter 9. Part of these authors' approach relies on the kinds of compartmental modelling techniques discussed in Chapters 1 and 2. Indeed, by modelling a disease in which there is a single stage of illness followed by recovery or death, they demonstrate that self-medication of defective treatments (i.e. maladaptive practice) can persist provided that individuals are unlikely to abandon treatment, and if natural recovery rates are high. Kendal and Walters also discuss the applicability of compartmental methods more generally by reviewing various binge-drinking models; this section of their chapter neatly introduces the notion of conformity bias (i.e. the tendency for individuals to conform to majority held practices or beliefs with a strength that varies non-linearly with the number of adopters) an issue explored in further by Bissell in Chapter 10. As demonstrated by Bissell, conformist-type behaviour may play a key role in societal ‘tipping points’ because (under certain conditions) conformity biasing provides a non-linear adoption mechanism for switching behaviour.

Most of the chapters outlined above focus on investigating models within relatively well-defined contexts (e.g. specific health or social problems, or medical applications), raising the question of how one should proceed when systems are more complex or nebulous. In Part IV, this problem is considered by addressing the more over-arching issue of The Resilience of Tipping Points, with a broader discussion of general approaches to thinking about inter-connected systems. As Towl emphasises in Chapter 11, given that incremental changes in operational practice can have a cumulatively non-linear affect on the success with which organisations are able to deliver services, the notion of ‘tipping points’ is one of key concern in studies of organisational risk and resilience. Towl begins by defining risk as the probability of a specified hazard, and goes on to consider two examples: first, suicide in prisons; and second, hazards which may ‘impair the functionality of the UK port system’. In the case of prisons, Towl argues that while previous work has focused on the mental states of individual prisoners, it makes greater sense to consider particular environmental dynamics which might lead to suicidal behaviour. This need for taking a system overview is further exemplified in Towl's example of risk management by the Port of London Authority, but it is not unproblematic: for example, successful operation can disguise the need for contingency planning.

Indeed, as Curtis describes in Chapter 12, knowledge about complex systems can be relatively limited or incomplete, making absolute prevention of system failure difficult; in these cases, the rational approach to resilience may be to promote preparedness by taking a system overview. After identifying some of the main features of complex systems, Curtis goes on to illustrate this point using case studies taken from risk governance in both psychiatric hospitals and elderly care networks. In these studies, Curtis shows that while it is often assumed that some kinds of critical events can be defined precisely, undue focus on mitigating them may inadvertently engender conditions which actually increase systemic risk. For example, one response to reducing the risk of patient escape from a psychiatric ward might be to tighten security measures; however, restriction of patient movements can curtail other efforts to maintain patient well-being (such as therapeutic exercise or social engagement), leading to increased stress or frustration amongst patients which might manifest itself in unexpected ways.

In a sense, this final part (Part IV) returns us to many of the underlying modelling issues of which the book as a whole is concerned, namely, that while various mathematical modelling approaches can be general, details are very much problem specific, and require input from expert practitioners if they are to be realistic. In some areas, especially social systems, modelling is very much in a developmental stage; for example, cross fertilisation from the field of mathematical epidemiology is a promising avenue for research, but will require considerable future efforts to improve model validation and predictive capability. In terms of ongoing modelling activity, therefore, an inter-disciplinary approach is likely to remain essential, and should involve continual dialogue between model developers and other practitioners: from the initial stages of determining what models are for and how they will be used, through to assumptions, the details of design, parameter choice, and solution.

J. J. Bissell, C. C. S. Caiado, S. E. Curtis, M. Goldstein, and B. Straughan
University of Durham