Mathematical Modeling in Population Health Research

There is a long history of using mathematical modeling to study and improve aspects of population health. This chapter provides a brief overview of the diversity of such applications to complex health-related outcomes, including biological modeling (highlighting applications in infectious disease and human physiology), statistical modeling, cost-effectiveness analysis, and operations research (highlighting applications in queueing systems, Bayesian decision-making, and constrained optimization). Motivating objectives, typical model structure, and analyses are briefly described for each. As computational power has increased, computer simulation is often used to model complex phenomena. This chapter reminds readers of the many examples in which mathematical equations are used to parsimoniously represent complex systems and to understand their behavior. When mathematical models are tractable, analysts can obtain closed-form equations characterizing steady-state system behavior and tipping conditions—which provide a powerful and often easy to use tool for decision makers.

Engaging Stakeholders in Mapping and Modeling Complex Systems Structure to Inform Population Health Research and Action

Systems science methods are designed to study “wholes” and to support decision-making in the context of complexity. While these methods are powerful in the hands of researchers, they can be transformative when used collaboratively with the stakeholders impacted by and capable of impacting a population health phenomena. This chapter introduces group model building (GMB), developed by practitioners of system dynamics seeking to meaningfully engage system stakeholders in all stages of model building and use. The authors describe the general approach, its alignment with community-based participatory research, and the role system dynamics artifacts and other system maps serve as “boundary objects” to facilitate co-learning and collaboration among individuals with diverse experiences, world views, disciplinary backgrounds, and/or organizational affiliations. The chapter introduces emerging examples of GMB processes, adapted for use with other systems science modeling methods, as well as other examples of collaborative system mapping that can accentuate the GMB toolbox and generate additional boundary objects

How Complex Systems Science Can Revolutionize Population Health Theory

This chapter discusses whether and how complex systems science (CSS) can revolutionize population health theory. First, the chapter defines theory and the practice of theory-building (or theorizing); second, it outlines some of the difficulties found in current population health theorizing; lastly, it characterizes the mechanisms through which CSS can influence, change, and revolutionize current theorizing efforts. The chapter also describes two examples of scholars who used CSS to challenge currently held assumptions and reframe complex health problems. Lastly, the author addresses the implications—of adopting a CSS approach to theorizing—for practice, policy development, and training of the future public health workforce.

Phase Transitions and Resilience in Physical and Psychological Health

Complexity science methods offer new opportunities for prognosis and treatment in healthcare and clinical psychology because of the increasing need for integration of the detailed knowledge of physiological and psychological subsystems and the increasing prevalence of multiple disease conditions in our aging societies. This chapter explains how the frequently occurring acute transitions and related tipping points in physical and mental processes in these populations can be monitored with time series and dynamical indicators of resilience. The authors introduce slowing down of recovery, increase in variance and autocorrelation, and increasing cross-correlation between subsystem time series as valid predictors of the proximity of tipping points in diseases such as depression, heart failure and syncope. Using wearable devices, together with these complex systems analyses, yields new methods of forecasting and may improve resilience of individual persons and their mental or physical (organ) subsystems

Population Health as a Complex Adaptive System of Systems

This chapter advocates a complex adaptive system of systems approach to understanding population-level processes in population health. A complex adaptive system consists of diverse, interacting adaptive entities whose aggregated behaviors result in emergent, system-level patterns and functionalities. A complex adaptive system of systems consists of multiple, connected complex systems. The connections can be hierarchical, horizontal, or a mixture of the two. The authors provide basic definitions, describe common tools of analysis, and introduce illustrative cases. For example, increased obesity levels have no single cause, nor do they arise from a single system. Instead, they arise from the interactions of multiple systems that operate at various levels of scale. Genetics and epigenetics play roles, as do nutrition, general health, advertising, infrastructure, social norms, exercise levels, and, as recent evidence suggests, the ecology of colonies of gut bacteria. Each of these contributors can be modeled as a complex adaptive system and the whole as a system of systems. Similarly, population-level disease outbreaks can be decomposed into separate systems, each with unique dynamics.

Complex Systems in a Nutshell

This chapter provides an overview of the key foundational concepts and principles of the study of complex systems. First, a definition for system is provided, and the distinctions between complicated and complex systems are demarcated, as are detail, disorganized, organized, and dynamic types of complexity. Common properties across complex systems are defined and described, including stable states and steady states, path dependence, resilience, critical transitions and tipping points, early warning signals, feedback loops, and nonlinearity. This chapter also delves into how complex issues often consist of networks, with random, scale-free, and small world networks defined and network concepts such as degrees, path length, and heterogeneity defined. The concept of emergence is also emphasized, as well as related principles such as adaptation and self-organization. Cardiometabolic disease (and associated comorbidities) is used in this chapter as a thematic population health example.

Bridging the Divide

This chapter contextualizes the volume and describes its organization. It begins by delving into the limitations of the prevailing reductionist paradigm in population health science and the need for a transition from a typically risk factor–based science to a science that recognizes the whole and relationships among parts of pressing population health problems. Next, it walks readers through distinctions between public and population health on the one hand and key concepts of complexity on the other, while offering a shared understanding of population health science and complex systems science. The chapter also lays out the design of and potential audiences for this book.

Harnessing Complex Systems

Many population health challenges have eluded scientists and policymakers for years because of misunderstanding of dynamic complexity. This chapter advocates an epistemological overhaul in population health science based on the premise that population health problems should be studied as complex systems because they operate as such. The proposed overhaul is predicated on the development of a new complex-systems-science–driven paradigm for a new population health science. It is founded on a fundamental shift in scientific thinking: from a quest for causes and accurate predictions to “control” problems, which inappropriate science and sheer uncontrollability of complex problems have curtailed, to knowledge generation, based on complex-systems-science–grounded theories and analytical methods to better understand, anticipate, curb, and manage health challenges, by way of harnessing their complexity. As both current and proposed epistemologies represent models of simpler and complex problems, respectively, appropriate use of each under the proposed paradigm can only strengthen population health science. These emerging ideas delve into the known as well as the possible and still unknown. Some ideas are grounded in long-standing scientific evidence, while others are of an emerging nature. Some are testable while others are partially tested, and still others remain untested “fantasies” about how to contend with intractable population health challenges.

Physical Sciences for Nonphysical Problems

To begin understanding noncommunicable diseases in a population, researchers must understand how people are connected to each other, how they interact with each other, and if there are external influences. Heterogeneity and complexity in human disease suggest new methodological and analytical ways in which the physical sciences can assist research in areas such as obesity, cardiovascular diseases, psychiatric disorders, or cancer. As it is becoming clear that human morbid states are not strictly deterministic diseases, this chapter overviews how statistical physics and nonlinear dynamics (e.g., percolation, cascades, control theory) grounded in stochastic approaches can contribute to the delineation and control of an array of complex population health outcomes.

Computational Simulation Modeling

This chapter illustrates computer simulation “model thinking,” with brief descriptions of five recent health models along an abstract to applied spectrum. The author starts with a very simple model to assess not only the cross-sectional but also the lifetime redistributive impact of Canada’s publicly funded healthcare. Next is a multilevel interacting agent model seeking to understand why the correlations between city-level income inequality and mortality are so different between Canada and the United States. Following are models that significantly generalize the concept of attributable fraction applied to health-adjusted life expectancy and a genetic missing model to support cost-effectiveness of risk-based breast cancer screening policy options. The fifth model is the most detailed and is being applied to develop projections of long-term care utilization and costs. While this is a diverse set of models, collectively, they illustrate the range of possibilities, and the benefits of “model thinking.”