Chris Bauch

• PhD in Mathematics
• Professor at University of Waterloo

The coupling of social and biological contagion in human populations can have positive or negative outcomes.

Forest-grassland mosaic ecosystems can exhibit alternative stables states, whereby under the same environmental conditions, the ecosystem could equally well reside either in one state or another, depending on the initial conditions. We develop a mathematical model that couples a simplified forest-grassland mosaic model to a dynamic model of opinion...

Mathematical models that couple disease dynamics and vaccinating behaviour often assume that the incentive to vaccinate disappears if disease prevalence is zero. Hence, they predict that vaccine refusal should be the rule, and elimination should be difficult or impossible. In reality, countries with non-mandatory vaccination policies have usually b...

Certain theories suggest that it should be difficult or impossible to eradicate a vaccine-preventable disease under voluntary vaccination: Herd immunity implies that the individual incentive to vaccinate disappears at high coverage levels. Historically, there have been examples of declining coverage for vaccines, such as MMR vaccine and whole-cell...

Voluntary vaccination policies for childhood diseases present parents with a subtle challenge: if a sufficient proportion of the population is already immune, either naturally or by vaccination, then even the slightest risk associated with vaccination will outweigh the risk from infection. As a result, individual self-interest might preclude comple...

We developed a coupled social-climate network model to understand the interaction between climate change opinion spread and the climate system and determine the role of this interaction in shaping collective actions and global temperature changes. In contrast to previous social-climate models that discretized opinions, we assumed opinions on climat...

Social behaviour models are increasingly integrated into climate change studies, and the significance of climate tipping points for `runaway' climate change is well recognised. However, there has been insufficient focus on tipping points in social-climate dynamics. We developed a coupled social-climate model consisting of an Earth system model and...

Individual attitudes vastly affect the transformations we are experiencing and are vital in mitigating or intensifying climate change. A socio-climate model by coupling a model of rumor dynamics in heterogeneous networks to a simple Earth System model is developed, in order to analyze how rumors about climate change impact individuals’ opinions whe...

Recent work has highlighted the utility of methods for early warning signal detection in dynamic systems approaching critical tipping thresholds. Often these tipping points resemble local bifurcations, whose low dimensional dynamics can play out on a manifold embedded in a much higher dimensional state space. In many cases of practical relevance, t...

Mathematical models that couple human behavior to environmental processes can offer valuable insights into how human behavior affects various types of ecological, climate, and epidemiological systems. This review focuses on human drivers of tipping events in coupled human–environment systems where changes to the human system can abruptly lead to de...

The critical community size (CCS) is the minimum closed population size in which a pathogen can persist indefinitely. Below this threshold, stochasticity eventually causes pathogen extinction. Here, we introduce a mechanism of behaviour-mediated persistence, by which the population response to the pathogen alters the CCS. We exemplify this with inf...

Sedimentation is a major coral reef stressor, with effects including suppressing algae consumption by herbivorous fish. This puts pressure on reef fish populations and the fisheries that harvest them. Deforestation causes much sedimentation on reefs, and is an ongoing concern in Pacific island states. Although ecosystem processes like deforestation...

Future climate change can cause more days with poor air quality. This could trigger more alerts telling people to stay inside to protect themselves, with potential consequences for health and health equity. Here, we study the change in US air quality alerts over this century due to fine particulate matter (PM 2.5 ), who they may affect, and how the...

Many natural and man-made systems are prone to critical transitions—abrupt and potentially devastating changes in dynamics. Deep learning classifiers can provide an early warning signal for critical transitions by learning generic features of bifurcations from large simulated training data sets. So far, classifiers have only been trained to predict...

Crown-of-thorns starfish (CoTS) outbreaks rank among the greatest threats to coral throughout the Indo-Pacific. In the future, reefs already stressed by CoTS will be further burdened by overfishing and nutrient loading. How much these two factors will exacerbate CoTS outbreak severity is still uncertain. Furthermore, the CoTS management literature...

Mathematical models that couple human behaviour to environmental processes can offer valuable insights into how human behaviour affects various types of ecological, climate and epidemiological systems. In many coupled systems, gradual changes to the human system can lead to abrupt tipping points in the overall system, leading to desirable or undesi...

The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and often irreversible shift is well established, but prediction of these events using standard forecast modelling techniques is quite difficult. This has led to the development of an alternative suite of methods that seek to identify signat...

Many natural and man-made systems are prone to critical transitions -- abrupt and potentially devastating changes in dynamics. Deep learning classifiers can provide an early warning signal (EWS) for critical transitions by learning generic features of bifurcations (dynamical instabilities) from large simulated training data sets. So far, classifier...

As environmental degradation progresses, economies and societies adapt to the loss of ecosystem services and public attention to degradation subsides. In systems experiencing such societal acclimation to degradation, net incentives for stakeholder mitigation peak during early degradation phases and subside over time. Using harmful algae blooms in w...

Humans and the environment form a single complex system where humans not only influence ecosystems but also react to them. Despite this, there are far fewer coupled human–environment system (CHES) mathematical models than models of uncoupled ecosystems. We argue that these coupled models are essential to understand the impacts of social interventio...

The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and potentially irreversible shift is well established, but prediction of these events using standard forecast modeling techniques is quite difficult. This has led to the development of an alternative suite of methods that seek to identify s...

Overfishing has the potential to severely disrupt coral reef ecosystems worldwide, while harvesting at more sustainable levels instead can boost fish yield without damaging reefs. The dispersal abilities of reef species mean that coral reefs form highly connected environments, and the viability of reef fish populations depends on spatially explicit...

Simulation models from the early COVID-19 pandemic highlighted the urgency of applying non-pharmaceutical interventions (NPIs), but had limited empirical data. Here we use data from 2020-2021 to retrospectively model the impact of NPIs in Ontario, Canada. Our model represents age groups and census divisions in Ontario, and is parameterised with epi...

Vaccines and climate change have much in common. In both cases, a scientific consensus contrasts with a divided public opinion. They also exemplify coupled human–environment systems involving common pool resources. Here we used machine learning algorithms to analyze the sentiment of 87 million tweets on climate change and vaccines in order to chara...

[This corrects the article DOI: 10.1371/journal.pone.0238979.].

Bark beetle outbreaks and forest fires have imposed severe ecological damage and caused billions of dollars in lost resources in recent decades. The impact of such combined disturbances is projected to become more severe, especially as climate change takes its toll on forest ecosystems in the coming years. Here, we investigate the impact of multipl...

Dietary patterns have long been a driver of global land use. Increasingly, they also respond to it, in part because of social processes that support adoption of eco-conscious diets. Here we develop a coupled social-and-land use mathematical model parameterised for 153 countries. We project global land use for future population, income, and agricult...

Significance Early warning signals (EWS) of tipping points are vital to anticipate system collapse or other sudden shifts. However, existing generic early warning indicators designed to work across all systems do not provide information on the state that lies beyond the tipping point. Our results show how deep learning algorithms (artificial intell...

Vaccinating individuals with more exposure to others can be disproportionately effective, in theory, but identifying these individuals is difficult and has long prevented implementation of such strategies. Here, we propose how the technology underlying digital contact tracing could be harnessed to boost vaccine coverage among these individuals. In...

Climate dynamics are inextricably linked to processes in social systems that are highly unequal. This suggests a need for coupled social-climate models that capture pervasive real-world asymmetries in the population distribution of the consequences of anthropogenic climate change and climate (in)action. Here, we use evolutionary game theory to deve...

Tuberculosis (TB) is among the 10 top causes of deaths worldwide, and one-quarter of the world population hosts latent TB pathogens. Therefore, avoiding the emergence of drug-resistant strains has become a central issue in TB control. In this work, we propose a nested model for TB transmission and control, wherein both within-host and between-host...

Sudden shifts in vaccine uptake, vaccine opinion, and infection incidence can occur in coupled behaviour-disease systems going through a bifurcation, as the perceived risk of the vaccine increases. Literature shows that such regime shifts are sometimes foreshadowed by early warning signals (EWS). We propose and compare the performance of various me...

Given trade's importance to maintaining food security, it is crucial to understand the relationship between human population growth, land use, food supply, and trade. We develop a metapopulation model coupling human population dynamics to agricultural land use and food production in "patches" (regions and countries) connected via trade networks. Pa...

Biogeochemistry has an important role to play in many environmental issues of current concern related to global change and air, water, and soil quality. However, reliable predictions and tangible implementation of solutions, offered by biogeochemistry, will need further integration of disciplines. Here, we refocus on how further developing and stre...

Recent attempts at cooperating on climate change mitigation highlight the limited efficacy of large-scale negotiations, when commitment to mitigation is costly and initially rare. Deepening existing voluntary mitigation pledges could require more stringent, legally-binding agreements that currently remain untenable at the global scale. Building-blo...

The critical community size (CCS) is the minimum closed population size in which a pathogen can persist indefinitely. Below this threshold, stochastic extinction eventually causes pathogen extinction. Here we use a simulation model to explore behaviour-mediated persistence: a novel mechanism by which the population response to the pathogen determin...

There is a pressing need for evidence-based scrutiny of plans to re-open childcare centres during the COVID-19 pandemic. Here we developed an agent-based model of SARS-CoV-2 transmission within a childcare centre and households. Scenarios varied the student-to-educator ratio (15:2, 8:2, 7:3), family clustering (siblings together versus random assig...

Background During the COVID-19 pandemic, authorities must decide which groups to prioritise for vaccination in a shifting social–epidemiological landscape in which the success of large-scale non-pharmaceutical interventions requires broad social acceptance. We aimed to compare projected COVID-19 mortality under four different strategies for the pri...

Shared resource extraction among profit-seeking individuals involves a tension between individual benefit and the collective well-being represented by the persistence of the resource. Many game theoretic models explore this scenario, but these models tend to assume either best response dynamics (where individuals instantly switch to better paying s...

Sudden shifts in population health and vaccination rates occur as the dynamics of some epidemiological models go through a critical point; literature shows that this is sometimes foreshadowed by early warning signals (EWS). We investigate different structural measures of a network as candidate EWS of infectious disease outbreaks and changes in popu...

In May 2020, many jurisdictions around the world began lifting physical distancing restrictions against the spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), giving rise to concerns about a possible second wave of coronavirus disease 2019 (COVID-19). These restrictions were imposed as a collective population response to the pr...

In May 2020, many jurisdictions around the world began lifting physical distancing restrictions against the spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). This gave rise to concerns about a possible second wave of coronavirus disease 2019 (COVID-19). These restrictions were imposed in response to the presence of COVID-19 in...

Background During the COVID-19 pandemic, authorities must decide which groups to prioritise for vaccination. These decision will occur in a constantly shifting social-epidemiological landscape where the success of large-scale non-pharmaceutical interventions (NPIs) like physical distancing requires broad population acceptance. Methods We developed...

Dietary patterns have long been a driver of global land use. Increasingly, they also respond to it, in part because of social forces that support adoption of sustainable diets. Here we develop a coupled social-land use dynamics model parameterised for 164 countries. We project global land use under 20 scenarios for future population, income, and ag...

Climate dynamics are inextricably linked to processes in social systems that are highly unequal. This suggests a need for coupled social-climate models that capture pervasive real-world asymmetries in the population distribution of the consequences of anthropogenic climate change and climate (in)action. Here we develop a simple social-climate model...

Invasive pests, such as emerald ash borer or Asian longhorn beetle, have been responsible for unprecedented ecological and economic damage in eastern North America. These and other wood-boring invasive insects can spread to new areas through human transport of untreated firewood. Behaviour, such as transport of firewood, is affected not only by imm...

In mosaic ecosystems, multiple land types coexist as alternative stable states exhibiting distinct spatial patterns. Forest-grassland mosaics are ecologically valuable, due to their high species richness. However, anthropogenic disturbances threaten these ecosystems. Designating protected areas is one approach to preserving natural mosaics. Such wo...

Significance During the COVID-19 pandemic, decision makers are grappling with how to reopen (and possibly reclose) their jurisdictions as the number of cases ebbs and flows. Establishing a criterion for each county/municipality to open and close based on their case count has appeal, given the wide disparity in COVID-19 rates in urban versus rural s...

There is a pressing need for evidence-based scrutiny of plans to re-open childcare during the COVID-19 pandemic. Here we developed an agent-based model of SARS-CoV-2 transmission within a childcare center and households. Scenarios varied the student-to-educator ratio (15:2, 8:2, 7:3), and family clustering (siblings together vs. random assignment)....

Recent attempts at cooperating on climate change mitigation highlight the limited efficacy of large-scale agreements, when commitment to mitigation is costly and initially rare. Bottom-up approaches using region-specific mitigation agreements promise greater success, at the cost of slowing global adoption. Here, we show that a well-timed switch fro...

Significance Collective risks trigger social dilemmas that require balancing selfish interests and common good. One important example is mitigating climate change, wherein without sufficient investments, worldwide negative consequences become increasingly likely. To study the social aspects of this problem, we organized a game experiment that revea...

Pre-exposure prophylaxis (PrEP) has been shown to be highly effective in reducing the risk of HIV infection in gay and bisexual men who have sex with men (GbMSM). However, PrEP does not protect against other sexually transmitted infections (STIs). In some populations, PrEP has also led to riskier behavior such as reduced condom usage, with the resu...

Regions with insufficient vaccination have hindered worldwide poliomyelitis eradication, as they are vulnerable to sporadic outbreaks through reintroduction of the disease. Despite Israel’s having been declared polio-free in 1988, a routine sewage surveillance program detected polio in 2013. To curtail transmission, the Israel Ministry of Health la...

In the late stages of an epidemic, infections are often sporadic and geographically distributed. Spatially structured stochastic models can capture these important features of disease dynamics, thereby allowing a broader exploration of interventions. Here we develop a stochastic model of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)...

The resurgence of infectious diseases due to vaccine refusal has highlighted the role of interactions between disease dynamics and the spread of vaccine opinion on social networks. Shifts between disease elimination and outbreak regimes often occur through tipping points. It is known that tipping points can be predicted by early warning signals (EW...

Theoretical models are typically developed through a deductive process where a researcher formulates a system of dynamic equations from hypothesized mechanisms. Recent advances in algorithmic methods can discover dynamic models inductively–directly from data. Most previous research has tested these methods by rediscovering models from synthetic dat...

Nitrogen runoff in certain southeastern Australian grasslands promotes the invasion of exotic grassland species at the expense of native species. Mitigation programs can reduce runoff and thus support native species, but their success may require the awareness and support of local populations. This situation represents a coupled socio-ecological sy...

It is widely recognized that coupled socio-ecological dynamics can be qualitatively different from the dynamics of social or ecological systems in isolation from one another. The influence of the type of ecological dynamics on the dynamics of the larger socio-ecological system is less well studied, however. Here, we carry out such a comparison usin...

The continued growth of the world’s population and increased interconnectivity heighten the risk that infectious diseases pose for human health worldwide. Epidemiological modelling is a tool that can be used to mitigate this risk by predicting disease spread or quantifying the impact of different intervention strategies on disease transmission dyna...

Geophysical models of climate change are becoming increasingly sophisticated, yet less effort is devoted to modelling the human systems causing climate change and how the two systems are coupled. Here, we develop a simple socio-climate model by coupling an Earth system model to a social dynamics model. We treat social processes endogenously—emergin...

An effective strategy to resolve conservation conflicts on lands outside of nature reserves is to consider the spatial arrangement of agricultural and native vegetation parcels such that the ecological value of the landscape is improved without reducing the amount of land used for agricultural production. Global optimization methods have been used...

The propagation of rumours about rare but severe adverse vaccination or infection events through social networks can strongly impact vaccination uptake. Here we model a coupled behaviour-disease system where individual risk perception regarding vaccines and infection are shaped by their personal experiences and the experiences of others. Informatio...

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has been fixed in the paper.

Natural Selection is frequently modelled via proportional selection where survival is proportional to the average payoff differential. There has been little attention devoted to modelling truncation selection where replicators below a threshold are culled and survivors reproduce. Here, we systematically explore truncation selection for two strategy...

Over-exploitation of natural resources can have profound effects on both ecosystems and their resident human populations. Simple theoretical models of the dynamics of a population of human harvesters and the abundance of a natural resource being harvested have been studied previously, but relatively few models consider the effect of metapopulation...

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has been fixed in the paper.

[This corrects the article DOI: 10.1371/journal.pone.0200781.].

Visitors can play an important role in the spread of infections. Here, we incorporate an epidemic model into a game theoretical framework to investigate the effects of travel strategies on infection control. Potential visitors must decide whether to travel to a destination that is at risk of infectious disease outbreaks. We compare the individually...

The Nilgiri Hills in the Western Ghats of India constitute a region of high biological and cultural diversity, and include an endangered shola forest-grassland mosaic ecosystem. A mosaic ecosystem is one consisting of adjacent, coexisting patches of highly distinct naturally occurring land states (in this case, shola forest and natural grassland)....

Global food security and agricultural land management represent two urgent and intimately related challenges that humans must face. We quantify the changes in the global agricultural land footprint if the world were to adhere to the dietary guidelines put forth by the United States Department of Agriculture (USDA), while accounting for the land use...

Text A and B, Tables A and B, Fig A. (PDF)

It is widely recognized that coupled socio-ecological dynamics can be qualitatively different from the dynamics of social or ecological systems in isolation from one another. The influence of the type of ecological dynamics on the dynamics of the larger socio-ecological system is less well studied, however. Here, we carry out such a comparison usin...

Early warning signals of sudden regime shifts are a widely studied phenomenon for their ability to quantify a system’s proximity to a tipping point to a new and contrasting dynamical regime. However, this effect has been little studied in the context of the complex interactions between disease dynamics and vaccinating behaviour. Our objective was t...

The Caribbean coral reef ecosystem has experienced a long history of deterioration due to various stressors. For instance, over-fishing of parrotfish - an important grazer of macroalgae that can prevent destructive overgrowth of macroalgae - has threatened reef ecosystems in recent decades and stimulated conservation efforts such as the formation o...

The relationship between socioeconomic development and environmental degradation measures such as SO2, CO, and NOx emissions and deforestation has sometimes been claimed to follow an environmental Kuznets curve. However, in an era of globalization where the populations that experience economic benefits may be geographically distant from the populat...

Significance Complex adaptive systems exhibit characteristic dynamics near tipping points such as critical slowing down (declining resilience to perturbations). We studied Twitter and Google search data about measles from California and the United States before and after the 2014–2015 Disneyland, California measles outbreak. We find critical slowin...

Resource over-exploitation can have profound effects on both ecosystems and the human populations residing in them. Models of population growth based on a depletable resources have been studied previously, but relatively few consider metapopulation effects. Here we analyze a socio-ecological metapopulation model where resources grow logistically on...

Global food security and agricultural land management represent two urgent and intimately related challenges that humans must face in the coming decades. Here, we quantify the changes in the global agricultural land footprint if the world were to adhere to the dietary guidelines put forth by the United States Department of Agriculture (USDA), while...

Two-strategy evolutionary games on graphs have been extensively studied in the literature. A variety of graph structures, degrees of graph dynamics, and behaviours of replicators have been explored. These models have primarily been studied in the framework of facilitation of cooperation, and much excellent work has shed light on this field of study...

Human and environmental systems are often treated as existing in isolation from one another, whereas in fact they are often two parts of a single, coupled human-environment system. Developing theoretical models of coupled human-environment systems is a continuing area of research, although relatively few of these models are based on differential eq...

Pair approximation models have been used to study the spread of infectious diseases in spatially distributed host populations, and to explore disease control strategies such as vaccination and case isolation. Here we introduce a pair approximation model of individual uptake of non-pharmaceutical interventions (NPIs) for an acute self-limiting infec...

Population transmission models have been helpful in studying the spread of HIV. They assess changes made at the population level for different intervention strategies. To further understand how individual changes affect the population as a whole, game-theoretical models are used to quantify the decision-making process. Investigating multiplayer non...

Endangered forest-grassland mosaics interspersed with expanding agriculture and silviculture occur across many parts of the world, including the southern Brazilian highlands. This natural mosaic ecosystem is thought to reflect alternative stable states driven by threshold responses of recruitment to fire and moisture regimes. The role of adaptive h...

As the global human population continues to grow, so too does our impact on the environment. The ingenuity with which our species has harnessed natural resources to fulfill our needs is dazzling. Even as we tighten our grip on the environment, however, the escalating extent of anthropogenic actions destabilizes long-standing ecological balances (1,...

In complex systems, a critical transition is a shift in a system's dynamical regime from its current state to a strongly contrasting state as external conditions move beyond a tipping point. These transitions are often preceded by characteristic early warning signals such as increased system variability. However, early warning signals in complex, c...