The science and management of infectious disease are entering a new stage. Increasingly public policy to manage epidemics focuses on motivating people, through social distancing policies, to alter their behavior to reduce contacts and reduce public disease risk. Person-to-person contacts drive human disease dynamics. People value such contacts and are willing to accept some disease risk to gain contact-related benefits. The cost-benefit trade-offs that shape contact behavior, and hence the course of epidemics, are often only implicitly incorporated in epidemiological models. This approach creates difficulty in parsing out the effects of adaptive behavior. We use an epidemiological-economic model of disease dynamics to explicitly model the trade-offs that drive person-toperson contact decisions. Results indicate that including adaptive human behavior significantly changes the predicted course of epidemics and that this inclusion has implications for parameter estimation and interpretation and for the development of social distancing policies. Acknowledging adaptive behavior requires a shift in thinking about epidemiological processes and parameters.susceptible-infected-recovered model | R 0 | reproductive number | bioeconomics T he science and management of infectious disease is entering a new stage. The increasing focus on incentive structures to motivate people to engage in social distancing-reducing interpersonal contacts and hence public disease risk (1)-changes what health authorities need from epidemiological models. Social distancing is not new-for centuries humans quarantined infected individuals and shunned the obviously ill, but new approaches are being used to deal with modern social interactions. Scientific development of social distancing public policies requires that epidemiological models explicitly address behavioral responses to disease risk and other incentives affecting contact behavior. This paper models the role of adaptive behavior in an epidemiological system. Recognizing adaptive behavior means explicitly incorporating behavioral responses to disease risk and other incentives into epidemiological models (2, 3). The workhorse of modern epidemiology, the compartmental epidemiological model (4, 5), does not explicitly include behavioral responses to disease risk. The transmission factors in these models combine and confound human behavior and biological processes. We develop a simple compartmental model that explicitly incorporates adaptive behavior and show that this modification alters understanding of standard epidemiological metrics. For example, the basic reproductive number, R 0 , is a function of biological processes and human behavior, but R 0 lacks a behavioral interpretation in the existing literature. Biological and behavioral feedbacks muddle R 0 's biological interpretation and confound its estimation.Prior approaches that incorporate behavior into epidemiological models generally fall into three categories: specification of nonlinear contact rate functions, expanded epidemiologi...

A timely literature on the design of economic incentives for nonpoint pollution control has been emerging. We describe the nonpoint pollution control problem, some of the peculiar challenges it poses for policy design, and the policyrelated contributions of the theoretical and empirical literature on the economics of nonpoint pollution.

We develop a multi-group epidemic framework via virtual dispersal where the risk of infection is a function of the residence time and local environmental risk. This novel approach eliminates the need to define and measure contact rates that are used in the traditional multi-group epidemic models with heterogeneous mixing. We apply this approach to a general n-patch SIS model whose basic reproduction number R0 is computed as a function of a patch residence-times matrix ℙ. Our analysis implies that the resulting n-patch SIS model has robust dynamics when patches are strongly connected: there is a unique globally stable endemic equilibrium when R0 > 1 while the disease free equilibrium is globally stable when R0 ≤ 1. Our further analysis indicates that the dispersal behavior described by the residence-times matrix ℙ has profound effects on the disease dynamics at the single patch level with consequences that proper dispersal behavior along with the local environmental risk can either promote or eliminate the endemic in particular patches. Our work highlights the impact of residence times matrix if the patches are not strongly connected. Our framework can be generalized in other endemic and disease outbreak models. As an illustration, we apply our framework to a two-patch SIR single outbreak epidemic model where the process of disease invasion is connected to the final epidemic size relationship. We also explore the impact of disease prevalence driven decision using a phenomenological modeling approach in order to contrast the role of constant versus state dependent ℙ on disease dynamics.

Agricultural nonpoint source water pollution has long been recognized as an important contributor to U.S. water quality problems and the subject of an array of local, state, and federal initiatives to reduce the problem. A "pay-the-polluter" approach to getting farmers to adopt best management practices has not succeeded in improving water quality in many impaired watersheds. With the prospects of reduced funding for the types of financial and technical assistance programs that have been the mainstay of agricultural water quality policy, alternative approaches need to be considered. Some changes to the way current conservation programs are implemented could increase their efficiency, but there are limits to how effective a purely voluntary approach can be. An alternative paradigm is the "polluter pays" approach, which has been successfully employed to reduce point source pollution. A wholesale implementation of the polluter-pays approach to agriculture is likely infeasible, but elements of the polluter-pays approach could be incorporated into agricultural water quality policy.

Many ecosystems appear subject to regime shifts-abrupt changes from one state to another after crossing a threshold or tipping point. Thresholds and their associated stability landscapes are determined within a coupled socioeconomic-ecological system (SES) where human choices, including those of managers, are feedback responses. Prior work has made one of two assumptions about managers: that they face no institutional constraints, in which case the SES may be managed to be fairly robust to shocks and tipping points are of little importance, or that managers are rigidly constrained with no flexibility to adapt, in which case the inferred thresholds may poorly reflect actual managerial flexibility. We model a multidimensional SES to investigate how alternative institutions affect SES stability landscapes and alter tipping points. With institutionally dependent human feedbacks, the stability landscape depends on institutional arrangements. Strong institutions that account for feedback responses create the possibility for desirable states of the world and can cause undesirable states to cease to exist. Intermediate institutions interact with ecological relationships to determine the existence and nature of tipping points. Finally, weak institutions can eliminate tipping points so that only undesirable states of the world remain.alternative stable states | multistability | bioeconomics | invasive species E cological multistability theory describes how distinct ecosystems, identical but for their initial states, can stabilize at very different long-run equilibria. A costly or irreversible "regime shift" can subsequently occur when a multistable (MS) system is moved past a threshold or tipping point and into an alternative equilibrium's basin of attraction (1-3) (Fig. 1). The management of MS systems has become a focal point of the science-policy interface (4-6) in response to fisheries collapse, climate change, vegetation changes, and invasive species, as these phenomena are often deemed causes and effects of regime shifts that reduce ecosystem services (7).Increasingly, human-impacted ecological systems, including MS systems, are regarded as coupled socioeconomic-ecological systems (SES) where human behaviors are feedback responses affecting, and affected by, ecological variables (8) (Fig. 2). The SES perspective means that solving ecological problems requires altering the SES's stability landscape or topology (i.e., the dynamic system's "shape", defining thresholds and basins of attraction) so the system moves to a preferred outcome (8,9). This result is achieved by imposing regulations or altering economic signals that influence human feedback responses (Fig. 2). An ensuing regime shift might be said to result from a shift in regulatory institutions, extending Beisner et al.'s (3) categorization (Fig. 1).SES management is often modeled using a bioeconomic framework that combines economic decision theory with ecological modeling (10). Work on MS-SESs has focused on problems such as rangeland ecosystems (9, 11), cora...