Adaptive human behavior in epidemiological models Eli P. Fenichela,1, Carlos Castillo-Chavezb, M. G. Ceddiac, Gerardo Chowellb,d, Paula A. Gonzalez Parrae, Graham J. Hicklingf, Garth Hollowayc, Richard Horang, Benjamin Morinb, Charles Perringsa, Michael Springbornh, Leticia Velazqueze, and Cristina Villalobosi aSchool of Life Sciences and ecoSERVICES Group, Arizona State University, Tempe, AZ 85287-4501; bSchool of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85287; cDepartment of Food Economics and Marketing, School of Agriculture Policy and Development, University of Reading, RG6 6AR Reading, United Kingdom; dDivision of Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, Bethesda, MD 20892-2220; eProgram in Computational Science, University of Texas at El Paso, El Paso, TX 79968-0514; fCenter for Wildlife Health, Department of Forestry, Wildlife, and Fisheries, and National Institute for Mathematical and Biological Synthesis, University of Tennessee, Knoxville, TN 37996-4563; gDepartment of Agricultural, Food, and Resource Economics, Michigan State University, East Lansing, MI 48824; hDepartment of Environmental Science and Policy, University of California, Davis, CA 95616; and iDepartment of Mathematics, University of Texas–Pan American, Edinburg, TX 78539 Edited by Partha Sarathi Dasgupta, University of Cambridge, Cambridge, United Kingdom, and approved February 23, 2011 (received for review July 30, 2010) The science and management of infectious disease are entering partments or agent-based models, and epidemiological–economic a new stage. Increasingly public policy to manage epidemics (epi-economic) models. Classical epidemiological models assume focuses on motivating people, through social distancing policies, contact rates are constant (frequency dependent) or proportional to alter their behavior to reduce contacts and reduce public disease to density (density dependent), although many extensions exist risk. Person-to-person contacts drive human disease dynamics. (6). A common extension is to specify a contact rate that is non- People value such contacts and are willing to accept some disease linear in the state variables—generally in the density of infected risk to gain contact-related benefits. The cost–benefit trade-offs individuals (e.g., refs. 6–8). Such extensions are a reduced-form that shape contact behavior, and hence the course of epidemics, approach to modeling behavioral responses to disease risks. This are often only implicitly incorporated in epidemiological models. This approach is limited in that it does not model the underlying de- approach creates difficulty in parsing out the effects of adaptive cision process and does not readily help decision makers design behavior. We use an epidemiological–economic model of disease incentives for socially desirable behaviors during an epidemic. dynamics to explicitly model the trade-offs that drive person-to- A second approach is to include behaviorally related compart- person contact decisions. Results indicate that including adaptive ments in addition to health status compartments. This approach human behavior significantly changes the predicted course of epi- involves developing behavioral rules for types of individuals in demics and that this inclusion has implications for parameter estima- different compartments, such as hospitalization and fear com- tion and interpretation and for the development of social distancing partments (9, 10) or spatial compartments joined as a network policies. Acknowledging adaptive behavior requires a shift in think- (11). Individuals in these compartments experience different ing about epidemiological processes and parameters. disease incidence. Extending this approach, so that all individuals have unique behavioral rules, yields an agent-based model (e.g., – – susceptible infected recovered model | R0 | reproductive number | ref. 12). This approach often requires the analyst to specify ex bioeconomics ante how changing incentives alters behavior and thus is restricted in its ability to aid in designing social distancing incentives. he science and management of infectious disease is entering Epi-economic models merge economics and epidemiology Ta new stage. The increasing focus on incentive structures to by explicitly analyzing individual behavioral choices in response motivate people to engage in social distancing—reducing in- to disease risk (13–18). People are assumed to make decisions terpersonal contacts and hence public disease risk (1)—changes to maximize utility, an index of well-being. People weigh the what health authorities need from epidemiological models. So- expected utility associated with decisions that include the pos- cial distancing is not new—for centuries humans quarantined sibility of future infection when choosing between behaviors such infected individuals and shunned the obviously ill, but new as vaccination choices (17) or different levels of interpersonal approaches are being used to deal with modern social inter- contact (12–15). Disease risks simultaneously affect and are af- actions. Scientific development of social distancing public poli- fected by agents’ decisions, creating a risk feedback—infection cies requires that epidemiological models explicitly address be- levels drive behaviors and contact rate decisions shape disease havioral responses to disease risk and other incentives affecting spread. The epi-economics literature is largely built on top of contact behavior. This paper models the role of adaptive be- classical epidemiology, so that the impact of economic behaviors havior in an epidemiological system. Recognizing adaptive be- on epidemiological processes and metrics generally is not ex- havior means explicitly incorporating behavioral responses to plored. In this paper, we explore how economic feedbacks alter disease risk and other incentives into epidemiological models (2, the underlying epidemiology and can fundamentally shift inter- 3). The workhorse of modern epidemiology, the compartmental pretation of epidemiological processes and metrics. epidemiological model (4, 5), does not explicitly include behav- The approach to modeling behavior has implications for ioral responses to disease risk. The transmission factors in these public health policy design. Nonlinear contact rate models and models combine and confound human behavior and biological models involving increasing compartmentalization generally fo- processes. We develop a simple compartmental model that ex- cus on estimating the basic reproductive number of the disease, plicitly incorporates adaptive behavior and show that this mod- ification alters understanding of standard epidemiological metrics. R Author contributions: E.P.F., C.C.-C., M.G.C., G.C., P.A.G.P., G.J.H., G.H., R.H., C.P., M.S., For example, the basic reproductive number, 0, is a function of L.V., and C.V. designed research; E.P.F. performed research; E.P.F. led modeling and led biological processes and human behavior, but R0 lacks a behav- the workshop where research was designed; M.S. contributed to modeling; and E.P.F., ioral interpretation in the existing literature. Biological and be- M.G.C., G.C., P.A.G.P., G.H., R.H., B.M., C.P., M.S., L.V., and C.V. wrote the paper. fl havioral feedbacks muddle R0’s biological interpretation and The authors declare no con ict of interest. confound its estimation. This article is a PNAS Direct Submission. Prior approaches that incorporate behavior into epidemiolog- 1To whom correspondence should be addressed. E-mail: [email protected]. fi ical models generally fall into three categories: speci cation of This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. nonlinear contact rate functions, expanded epidemiological com- 1073/pnas.1011250108/-/DCSupplemental. 6306–6311 | PNAS | April 12, 2011 | vol. 108 | no. 15 www.pnas.org/cgi/doi/10.1073/pnas.1011250108 Downloaded by guest on September 27, 2021 R0,defined as the number of secondary infections in a naive management choices (e.g., vaccination and treatment). Ab- population that result from the initial introduction of a patho- stracting from these features facilitates clear illustration of how gen. Most of the literature recommends adopting public health adaptive contact behavior affects epidemiological dynamics policies to reduce R0. Roberts and Heesterbeek (ref. 19, p. 1359) and metrics. state that R0 is “the most pervasive and useful concept in System Eqs. 1–3 imply R0 = βC(·)N/v|lim S→N, lim I→0, lim Z→0 mathematical epidemiology” due to its perceived role in guiding (27); ergo this metric depends on contact behavior, as do system disease management. However, R0 implicitly includes disease- dynamics. In classical epidemiological models, C(·)isassumed free behavior and should be thought of as a reduced-form the same for all individuals regardless of health status, and mixing function. Estimates of R0 confound biological aspects of the is assumed to be homogeneous. It is common to assume either pathogen with social aspects of adaptive human responses to contacts are proportional to N,i.e.,C(·)=cN,sothatβC(·)I/N = disease risk. Moreover, R0 represents past events that may not be cβI, or contacts are constant, i.e., C(·)=c,soβC(·)I/N = cβI/N (6). informative of future events when behavior is adaptive. In each case, c is a fixed parameter, implying fixed (nonadaptive) The epi-economic literature on health policy focuses on the contact behavior and relegating behavior