Math Biology Seminar: Carlos Castillo Chavez

Person-to-person contacts drive human disease dynamics and managing epidemics has begun to focus on motivating people, via social distancing policies that alter behaviors aimed at reducing contacts and disease risk. However, individuals value such contacts and are willing to accept some disease risk to gain contact-related benefits. Epidemiological–economic model of disease dynamics that explicitly model the trade-offs that drive person-to- person contact decisions need to be systematically developed. Preliminary results ((Adaptive human behavior in epidemiological models, PNAS 2011, Fenichel et al.) show, not surprisingly, that including adaptive human behavior significantly changes the course of epidemics a result with implications for parameter estimation and interpretation as well as for the development of social distancing policies. Acknowledging adaptive behavior requires a shift in thinking about epidemiological processes and parameters. The cost–benefit trade-offs that shape contact behavior and its dynamics are implicitly incorporated in epidemiological models making it difficulty to parse out the effects of adaptive behavior. We revisit and apply unpublished theoretical results by S.P. Blythe, the late K. Cooke and Castillo-Chavez (Steve Blythe, Kenneth Cooke and Castillo-Chavez) to the study of the impact of individuals’ adaptive responses to epidemics that account for epidemiological and economic factors. The resulting generalized SIR framework supports multiple equilibria and oscillatory epidemiological dynamics. Its analysis facilitates the study of disease dynamics as a complex adaptive system (Morin et al. 2013, RMA). In this lecture, I will discuss multiple approaches for incorporating the role of behavior; highlight some preliminary results from Blythe et al (1991), E. Diaz (2011), Fenichel et al (2011) and Morin et al. (2013) and Yun Kang and CCC (2012, 2014)