18 research outputs found
Boeing Award for Excellence
No full textof community health and infectious disease, submitted, 2013. Timothy C. Reluga and Allison Shaw. Optimal migratory behavior in spatially-explicit seasonal environments Submitted July, 2013. Assieh Saadatpour, Reka Albert, and Timothy Reluga. A reduction method for Boolean networks proven to conserve attractors. accepted to SIAM Journal on Applied Dynamica
Equilibria of an Epidemic Game with Piecewise Linear Social Distancing Cost
No full textAround the world, infectious disease epidemics continue to threaten people’s health. When epidemics strike, we often respond by changing our behaviors to reduce our risk of infection. This response is sometimes called “social distancing”. Since behavior changes can be costly, we would like to know the optimal social distancing behavior. But the benefits of changes in behavior depend on the course of the epidemic, which itself depends on our behaviors. Differential population game theory provides a method for resolving this circular dependence. Here, I present the analysis of a special case of the differential SIR epidemic population game with social distancing when the relative infection rate is linear but bounded below by zero. Equilibrium solutions are constructed in closed-form for an open-ended epidemic. Constructions are also provided for epidemics that are stopped by the deployment of a vaccination that becomes available a fixed-time after the start of the epidemic. This can be used to anticipate a window of opportunity during which mass vaccination can significantly reduce the cost of an epidemic. c ○ 2013 Tim Reluga2 Reluga 1
Game theory of social distancing in response to an epidemic
No full textAuthor Summary Social distancing practices are changes in behavior that prevent disease transmission by reducing contact rates between susceptible individuals and infected individuals who may transmit the disease. Social distancing practices can reduce the severity of an epidemic, but the benefits of social distancing depend on the extent to which it is used by individuals. Individuals are sometimes reluctant to pay the costs inherent in social distancing, and this can limit its effectiveness as a control measure. This paper formulates a differential-game to identify how individuals would best use of social distancing and related self-protective behaviors during an epidemic. The epidemic is described by a simple, well-mixed ordinary differential equation model. We use the differential game to stud
Erratic Flu Vaccination Emerges from Short-Sighted Behavior in Contact Networks
No full textDaniel M. Cornforth is with UT Austin, Timothy C. Reluga is with Pennsylvania State University, Eunha Shim is with Yale University School of Medicine, Chris T. Bauch is with University of Guelph, Alison P. Galvani is with Yale University School of Medicine, Lauren Ancel Meyers is with UT Austin and the Santa Fe Institute.The effectiveness of seasonal influenza vaccination programs depends on individual-level compliance. Perceptions about risks associated with infection and vaccination can strongly influence vaccination decisions and thus the ultimate course of an epidemic. Here we investigate the interplay between contact patterns, influenza-related behavior, and disease dynamics by incorporating game theory into network models. When individuals make decisions based on past epidemics, we find that individuals with many contacts vaccinate, whereas individuals with few contacts do not. However, the threshold number of contacts above which to vaccinate is highly dependent on the overall network structure of the population and has the potential to oscillate more wildly than has been observed empirically. When we increase the number of prior seasons that individuals recall when making vaccination decisions, behavior and thus disease dynamics become less variable. For some networks, we also find that higher flu transmission rates may, counterintuitively, lead to lower (vaccine-mediated) disease prevalence. Our work demonstrates that rich and complex dynamics can result from the interaction between infectious diseases, human contact patterns, and behavior.This research was supported by NIH grant U01 GM087719, grants from the James F. McDonnell Foundation and Bill and Stephanie Sick to LAM, and the Bill and Melinda Gates Foundation grant 49276 to TCR. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Biological Sciences, School o
Total costs and savings.
No full text<p>Plots of the total per-capita cost of an epidemic (left) under equilibrium social distancing for the infinite-horizon problem with several efficiencies under Eq. (6), and the corresponding per-capita savings (right). Savings in expected cost compared to universal abstention from social distancing are largest for moderate basic reproduction numbers, but are relatively small, even in the limit of infinitely efficient social distancing. The case corresponds to infection of the minimum number of people necessary to reduce the reproduction ratio below .</p
Epidemic solutions with equilibrium social distancing and without social distancing.
No full text<p>Social distancing reduces the epidemic peak and prolongs the epidemic, as we can see by comparing a time series with subgame-perfect social distancing (top left) and a time series with the same initial condition but no social distancing (bottom left) (parameters , ). In the phase plane (right), we see that both epidemics track each other perfectly until , when individuals begin to use social distancing to reduce transmission. Eventually, social distancing leads to a smaller epidemic. The convexity change appearing at the bottom the phaseplane orbit with social distancing corresponds to the cessation of social distancing.</p
Social distancing threshold.
No full text<p>This is the threshold that dictates whether or not equilibrium behavior involves some social distancing. It depends on both the basic reproduction number and the maximum efficiency , and is independent of the exact form of . As rough rules of thumb, if or , then equilibrium behavior involves no social distancing.</p
Contour plots of relative risk surface for equilibrium strategies.
No full text<p>The relative risk is presented in feedback form with implicit coordinates (left) and transformed to explicit coordinates (right) for the infinite-horizon problem with maximum efficiency . The greater the value of the susceptible state (), the greater the instantaneous social distancing. We find that increasing the number of susceptible individuals always decreases the investment in social distancing, and the greatest investments in social distancing occur when the smallest part of the population is susceptible. Note that in the dimensionless model, the value of the infection state .</p
