Preface to Special Issue on Dynamic Games for Modeling and Control of Epidemics

This preface introduces the special issue on Dynamic Games for Modeling and Control of Epidemics. It showcases 12 papers with timely contributions to dynamic games and their applications to the modeling, analysis, and control of epidemics. The papers in this collection connect dynamic games and epidemic models to address the recent challenges related to screening, containment, and mitigation strategies for epidemics. This collection covers broad application areas in networks, human behaviors, and epidemiology as well as a diverse range of dynamic game methods, including evolutionary games, differential games, and mean-field games.

The Mask Game with Multiple Populations

Masks save lives. Therefore, while the culture of wearing masks is promoted, it is critical to understand the various aspects of how that culture is adopted. The main contribution of this paper is in the modeling of the mask game. Wearing a mask provides partial protection against epidemics at some cost of comfort. Players can be differentiated according to both their risk state as well as their health state (susceptible, infected and removed). We formulate the problem as a Bayesian game in which players know their own risk state and ignore their own health state and the health and risk states of their counterparts. Using ideas from evolutionary games, we reduce the problem to a one-shot equivalent game and describe the structure of the symmetric equilibria. We prove that the policies adopted by the players at such equilibria admit a threshold structure. More specifically, players wear masks only if their risk state is equal to or bigger than a given threshold.

On the True Number of COVID-19 Infections: Effect of Sensitivity, Specificity and Number of Tests on Prevalence Ratio Estimation.

In this paper, a formula for estimating the prevalence ratio of a disease in a population that is tested with imperfect tests is given. The formula is in terms of the fraction of positive test results and test parameters, i.e., probability of true positives (sensitivity) and the probability of true negatives (specificity). The motivation of this work arises in the context of the COVID-19 pandemic in which estimating the number of infected individuals depends on the sensitivity and specificity of the tests. In this context, it is shown that approximating the prevalence ratio by the ratio between the number of positive tests and the total number of tested individuals leads to dramatically high estimation errors, and thus, unadapted public health policies. The relevance of estimating the prevalence ratio using the formula presented in this work is that precision increases with the number of tests. Two conclusions are drawn from this work. First, in order to ensure that a reliable estimation is achieved with a finite number of tests, testing campaigns must be implemented with tests for which the sum of the sensitivity and the specificity is sufficiently different than one. Second, the key parameter for reducing the estimation error is the number of tests. For a large number of tests, as long as the sum of the sensitivity and specificity is different than one, the exact values of these parameters have very little impact on the estimation error.