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.

Psychological Distress and Tobacco Use Among Hospital Workers During COVID-19.

Background and Aims: This work aims to assess the impact of the COVID-19 pandemic on hospital workers' psychological parameters and attitudes toward substance use, before and during the French COVID-19 lockdown. Methods: An online survey was proposed to the staff of the University Hospital of Nice and Sainte-Marie psychiatric hospital in France from May 18 to June 6, 2020 assessing changes in daily habits, psychological distress and changes in substance use, including smoking. Results: A total of 702 respondents (80.3% female) filled out the survey. Overall, most of the workers reported increased stress, irritability, sadness, decreased motivation, and a worse quality of sleep after the beginning of the COVID-19 lockdown. Additionally, hospital workers who were more likely to use tobacco during the COVID-19 lockdown reported increased sadness (OR = 1.23, p < 0.001), loss of motivation (OR = 0.86, p < 0.05), alcohol consumption (OR = 3.12, p < 0.001), lower incomes (OR = 1.69, p < 0.05), living alone (OR = 1.77, p < 0.001) and doing less physical activity (OR = 0.36, p < 0.001). Conclusion: During the first lockdown, significant psychological changes (sadness, distress, irritability) associated with changes in tobacco use and physical activity were reported. Such results should encourage hospital leaders to implement dedicated policies to better accompany hospital workers' psychological distress.

An Upper Bound on the Error Induced by Saddlepoint Approximations-Applications to Information Theory.

This paper introduces an upper bound on the absolute difference between: ( a ) the cumulative distribution function (CDF) of the sum of a finite number of independent and identically distributed random variables with finite absolute third moment; and ( b ) a saddlepoint approximation of such CDF. This upper bound, which is particularly precise in the regime of large deviations, is used to study the dependence testing (DT) bound and the meta converse (MC) bound on the decoding error probability (DEP) in point-to-point memoryless channels. Often, these bounds cannot be analytically calculated and thus lower and upper bounds become particularly useful. Within this context, the main results include, respectively, new upper and lower bounds on the DT and MC bounds. A numerical experimentation of these bounds is presented in the case of the binary symmetric channel, the additive white Gaussian noise channel, and the additive symmetric α -stable noise channel.

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.