Incentives, lockdown, and testing: from Thucydides's analysis to the COVID-19 pandemic

Abstract

We consider the control of the COVID-19 pandemic via incentives, through either stochastic SIS or SIR compartmental models. When the epidemic is ongoing, the population can reduce interactions between individuals in order to decrease the rate of transmission of the disease, and thus limit the epidemic. However, this effort comes at a cost for the population. Therefore, the government can put into place incentive policies to encourage the lockdown of the population. In addition, the government may also implement a testing policy in order to know more precisely the spread of the epidemic within the country, and to isolate infected individuals. We provide numerical examples, as well as an extension to a stochastic SEIR compartmental model to account for the relatively long latency period of the COVID-19 disease. The numerical results confirm the relevance of a tax and testing policy to improve the control of an epidemic. More precisely, if a tax policy is put into place, even in the absence of a specific testing policy, the population is encouraged to significantly reduce its interactions, thus limiting the spread of the disease. If the government also adjusts its testing policy, less effort is required on the population side, so individuals can interact almost as usual, and the epidemic is largely contained by the targeted isolation of positively-tested individuals.

Finite State Graphon Games with Applications to Epidemics

“…In order to accurately asses the risks in the decision making process, in reality the population needs to be tested for the disease. Two recent papers studying optimal testing policies are [16,37]. The effects of vaccination and related decision makings are not studied in this paper, but they have been analyzed in MFG-related settings since before the COVID-19 pandemic [44,45,51,38,28,32].…”

“…In such models, the members in the populations are taking actions based on policies issued by the regulator, while the regulator anticipates the population's reaction and optimizes the policy. The case of a cooperative population has been studied in [37], while in [3], a population of selfish agents with contact factor control has been studied.…”

Office automation at the Department of Management Studies, the University of Hong Kong : a feasibility study

“…Assumption 4.1 is a technical condition used to show the component-wise properties of the Lyapunov equation (32) in Proposition B.4, which eventually allows us to compare the cost functionals of the follower under the two games using the representation in (30). Statements 1) and 2) suggest that each player values his difference with the other players only moderately.…”

“…In this case, we can apply comparison theorems for ODEs to determine the relative size of the corresponding components of the associated Lyapunov-Riccati equations under the two games, which mainly depend on the signs of the coefficients representing the interactions between two different players, e.g., A β , B α , etc. Using the representation (30) and by taking into account of the size of the initial conditions, we are able to arrive at Theorem 4.2. be the optimal cost functional in (30) for the follower in the Nash and the Pareto game, respectively. Suppose that Assumptions 3.1 and 4.1, and at least one of Assumptions 3.2 and 3.3 holds.…”

“…For a detailed introduction to the subject, consult the monographs by Bensoussan et al [12], Carmona and Delarue [17], and the references therein. The simplicity and competence of mean field theory in modeling multi-agent systems have prompted fruitful interdisciplinary applications, for instance, in finance [15,19,25,28]; economics [1,2]; industrial engineering [4,23,32]; and more recently in machine learning [36] and studies on the pandemic [24,30].…”