A scalable Bayesian persuasion framework for epidemic containment on heterogeneous networks

During an epidemic, the information available to individuals in the society deeply influences their belief of the true infectiousness of the disease, and thereby the preventive measures they take to stay safe from the infection. In this paper, we develop a scalable framework for ascertaining the optimal choice of the test for determining the infectiousness of the disease whose results must be truthfully communicated to individuals for the purpose of epidemic containment. We use a networked public goods model to capture the underlying societal structure and the individuals’ incentives during an epidemic, and the Bayesian persuasion framework for modelling the choice of the test. Our first main result is a structural decomposition of the government’s objectives into two independent components – a component dependent on the utility function of individuals, and another dependent on properties of the underlying network. Since the network dependent term in this decomposition is unaffected by the testing strategies adopted by the government, this characterization simplifies the problem of finding the optimal testing methodology. We find explicit conditions, in terms of certain concavity measures, under which perfectly accurate tests, uninformative tests, tests which exaggerate the infectiousness, and ones which downplay it are optimal. Furthermore, we explicitly evaluate these optimal tests for exponential and quadratic benefit functions and study their dependence on underlying parameter values. The structural decomposition results are also helpful in studying other forms of interventions like incentive design and network design.