Abstract

Control theory is an important technique with which to understand the behaviour of information processing agents. We study rational decision making for agents that face the possibility of infection with an SIR -type disease. Infection carries a cost, encoded in objective function. Agents can modify their behaviour (infectivity) to exert some control, but this also carries a cost. We investigate how the optimal behavioiur,  maximising an objective function, depends on the cost of infectuon, whether the agents are selfish or utilitarian, with nonlinear infection costs to mimic health care capacity limits and uncertain vaccination development times. We introduce another layer of control at the government level with an objective function that may or may not be aligned with the population and study the coupled control theory problem to establish optimal policy. We find a sharp switch in policy roughly equivalent to “lockdown” and “herd immunity” strategies at a crtitical infection cost. Finally we formulate a form of physics inspired machine learning to attack the inverse problem of inferring the objective function of selfish agents from their behaviour.  This work is joint work together with Prof Ryoichi Yamamoto (Kyoto Univ), Dr John Molina (Kyoto Univ) and Dr Simon Schnyder (Tokyo Univ).