The theory of epidemics with altruism

Abstract

Social distancing can mitigate the spread of diseases in humans and animals. Social distancing allows susceptible individuals to protect themselves (and others) but confers no personal benefit for infected individuals if recovery provides immunity. However, individuals are likely to be at least weakly altruistic and may be interested in protecting others when infected. A strongly altruistic population where individuals value others as equal to themselves would be expected to self-isolate when infected. This would strongly suppress the disease, avoid Herd Immunity, and vastly improve outcomes. Still, little is known about how weaker altruism affects behavior during epidemics. Here we show using game theory that even extremely weakly altruistic individuals, valuing their own lives equivalent to roughly 100,000 others, can rationally achieve almost identical outcomes. Individuals self-isolate in order to avoid setting off chains of infections that they would perceive as costly to them even at such small altruism. Our results are robust to a moderate fraction of asymptomatic cases or completely selfish individuals. The resulting behavior, while emerging from a complex optimization problem, is simple enough that it could have evolved as a behavioral response in social animals, as well as being easy to communicate and understand for humans.