# The theory of epidemics with altruism

## TL;DR

This paper uses game theory to show that even slightly altruistic individuals can rationally choose to self-isolate when sick, helping control disease spread.

## Contribution

The paper introduces a game-theoretic model showing that minimal altruism can lead to rational social distancing during epidemics.

## Key findings

- Individuals valuing their life as equivalent to 100,000 others may rationally self-isolate to prevent infections.
- Even weak altruism can lead to significant disease suppression and avoid herd immunity.
- The model is robust to asymptomatic cases and selfish individuals.

## Abstract

The question of whether to social distance when infected with a dangerous disease can be viewed as a problem in game theory. We find that such behavior is only rational for individuals with a minimum level of altruism, quantifying how much they care about the outcomes of others in the population. Remarkably, the altruism threshold above which it is rational to protect others like this can be extremely low: valuing one’s own life as equivalent to 100,000 others. Our work may be useful for policy makers. It may also help understand the behavior of animals living in groups of related kin. Here, a similar Nash equilibrium exists in which it would be advantageous for animals to socially distance when sick.

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.