Rational social distancing policy during epidemics with limited healthcare capacity
Fig 2
Comparison of social distancing behaviour.
(A) Population behaviour k(t), (B) government intervention ε(t) and (C, D) dynamics of the disease s, i for a range of scenarios with i0 = 3 ⋅ 10−8, f = 1, and κ* = 4 throughout: a baseline where there is no behavioural modification (corresponding to equilibrium behaviour at an infection cost α = 0, grey lines); the Nash equilibrium for α = 400 (black lines), calculated numerically via forward-backward sweep, see section C in S1 Text (In order to demonstrate that the numerical solution is accurate, we also show the analytical solution of the same equations [62] as black dots); the utilitarian maximum for α = 400 (gold dashes); and finally the population behaviour for two optimal government policies, one being without cost to the government, γg = 0 (gold lines), and one being costly, γg = 0.5, with α = 400 (cyan lines). When government interventions are cost-free, they enable the population to reach the utilitarian maximum.