Economic prospects: Some observations
5 May 2020
1. The prospects for the economy are bound up with the prospects for the COVID 19 epidemic. The simplest model for the epidemic is the SIR model. The population is divided up into the susceptible (S), the infected (I) and the recovered or deceased (R). The evolution of the epidemic is determined by the initial conditions (the distribution of the population today across the three categories), and two parameters, β (beta) and γ (gamma).
β represents the rate of infection and γ the rate of removal from infection by recovery or death, it being assumed that the recovered are immune from re-infection over the projection period. Without intervention, β and γ reflect the characteristics of the virus: β depends directly on how infectious it is, and γ depends on the rate of removal from the infectious state, and therefore inversely on how long illness lasts.
The purpose of intervention is to reduce β (by confinement to home and social distancing) and to increase γ (by isolating the infected, effectively putting them in the R category). The ratio R0= β/γ is the basic reproduction number, which is the expected number of new infections resulting from a single infection in the population.
If R0 is less than one, the epidemic dies out. If it is greater than one, the epidemic spreads and the higher R0 is, the faster the spread will be. The problem is that no-one knows exactly what the initial conditions are, or the values of β and γ without intervention, or how β and γ are changed by intervention policies and their effectiveness. This creates the possibility of waves of infection and consequent cycles of intervention. A period of relaxation of confinement (with a corresponding increase in β) may be followed by a period of tightening, as countries attempt to avoid the overwhelming of their health systems The consequence will be a stop-go-stop evolution of the economy.