Natural versus artificial herd immunity: Is vaccine research investment always optimal?

Under the threat of a rapid expanding virus like the 2020 COVID-19, policy-makers need to decide relatively fast whether and under which conditions to invest in a vaccine, and eventually adopt other protective measures like social distancing or lockdowns, or to wait for natural herd immunity. Taking into account that vaccines take time to be fully developed and effective, this paper considers a unified framework at the crossroad between economics and epidemiology to study optimal public spending in medical research to obtain a vaccine against an infectious disease evolving according to a SIR dynamics. We prove that developed economies always invest in the search of a vaccine. The more individuals care about consumption, the more they actually reduce their current consumption and the more they invest in the vaccine research program to recover their consumption potential at the earliest. Our model would only recommend economies with very poor technology to restrain from investment and wait for herd immunity.