Journal article: Herd immunity is a central concept in epidemiology. It refers to a situation where the amount of recovered and immune individuals is high enough to protect susceptibles from contracting the disease. Herd immunity can be obtained naturally when individuals recover from the disease, or artificially after the administration of an appropriate vaccine. The present paper addresses the question of the amount of public spending in medical research to obtain a vaccine which maximizes welfare. Public spending is assumed to reduce the waiting time to discover a vaccine against an infectious disease evolving according to a SIR model. Both linear and logarithmic preferences are considered with and without time discounting. Worth to note, we show that if an economy has a sufficiently performing technology, then the government should invest as much as the initial public budget allows.