Which is more effective for suppressing an infectious disease: Imperfect vaccination or defense against contagion?

We consider two imperfect ways to protect against an infectious disease such as influenza, namely vaccination giving only partial immunity and a defense against contagion such as wearing a mask. We build up a new analytic framework considering those two cases instead of perfect vaccination, conventionally assumed as a premise, with the assumption of an infinite and well-mixed population. Our framework also considers three different strategy-updating rules based on evolutionary game theory: conventional pairwise comparison with one randomly selected agent, another concept of pairwise comparison referring to a social average, and direct alternative selection not depending on the usual copying concept. We successfully obtain a phase diagram in which vaccination coverage at equilibrium can be compared when assuming the model of either imperfect vaccination or a defense against contagion. The obtained phase diagram reveals that a defense against contagion is marginally inferior to an imperfect vaccination as long as the same coefficient value is used. Highlights - We build a new analytical framework for a vaccination game combined with the susceptible-infected-recovered (SIR) model. - Our model can evaluate imperfect provisions such as vaccination giving only partial immunity and a defense against contagion. - We obtain a phase diagram with which to compare the quantitative effects of partial vaccination and a defense against contagion.