摘要：One crucial condition for the uniqueness of Nash equilibrium set in
vaccination games is that the attack ratio monotonically decreases as
the vaccine coverage level increasing. We consider several deterministic vaccination models in homogeneous mixing population and in
heterogeneous mixing population. Based on the final size relations
obtained from the deterministic epidemic models, we prove that the
attack ratios can be expressed in terms of the vaccine coverage levels,
and also prove that the attack ratios are decreasing functions of vaccine coverage levels. Some thresholds are presented, which depend
on the vaccine efficacy. It is proved that for vaccination games in
homogeneous mixing population, there is a unique Nash equilibrium
for each game.
关键词：Epidemiology; game theory;
uniqueness of Nash
equilibrium; vaccination
game; homogeneous mixing
population; heterogeneous
mixing population;
compartmentalepidemic
models; final size relations;
population dynamics
