  Facing the threats of infectious diseases, we take various actions to protect
ourselves, but few studies considered an evolving system with competing
strategies. In view of that, we propose an evolutionary epidemic model coupled
with human behaviors, where individuals have three strategies: vaccination,
self-protection and laissez faire, and could adjust their strategies according
to their neighbors' strategies and payoffs at the beginning of each new season
of epidemic spreading. We found a counter-intuitive phenomenon analogous to the
well-known \emph{Braess's Paradox}, namely a better condition may lead to worse
performance. Specifically speaking, increasing the successful rate of
self-protection does not necessarily reduce the epidemic size or improve the
system payoff. This phenomenon is insensitive to the network topologies, and
can be well explained by a mean-field approximation. Our study demonstrates an
important fact that a better condition for individuals may yield a worse
outcome for the society.
