For emerging and reemerging mosquito-borne diseases, it is important to
understand the conditions and mechanisms triggering an outbreak and
recurrence of an endemic. In this talk, I will present bifurcation
analysis for dynamical models to explore the threshold conditions
and mechanisms for the dynamics for some models of general
mosquito-borne diseases. The bifurcations include backward bifurcations,
Hopf bifurcations and Bogdanov-Takens bifurcations of codimension two
and three, and bifurcation of nilpotent singularities.