An approximate threshold condition for non-autonomous system: an   application to a vector-borne infection
  An non-autonomous system is proposed to model the seasonal pattern of dengue fever. We found that an approximate threshold condition for infection persistence describes all possible behavior of the system. As far as we know, the kind of analysis here proposed is entirely new. No precise mathematical theorems are demonstrated but we give enough numerical evidence to support the conclusions. 
F. A. B. Coutinho, M. N. Burattini, L. F. Lopez, E. Massad