On the Dynamics of Dengue Virus type 2 with Residence Times and Vertical   Transmission
  A two-patch mathematical model of Dengue virus type 2 (DENV-2) that accounts for vectors' vertical transmission and between patches human dispersal is introduced. Dispersal is modeled via a Lagrangian approach. A host-patch residence-times basic reproduction number is derived and conditions under which the disease dies out or persists are established. Analytical and numerical results highlight the role of hosts' dispersal in mitigating or exacerbating disease dynamics. The framework is used to explore dengue dynamics using, as a starting point, the 2002 outbreak in the state of Colima, Mexico. 
Derdei Bichara, Susan A. Holechek, Jorge Velazquez-Castro, Anarina L.   Murillo and Carlos Castillo-Chavez
q-bio.PE