  A multi-patch and multi-group modeling framework describing the dynamics of a
class of diseases driven by the interactions between vectors and hosts
structured by groups is formulated. Hosts' dispersal is modeled in terms of
patch-residence times with the nonlinear dynamics taking into account the
\textit{effective} patch-host size. The residence times basic reproduction
number $\mathcal R_0$ is computed and shown to depend on the relative
environmental risk of infection. The model is robust, that is, the disease free
equilibrium is globally asymptotically stable (GAS) if $\mathcal R_0\leq1$ and
a unique interior endemic equilibrium is shown to exist that is GAS whenever
$\mathcal R_0>1$ whenever the configuration of host-vector interactions is
irreducible. The effects of \textit{patchiness} and \textit{groupness}, a
measure of host-vector heterogeneous structure, on the basic reproduction
number $\mathcal R_0$, are explored. Numerical simulations are carried out to
highlight the effects of residence times on disease prevalence.
