  In this paper, we develop a multi-group epidemic framework via virtual
dispersal where the risk of infection is a function of the residence time and
local environmental risk. This novel approach eliminates the need to define and
measure contact rates that are used in the traditional multi-group epidemic
models with heterogeneous mixing. We apply this approach to a general $n$-patch
SIS model whose basic reproduction number $\mathcal R_0 $ is computed as a
function of a patch residence-times matrix $\mathbb P$. Our analysis implies
that the resulting $n$-patch SIS model has robust dynamics when patches are
strongly connected: there is a globally stable endemic equilibrium when
$\mathcal R_0>1 $ while the disease free equilibrium is globally stable when
$\mathcal R_0\leq1 $. Our further analysis indicates that the dispersal
behavior described by the residence-times matrix $\mathbb P$ has profound
effects on the disease dynamics at the single patch level with consequences
that proper dispersal behavior along with the local environmental risk can
either promote or eliminate the endemic in particular patches. Our work
highlights the impact of residence times matrix if the patches are not strongly
connected. Our framework can be generalized in other endemic and disease
outbreak models. As an illustration, we apply our framework to a two-patch SIR
single outbreak epidemic model where the process of disease invasion is
connected to the final epidemic size relationship. We also explore the impact
of disease prevalence driven decision using a phenomenological modeling
approach in order to contrast the role of constant versus state dependent
$\mathbb P$ on disease dynamics.
