  We develop a multi-patch and multi-group model that captures the dynamics of
an infectious disease when the host is structured into an arbitrary number of
groups and interacts into an arbitrary number of patches where the infection
takes place. In this framework, we model host mobility that depends on its
epidemiological status, by a Lagrangian approach. This framework is applied to
a general SEIRS model and the basic reproduction number $\mathcal{R_0}$ is
derived. The effects of heterogeneity in groups, patches and mobility patterns
on $\mathcal{R_0}$ and disease prevalence are explored. Our results show that
for a fixed number of groups, the basic reproduction number increases with
respect to the number of patches and the host mobility patterns. Moreover, when
the mobility matrix of susceptible individuals is of rank one, the basic
reproduction number is explicitly determined and was found to be independent of
the latter. The cases where mobility matrices are of rank one capture important
modeling scenarios. Additionally, we study the global analysis of equilibria
for some special cases. Numerical simulations are carried out to showcase the
ramifications of mobility pattern matrices on disease prevalence and basic
reproduction number.
