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We develop a multi-patch and multi-group model that captures the dynamics ofan infectious disease when the host is structured into an arbitrary number ofgroups and interacts into an arbitrary number of patches where the infectiontakes place. In this framework, we model host mobility that depends on itsepidemiological status, by a Lagrangian approach. This framework is applied toa general SEIRS model and the basic reproduction number $\mathcal{R_0}$ isderived. The effects of heterogeneity in groups, patches and mobility patternson $\mathcal{R_0}$ and disease prevalence are explored. Our results show thatfor a fixed number of groups, the basic reproduction number increases withrespect to the number of patches and the host mobility patterns. Moreover, whenthe mobility matrix of susceptible individuals is of rank one, the basicreproduction number is explicitly determined and was found to be independent ofthe latter. The cases where mobility matrices are of rank one capture importantmodeling scenarios. Additionally, we study the global analysis of equilibriafor some special cases. Numerical simulations are carried out to showcase theramifications of mobility pattern matrices on disease prevalence and basicreproduction number.

Multi-Patch and Multi-Group Epidemic Models: A New Framework