Multi-patch and multi-group epidemic models: A new framework

Derdei Bichara (1) , Abderrahman Iggidr (2, 3)

1 Department of Mathematics [Fullerton]
2 IECL - Institut Élie Cartan de Lorraine
3 NEUROSYS - Analysis and modeling of neural systems by a system neuroscience approach

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 R0 is derived. The effects of heterogeneity in groups, patches and mobility patterns on R0 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 if the matrix is also stochastic. 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.

Mots clés: Multi-Group; Mobility; Global Stability; Multi-Patch; Residence Times; Heterogeneity

Domaines: Santé publique et épidémiologie; Maladies infectieuses; Systèmes dynamiques [math.DS]

Derdei Bichara, Abderrahman Iggidr. Multi-patch and multi-group epidemic models: A new framework. Journal of Mathematical Biology, 2018, 77 (1), pp.107-134. ⟨10.1007/s00285-017-1191-9⟩. ⟨hal-01490764v2⟩