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

Abstract

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 [Formula: see text] is derived. The effects of heterogeneity in groups, patches and mobility patterns on [Formula: see text] 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.

Global analysis of multi-host and multi-vector epidemic models

“…where denotes the Hadamard division. Relations (4) and (5) imply the attractivity of the DFE. Moreover, by [16,43], the DFE is locally asymptotically stable whenever R 2 0 (m, n, p) < 1.…”

Epidemiological Models Incorporating Mobility, Behavior, and Time Scales

“…We revisit this framework in possibly the simplest general setting that of a susceptible-infected-susceptible (SIS) epidemic multi-group model. We collect some of the mathematical formulae and results in the context of this general SIS multi-group model as reported in the literature [4,6,7,11]. We proceed to identify basic reproduction numbers R 0 as a function of the associated multi-patch residence-time matrix P (p i,j : i, j = 1, 2, 3 .…”

“…We have used simulations to generate insights on the impact that the residence matrix P has on infection levels within each patch. Model results [4,6,7,11] show that the infection risk vector, which characterizes environments by risk to a pre-specified disease (measured by B), and the residence-time matrix P both play an important role in determining, for example, whether or not endemicity is reached at the patch level. Further, it is shown that the right combinations of environmental risks (B) and mobility behavior (P) are capable of promoting or suppressing infection within particular patches.…”

“…Further, it is shown that the right combinations of environmental risks (B) and mobility behavior (P) are capable of promoting or suppressing infection within particular patches. The theoretical results [4,6,7,11] are used to characterize patchspecific disease dynamics as a function of the time spent by residents and visitors in patches of interest. These results have helped classify patches as sources or sinks of infection, depending, of course, on the risk (B) and mobility (P) matrices.…”

“…In fact the entries of P may depend on disease prevalence levels. We have explored some simple situations, via simulations, when the entries of the matrix P are state-dependent [4,6,7,11]. The analysis and simulations for specific diseases are illustrated later in this chapter.…”