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 R0 is computed as a function of a patch residence-times matrix ℙ. Our analysis implies that the resulting n-patch SIS model has robust dynamics when patches are strongly connected: there is a unique globally stable endemic equilibrium when R0 > 1 while the disease free equilibrium is globally stable when R0 ≤ 1. Our further analysis indicates that the dispersal behavior described by the residence-times matrix 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 ℙ on disease dynamics.

The dynamics, control, and evolution of communicable and vectorborne diseases are intimately connected to the joint dynamics of epidemiological, behavioral, and mobility processes that operate across multiple spatial, temporal, and organizational scales. The identification of a theoretical explanatory framework that accounts for the pattern regularity exhibited by a large number of host-parasite systems, including those sustained by host-vector epidemiological dynamics, is but one of the challenges facing the coevolving fields of computational, evolutionary, and theoretical epidemiology. Host-parasite epidemiological patterns, including epidemic outbreaks and endemic recurrent dynamics, are characteristic to well-identified regions of the world; the result of processes and constraints such as strain competition, host and vector mobility, and population structure operating over multiple scales in response to recurrent disturbances (like El Niño) and climatological and environmental perturbations over thousands of years. It is therefore important to identify and quantify the processes responsible for observed epidemiological macroscopic patterns: the result of individual interactions in changing social and ecological landscapes. In this perspective, we touch on some of the issues calling for the identification of an encompassing theoretical explanatory framework by identifying some of the limitations of existing theory, in the context of particular epidemiological systems. Fostering the reenergizing of research that aims at disentangling the role of epidemiological and socioeconomic forces on disease dynamics, better understood as complex adaptive systems, is a key aim of this perspective.infectious disease | risk | complex adaptive systems | mobility | behavior

International audienceWe consider SIS, SIR and MSIR models with standard mass action and varying population, with $n$ different pathogen strains of an infectious disease. We also consider the same models with vertical transmission. We prove that under generic conditions a competitive exclusion principle holds. To each strain a basic reproduction ratio can be associated. It corresponds to the case where only this strain exists. The basic reproduction ratio of the complete system is the maximum of each individual basic reproduction ratio. Actually we also define an equivalent threshold for each strain. The winner of the competition is the strain with the maximum threshold. It turns out that this strain is the most virulent, i.e., this is the strain for which the endemic equilibrium gives the minimum population for the susceptible host population. This can be interpreted as a pessimization principle.On considère les modèles SIS, SIR et MSIR avec la loi de l'action de masse standard et une population non constante, avec n différentes souches de pathogènes. Nous considérons aussi les même modèles avec transmission verticale. On prouve que sous une condition générique, le principe de compétition exclusive est vérifié. Pour chaque souche, un nombre de reproduction de base est associé. Il correspond au cas où seule cette souche existe. Le nombre de reproduction de base du système complet est le maximum de tous les nombres de reproduction de base pris individuellement. Nous définissons aussi un seuil équivalent pour chaque souche. La souche qui gagne la compétition est celle qui maximise le nombre de reproduction de base. C'est aussi la souche la plus virulente, i.e., c'est la souche pour laquelle l'équilibre endémique donne le minimum des individus susceptibles dans la population hôte. C'est le principe de pessimisation