Epidemiological Models Incorporating Mobility, Behavior, and Time Scales

Abstract

The work of Eubank et al. [24], Sara del Valle et al. [44], Chowell et al. [7, 18], and Castillo-Chavez and Song [13] have highlighted the impact of modified modeling approaches that incorporate heterogeneous modes of mobility within variable environments in order to study their impact on the dynamics of infectious diseases. Castillo-Chavez and Song [13], for example, proceeded to highlight a Lagrangian perspective, that is, the use of models that keep track at all times of the identity of each individual. This approach was used to study the consequences of deliberate efforts to transmit smallpox in a highly populated city, involving transient subpopulations and the availability of massive modes of public transportation. Here, a multi-group epidemic Lagrangian framework where mobility and the risk of infection are functions of patch residence time and local environmental risk is introduced. This Lagrangian approach has been used within classical contact epidemiological (that is, transmission is due to "contacts" between individuals) formulations in the context of a possible deliberate release of biological agents [2, 13]. The Lagrangian approach is introduced here as a modeling approach that explicitly avoids the assignment of heterogeneous contact rates to individuals. The use of contacts or activity levels and the view that transmission is due to collisions between individuals has a long history and it is conceptually consistent with the way we envision disease transmission between susceptible and infectious individuals. However, contacts are hard to define and consequently, at least in the context of communicable diseases, impossible to measure in various settings. Is it possible to capture interactions of individual mathematically in a way different from the notion of contacts? The approach that is proposed focuses on the use of modeling frameworks that involve patches/environments defined or characterized by risks of infection that are functions of the time spent in each environment/patch. These patches/environments may or may not have permanent hosts and they may be used to account for places of "transitory" residence like mass transportation systems or