A Spatial Kinetic Model of Crowd Evacuation Dynamics with Infectious Disease Contagion

Abstract

This paper proposes a kinetic theory approach coupling together the modeling of crowd evacuation from a bounded domain with exit doors and infectious disease contagion. The spatial movement of individuals in the crowd is modeled by a proper description of the interactions with people in the crowd and the environment, including walls and exits. At the same time, interactions among healthy and infectious individuals may generate disease spreading if exposure time is long enough. Immunization of the population and individual awareness to contagion is considered as well. Interactions are modeled by tools of game theory, that let us propose the so-called tables of games that are introduced in the general kinetic equations. The proposed model is qualitatively studied and, through a series of case studies, we explore different scenarios related to crowding and gathering formation within indoor venues under the spread of a respiratory infectious disease, obtaining insights on specific policies to reduce contagion that may be implemented.

Prescriptive, descriptive or predictive models: What approach should be taken when empirical data is limited? Reply to comments on “Mathematical models for Dengue fever epidemiology: A 10-year systematic review”

“…For a broader perspective of this modelling strategy, please refer to Chang's review [72]. Lastly, some recent contributions on how tools of game theory can be used to model human interactions regarding disease contagion can be found in [73,74,75] for an airborne transmitted disease and in [76] for contagion within a crowd, where cooperative and competitive interactions are taken into account. We believe that some of the therein proposed ideas can be extended to the case of a vector-borne disease like dengue to model the so-called effect of individual's decision making on global regulation [77].…”

Behavioral Human Crowds and Society

“…Similarly, for contagion awareness, they correspond to no awareness and maximum awareness, respectively. See also [1,19], where a sophisticated model is developed to describe the progression of a pathology.…”