Abstract
We formulate a generalized susceptible exposed infectious recovered (SEIR) model on a graph, describing the population dynamics of an open crowded place with an arbitrary topology. As a sample calculation, we discuss three simple cases, both analytically, and numerically, by means of a cellular automata simulation of the individual dynamics in the system. As a result, we provide the infection ratio in the system as a function of controllable parameters, which allows for quantifying how acting on the human behavior may effectively lower the disease spread throughout the system.
Highlights
Compartmental models provide a conceptually simple and widely used mean to mathematically modeling the dynamics of infection transmission in isolated populations [1,2,3,4]
(4) In the Appendix, we review the basic formulations of the compartmental susceptible exposed infectious recovered (SEIR) model
We describe the dynamics of small populations, each one residing at the sites of a pertinently designedone-dimensional lattice, and connected to each other by means of a finite rate for individuals to “hop” from one site to the others
Summary
Compartmental models provide a conceptually simple and widely used mean to mathematically modeling the dynamics of infection transmission in isolated populations [1,2,3,4]. The topology strongly affects the rates that eventually enter the differential equations describing the population dynamics and it determines the specific stationary solution, describing the system over long timescales [11] For this reason, in recent years, a remarkable amount of work has been devoted to discussing the dynamics of epidemic processes in metapopulation models [12,13,14,15,16,17] on graphs and hypergraphs [18,19,20,21]. Previous metapopulation movement-contagion descriptions focus on large-scale models, rather than on local traffic flows, that are fundamental for the description of the infection spread in small areas In these systems, time and space inhomogeneity leads to nontrivial consequences on the population dynamics [22,23,24,25,26,27]. IV, we provide our main conclusions and discuss about possible further perspectives of our work. (4) In the Appendix, we review the basic formulations of the compartmental SEIR model
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