Abstract
A directed graph with cities as vertices and arcs determined by outgoing (or return) travel represents the mobility component in a population of individuals who travel between n cities. A model with 4 epidemiological compartments in each city that describes the propagation of a disease in this population is formulated as a system of 4n 2 ordinary differential equations. Terms in the system account for disease transmission, latency, recovery, temporary immunity, birth, death, and travel between cities. The basic reproduction number \(\mathcal{R}_0\) is determined as the spectral radius of a nonnegative matrix product, and easily computable bounds on \(\mathcal{R}_0\) are obtained.
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Rights and permissions
About this paper
Cite this paper
Arino, J., van den Driessche, P. The Basic Reproduction Number in a Multi-city Compartmental Epidemic Model. In: Benvenuti, L., De Santis, A., Farina, L. (eds) Positive Systems. Lecture Notes in Control and Information Science, vol 294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44928-7_19
Download citation
DOI: https://doi.org/10.1007/978-3-540-44928-7_19
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40342-5
Online ISBN: 978-3-540-44928-7
eBook Packages: Springer Book Archive