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The Basic Reproduction Number in a Multi-city Compartmental Epidemic Model
 

Summary: The Basic Reproduction Number in a
Multi-city Compartmental Epidemic Model
Julien Arino1
and Pauline van den Driessche2
1
Department of Mathematics, McMaster University, Canada,
arino@math.mcmaster.ca
2
Department of Mathematics, University of Victoria, Canada,
pvdd@math.uvic.ca
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 4n2
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 R0 is determined as the spectral
radius of a nonnegative matrix product, and easily computable bounds on R0 are
obtained.

  

Source: Arino, Julien - Department of Mathematics, University of Manitoba

 

Collections: Mathematics