# Epidemiological implications of mobility between a large urban centre and smaller satellite cities

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## Abstract

An SIR infectious disease propagation model is considered that incorporates mobility of individuals between a large urban centre and smaller satellite cities. Because of the difference in population sizes, the urban centre has standard incidence and satellite cities have mass action incidence. It is shown that the general basic reproduction number \({\mathcal {R}}_{0}\) acts as a threshold between global asymptotic stability of the disease free equilibrium and disease persistence. The case of Winnipeg (MB, Canada) and some neighbouring satellite communities is then considered numerically to complement the mathematical analysis, highlighting the importance of taking into account not only \({\mathcal {R}}_{0}\) but also other measures of disease severity. It is found that the large urban centre governs most of the behaviour of the general system and control of the spread is better achieved by targeting it rather than reducing movement between the units. Also, the capacity of a satellite city to affect the general system depends on its population size and its connectivity to the main urban centre.

## Keywords

Metapopulation Mobility Urbanism Incidence functions Reproduction number Attack rate## Mathematics Subject Classification

92D30## Notes

### Acknowledgments

This work was supported in part by NSERC. An earlier version of the model was studied by Lindsay Wessel as part of a MITACS-CDM funded undergraduate research internship at the University of Manitoba. Transportation data was obtained from the University of Manitoba Transport Infrastructure Group (UMTIG). The authors acknowledge suggestions from an anonymous referee and an editor that helped improve the quality of the manuscript.

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