# Impact of Spring Bird Migration on the Range Expansion of *Ixodes scapularis* Tick Population

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## Abstract

Many observational studies suggest that seasonal migratory birds play an important role in spreading *Ixodes scapularis*, a vector of Lyme disease, along their migratory flyways, and they are believed to be responsible for geographic range expansion of *I. scapularis* in Canada. However, the interplay between the dynamics of *I. scapularis* on land and migratory birds in the air is not well understood. In this study, we develop a periodic delay meta-population model which takes into consideration the local landscape for tick reproduction within patches and the times needed for ticks to be transported by birds between patches. Assuming that the tick population is endemic in the source region, we find that bird migration may boost an already established tick population at the subsequent region and thus increase the risk to humans, or bird migration may help ticks to establish in a region where the local landscape is not appropriate for ticks to survive in the absence of bird migration, imposing risks to public health. This theoretical study reveals that bird migration plays an important role in the geographic range expansion of *I. scapularis*, and therefore our findings may suggest some strategies for Lyme disease prevention and control.

## Keywords

Bird migration*Ixodes scapularis*Range expansion Meta-population model Lyme disease

## Mathematical Subject Classification

34C25 37N25 92D40## Notes

### Acknowledgments

This research was supported by NSERC of Canada and by the European Union and the State of Hungary, co-financed by the European Social Fund in the framework of the TÁMOP 4.2.4. A/2-11-1-2012-0001 “National Excellence Programme.” GR was also supported by ERC Starting Grant No. 259559 and OTKA K109782. We thank Dr. Patrick A. Leighton at Université de Montréal for valuable discussion of parameter estimation and Dr. Nicholas Ogden at Public Health Agency of Canada for sharing the tick data. We would also like to thank the three anonymous referees for their helpful/useful comments which have helped us improve the presentation in the revision.

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