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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Range expansion of Ixodes scapularis ticks and of Borrelia burgdorferi by migratory birds

Pages: 3147 - 3167, Volume 19, Issue 10, December 2014      doi:10.3934/dcdsb.2014.19.3147

 
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Jane M. Heffernan - Mprime Centre for Disease Modelling, York Institute of Health Research, Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada (email)
Yijun Lou - Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China (email)
Jianhong Wu - Mprime Centre for Disease Modelling, York Institute of Health Research, Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada (email)

Abstract: Recent studies have suggested that the risk of exposure to Lyme disease is emerging in Canada because of the expanding range of I. scapularis ticks. The wide geographic breeding range of I. scapularis-carrying migratory birds is consistent with the widespread geographical occurrence of I. scapularis in Canada. However, how important migratory birds from the United States are for the establishment and the stable endemic transmission cycle of Lyme disease in Canada remains an issue of theoretical challenge and practical significance. In this paper, we design and analyze a periodic model of differential equations with a forcing term modeling the annual bird migration to address the aforementioned issue. Our results show that ticks can establish in any migratory bird stopovers and breeding sites. Moreover, bird-transported ticks may increase the probability of B. burgdorferi establishment in a tick-endemic habitat.

Keywords:  Lyme disease, ticks, bird migration, spatial expansion, periodic system.
Mathematics Subject Classification:  Primary: 34C25; Secondary: 37N25.

Received: April 2014;      Revised: May 2014;      Available Online: October 2014.

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