The effects of human movement on the persistence of vector-borne diseases

C. Cosner, J. C. Beier, R. S. Cantrell, D. Impoinvil, L. Kapitanski, M. D. Potts, A. Troyo, S. Ruan

Research output: Contribution to journalArticlepeer-review

121 Scopus citations


With the recent resurgence of vector-borne diseases due to urbanization and development there is an urgent need to understand the dynamics of vector-borne diseases in rapidly changing urban environments. For example, many empirical studies have produced the disturbing finding that diseases continue to persist in modern city centers with zero or low rates of transmission. We develop spatial models of vector-borne disease dynamics on a network of patches to examine how the movement of humans in heterogeneous environments affects transmission. We show that the movement of humans between patches is sufficient to maintain disease persistence in patches with zero transmission. We construct two classes of models using different approaches: (i) Lagrangian models that mimic human commuting behavior and (ii) Eulerian models that mimic human migration. We determine the basic reproduction number R0 for both modeling approaches. We show that for both approaches that if the disease-free equilibrium is stable (R0 < 1) then it is globally stable and if the disease-free equilibrium is unstable (R0 > 1) then there exists a unique positive (endemic) equilibrium that is globally stable among positive solutions. Finally, we prove in general that Lagrangian and Eulerian modeling approaches are not equivalent. The modeling approaches presented provide a framework to explore spatial vector-borne disease dynamics and control in heterogeneous environments. As an example, we consider two patches in which the disease dies out in both patches when there is no movement between them. Numerical simulations demonstrate that the disease becomes endemic in both patches when humans move between the two patches.

Original languageEnglish (US)
Pages (from-to)550-560
Number of pages11
JournalJournal of theoretical biology
Issue number4
StatePublished - Jun 21 2009


  • Basic reproduction number
  • Discrete diffusion
  • Disease-free and endemic equilibria
  • Human movement
  • Stability
  • Vector-borne disease

ASJC Scopus subject areas

  • Medicine(all)
  • Immunology and Microbiology(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Modeling and Simulation
  • Statistics and Probability
  • Applied Mathematics


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