Asymmetry in the Presence of Migration Stabilizes Multistrain Disease Outbreaks
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We study the effect of migration between coupled populations, or patches, on the stability properties of multistrain disease dynamics. The epidemic model used in this work displays a Hopf bifurcation to oscillations in a single, well-mixed population. It is shown numerically that migration between two non-identical patches stabilizes the endemic steady state, delaying the onset of large amplitude outbreaks and reducing the total number of infections. This result is motivated by analyzing generic Hopf bifurcations with different frequencies and with diffusive coupling between them. Stabilization of the steady state is again seen, indicating that our observation in the full multistrain model is based on qualitative characteristics of the dynamics rather than on details of the disease model.
KeywordsDengue Metapopulation models
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- Aguiar, M., & Stollenwerk, N. (2007). A new chaotic attractor in a basic multistrain epidemiological model with temporary cross immunity. arXiv:0704.3174.
- Barbazan, P., Tuntaprasart, W., Souris, M., Demoraes, F., Nitatpattana, N., Boonyuan, W., & Gonzalez, J.-P. (2008). Assessment of a new strategy, based on Aedes aegypti (L.) pupal productivity, for the surveillance and control of dengue transmission in Thailand. Ann. Trop. Med. Parasitol., 102, 161–71. CrossRefGoogle Scholar
- Cummings, D. A. T., Iamsirithaworn, S., Lessler, J. T., McDermott, A., Prasanthong, R., Nisalak, A., Jarman, R. G., Burke, D. S., & Gibbons, R. V. (2009). The impact of the demographic transition on dengue in Thailand: insights from a statistical analysis and mathematical modeling. PLoS Med., 9, e1000139. CrossRefGoogle Scholar
- Doedel, E., et al. (1997). Auto97: Continuation and bifurcation software for ordinary differential equations. Available from ftp://ftp.cs.concordia.ca/pub/doedel/auto/auto.ps.gz.
- Hu, D. J., Dondero, T. J., Rayfield, M. A., George, J. R., Schochetman, G., Jaffe, H. W., Luo, C. C., Kalish, M. L., Weniger, B. G., Pau, C. P., Schable, C. A., & Curran, J. W. (1996). The emerging genetic diversity of HIV. the importance of global surveillance for diagnostics, research, and prevention. JAMA J. Am. Med. Assoc., 275, 210–216. CrossRefGoogle Scholar
- Nisalak, A., Endy, T. P., Nimmannitya, S., Kalayanarooj, S., Thisayakorn, U., Scott, R. M., Burke, D. S., Hoke, C. H., Innis, B. L., & Vaughn, D. W. (2003). Serotype specific virus circulation and dengue disease in Bangkok, Thailand from 1973 to 1999. Am. J. Trop. Med. Hyg., 68, 191–202. Google Scholar
- Strogatz, S. H. (2001). Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering. Boulder: Westview Press. Google Scholar
- Vaughn, D. W., Green, S., Kalayanarooj, S., Innis, B. L., Nimmannitya, S., Suntayakorn, S., Endy, T. P., Raengsakulrach, B., Rothman, A. L., Ennis, F. A., & Nisalak, A. (2000). Dengue viremia titer, antibody response pattern, and virus serotype correlate with disease severity. J. Infect. Dis., 181, 2–10. CrossRefGoogle Scholar
- World Health Organization Website (2006). http://www.who.int/mediacentre/factsheets/fs117/en/.