Skip to main content
NCBI home page
Springer Nature - PMC COVID-19 Collection logoLink to Springer Nature - PMC COVID-19 Collection
. 2010 May 13;73(1):248–260. doi: 10.1007/s11538-010-9541-4

Asymmetry in the Presence of Migration Stabilizes Multistrain Disease Outbreaks

Simone Bianco 1,✉, Leah B Shaw 1
PMCID: PMC2995850  NIHMSID: NIHMS225438  PMID: 20464521

Abstract

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.

Keywords: Dengue, Metapopulation models

References

  1. Aguiar, M., & Stollenwerk, N. (2007). A new chaotic attractor in a basic multistrain epidemiological model with temporary cross immunity. arXiv:0704.3174.
  2. Andreasen V., Lin J., Levin S. A. The dynamics of cocirculating influenza strains conferring partial cross-immunity. J. Math. Biol. 1997;35:825–842. doi: 10.1007/s002850050079. [DOI] [PubMed] [Google Scholar]
  3. Barbazan P., Tuntaprasart W., Souris M., Demoraes F., Nitatpattana N., Boonyuan W., Gonzalez J.-P. 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. 2008;102:161–71. doi: 10.1179/136485908X252296. [DOI] [PubMed] [Google Scholar]
  4. Bianco S., Shaw L. B., Schwartz I. B. Epidemics with multistrain interactions: The interplay between cross immunity and antibody-dependent enhancement. Chaos. 2009;19:043123. doi: 10.1063/1.3270261. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Billings L., Schwartz I. B., Shaw L. B., Burke D. S., Cummings D. A. T. Instabilities in multiserotype disease models with antibody-dependent enhancement. J. Theor. Biol. 2007;246:18–27. doi: 10.1016/j.jtbi.2006.12.023. [DOI] [PubMed] [Google Scholar]
  6. Billings L., Fiorillo A., Schwartz I. B. Vaccinations in disease models with antibody-dependent enhancement. Math. Biosci. 2008;211:265–281. doi: 10.1016/j.mbs.2007.08.004. [DOI] [PubMed] [Google Scholar]
  7. Bolker B., Grenfell B. Space, persistence and dynamics of measles epidemics. Philos. Trans. R. Soc. Lond. B. 1995;348:309–320. doi: 10.1098/rstb.1995.0070. [DOI] [PubMed] [Google Scholar]
  8. Colizza V., Vespignani A. Epidemic modeling in metapopulation systems with heterogenous coupling patter: Theory and simulations. J. Theor. Biol. 2008;251:450–467. doi: 10.1016/j.jtbi.2007.11.028. [DOI] [PubMed] [Google Scholar]
  9. Cummings D. A. T., Irizarry R. A., Huang N. E., Endy T. P., Nisalak A., Ungchusak K., Burke D. S. Travelling waves in the occurrence of dengue haemorrhagic fever in Thailand. Nature. 2004;427:344–347. doi: 10.1038/nature02225. [DOI] [PubMed] [Google Scholar]
  10. Cummings D. A. T., Schwartz I. B., Billing L., Shaw L. B., Burke D. S. Dynamic effect of antibody-dependent enhancement on the fitness of viruses. Proc. Natl. Acad. Sci. USA. 2005;102(42):15259. doi: 10.1073/pnas.0507320102. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Cummings D. A. T., Iamsirithaworn S., Lessler J. T., McDermott A., Prasanthong R., Nisalak A., Jarman R. G., Burke D. S., Gibbons R. V. The impact of the demographic transition on dengue in Thailand: insights from a statistical analysis and mathematical modeling. PLoS Med. 2009;9:e1000139. doi: 10.1371/journal.pmed.1000139. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. 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.
  13. Ferguson N., Anderson R., Gupta S. The effect of antibody-dependent enhancement on the transmission dynamics and persistence of multiple-strain pathogens. Proc. Natl. Acad. Sci. USA. 1999;96:790. doi: 10.1073/pnas.96.2.790. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Ferguson N. M., Donnelly C. A., Anderson R. M. Transmission dynamics and epidemiology of dengue: insights from age-stratified sero-prevalence surveys. Philos. Trans. R. Soc. Lond. Ser. B, Biol. Sci. 1999;354:757–768. doi: 10.1098/rstb.1999.0428. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Fussmann G. F., Ellner S. P., Shertzer K. W. Crossing the Hopf bifurcation in a live predator-prey system. Science. 2000;290:1358–1360. doi: 10.1126/science.290.5495.1358. [DOI] [PubMed] [Google Scholar]
  16. Grais R. F., Ellis J. H., Glass G. E. Assessing the impact of airline travel on the geographic spread of pandemic influenza. Eur. J. Epidemiol. 2003;18:1065–1072. doi: 10.1023/A:1026140019146. [DOI] [PubMed] [Google Scholar]
  17. Greenhalgh D., Khan Q., Lewis F. Hopf bifurcation in two SIRS density dependent epidemic models. Math. Comput. Model. 2004;39:1261–1283. doi: 10.1016/j.mcm.2004.06.007. [DOI] [Google Scholar]
  18. Hagenaars T. J., Donnelly C. A., Ferguson N. M. Spatial heterogeneity and the persistence of infectious diseases. J. Theor. Biol. 2004;229:349–359. doi: 10.1016/j.jtbi.2004.04.002. [DOI] [PubMed] [Google Scholar]
  19. Halstead S. B. Dengue. Lancet. 2007;370:1644–1652. doi: 10.1016/S0140-6736(07)61687-0. [DOI] [PubMed] [Google Scholar]
  20. Halstead S. B., Deen J. The future of dengue vaccines. Lancet. 2002;360:1243. doi: 10.1016/S0140-6736(02)11276-1. [DOI] [PubMed] [Google Scholar]
  21. Halstead S. B., O’Rourke E. J. Antibody-enhanced dengue virus infection in primate leukocytes. Nature. 1977;265:739. doi: 10.1038/265739a0. [DOI] [PubMed] [Google Scholar]
  22. He D., Stone L. Spatio-temporal synchronization of recurrent epidemics. Proc. R. Soc. Biol. Sci. 2003;270(1523):1519–1526. doi: 10.1098/rspb.2003.2366. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. 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. The emerging genetic diversity of HIV. the importance of global surveillance for diagnostics, research, and prevention. JAMA J. Am. Med. Assoc. 1996;275:210–216. doi: 10.1001/jama.275.3.210. [DOI] [PubMed] [Google Scholar]
  24. Kawaguchi I., Sasaki A., Boots M. Why are dengue virus serotypes so distantly related? Enhancement and limiting serotype similarity between dengue virus strains. Proc. R. Soc. Biol. Sci. 2003;270:2241–2247. doi: 10.1098/rspb.2003.2440. [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. Keeling M. J., Rohani P. Estimating spatial coupling in epidemiological systems: a mechanistic approach. Ecol. Lett. 2002;5:20–29. doi: 10.1046/j.1461-0248.2002.00268.x. [DOI] [Google Scholar]
  26. Liebovitch L. S., Schwartz I. B. Migration induced epidemics: dynamics of flux-based multipatch models. Phys. Lett. A. 2004;332:256–267. doi: 10.1016/j.physleta.2004.09.071. [DOI] [Google Scholar]
  27. Lloyd A. L., May R. M. Spatial heterogeneity in epidemic models. J. Theor. Biol. 1996;179:1–11. doi: 10.1006/jtbi.1996.0042. [DOI] [PubMed] [Google Scholar]
  28. Nagao Y., Koelle K. Decreases in dengue transmission may act to increase the incidence of dengue hemorrhagic fever. Proc. Nat. Acad. Sci. USA. 2008;105:2238–2243. doi: 10.1073/pnas.0709029105. [DOI] [PMC free article] [PubMed] [Google Scholar]
  29. 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. Serotype specific virus circulation and dengue disease in Bangkok, Thailand from 1973 to 1999. Am. J. Trop. Med. Hyg. 2003;68:191–202. [PubMed] [Google Scholar]
  30. Rigau-Perez J., Clark G., Gubler D., Reiter P., Sanders E., Vancevorndam A. Dengue and dengue haemorrhagic fever. Lancet. 1998;352:971–977. doi: 10.1016/S0140-6736(97)12483-7. [DOI] [PubMed] [Google Scholar]
  31. Rohani P., Earn D. J. D., Grenfell B. T. Opposite patterns of synchrony in sympatric disease metapopulations. Science. 1999;286:968–971. doi: 10.1126/science.286.5441.968. [DOI] [PubMed] [Google Scholar]
  32. Ruan S., Wang W., Levin S. A. The effect of global travel on the spread of SARS. Math. Biosci. Eng. 2006;3(1):205–218. doi: 10.3934/mbe.2006.3.205. [DOI] [PubMed] [Google Scholar]
  33. Sattenspiel L., Dietz K. A structured epidemic model incorporating geographic mobility among regions. Math. Biosci. 1995;127:71–91. doi: 10.1016/0025-5564(94)00068-B. [DOI] [PubMed] [Google Scholar]
  34. Schwartz I. B., Shaw L. B., Cummings D. A. T., Billings L., McCrary M., Burke D. S. Chaotic desynchronization of multistrain diseases. Phys. Rev. E. 2005;72:066201. doi: 10.1103/PhysRevE.72.066201. [DOI] [PubMed] [Google Scholar]
  35. Slosek J. Aedes aegypti mosquitoes in the Americas: a review of their interactions with the human population. Soc. Sci. Med. (1982) 1986;23:249–257. doi: 10.1016/0277-9536(86)90345-X. [DOI] [PubMed] [Google Scholar]
  36. Strogatz S. H. Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering. Boulder: Westview Press; 2001. [Google Scholar]
  37. Takada A., Feldmann H., Ksiazek T. G., Kawaoka Y. Antibody-dependent enhancement of ebola virus infection. J. Virol. 2003;77(13):7539–7544. doi: 10.1128/JVI.77.13.7539-7544.2003. [DOI] [PMC free article] [PubMed] [Google Scholar]
  38. 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. Dengue viremia titer, antibody response pattern, and virus serotype correlate with disease severity. J. Infect. Dis. 2000;181:2–10. doi: 10.1086/315215. [DOI] [PubMed] [Google Scholar]
  39. Wearing H. J., Rohani P. Ecological and immunological determinants of dengue epidemics. Proc. Natl. Acad. Sci. USA. 2006;103(31):11802. doi: 10.1073/pnas.0602960103. [DOI] [PMC free article] [PubMed] [Google Scholar]
  40. World Health Organization Website (2006). http://www.who.int/mediacentre/factsheets/fs117/en/.

Articles from Bulletin of Mathematical Biology are provided here courtesy of Nature Publishing Group

RESOURCES