Journal of Mathematical Biology

, Volume 55, Issue 1, pp 1–19 | Cite as

Using dimension reduction to improve outbreak predictability of multistrain diseases



Multistrain diseases have multiple distinct coexisting serotypes (strains). For some diseases, such as dengue fever, the serotypes interact by antibody-dependent enhancement (ADE), in which infection with a single serotype is asymptomatic, but contact with a second serotype leads to higher viral load and greater infectivity. We present and analyze a dynamic compartmental model for multiple serotypes exhibiting ADE. Using center manifold techniques, we show how the dynamics rapidly collapses to a lower dimensional system. Using the constructed reduced model, we can explain previously observed synchrony between certain classes of primary and secondary infectives (Schwartz et al. in Phys Rev E 72:066201, 2005). Additionally, we show numerically that the center manifold equations apply even to noisy systems. Both deterministic and stochastic versions of the model enable prediction of asymptomatic individuals that are difficult to track during an epidemic. We also show how this technique may be applicable to other multistrain disease models, such as those with cross-immunity.


Center manifold analysis Epidemic models Multistrain disease Dengue 

Mathematics Subject Classification



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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Leah B. Shaw
    • 1
  • Lora Billings
    • 2
  • Ira B. Schwartz
    • 1
  1. 1.Naval Research Laboratory, Plasma PhysicsDivisionNonlinear Systems Dynamics SectionWashingtonUSA
  2. 2.Department of Mathematical SciencesMontclair State UniversityUpper MontclairUSA

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