Using dimension reduction to improve outbreak predictability of multistrain diseases

Leah B. Shaw, Lora Billings, Ira B. Schwartz

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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.

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalJournal of Mathematical Biology
Issue number1
StatePublished - Jul 2007


  • Center manifold analysis
  • Dengue
  • Epidemic models
  • Multistrain disease


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