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Using dimension reduction to improve outbreak predictability of multistrain diseases

Leah B Shaw1, Lora Billings, Ira B Schwartz

  • 1Naval Research Laboratory, Plasma PhysicsDivision, Nonlinear Systems Dynamics Section, Washington, DC 20375, USA. lshaw@nls6.nrl.navy.mil

Journal of Mathematical Biology
|February 24, 2007
PubMed

Insights

This study models multistrain diseases with antibody-dependent enhancement (ADE). Our dynamic model simplifies complex interactions, explaining disease synchrony and predicting asymptomatic cases during epidemics.

Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Infectious Disease Dynamics

Background:

  • Multistrain diseases involve coexisting serotypes, complicating epidemiological modeling.
  • Antibody-dependent enhancement (ADE) can increase viral load and infectivity upon secondary infection with a different serotype, as seen in dengue fever.

Purpose of the Study:

  • To develop and analyze a dynamic compartmental model for multistrain diseases exhibiting ADE.
  • To simplify the complex dynamics of ADE using mathematical techniques.
  • To explain observed synchrony in disease progression and predict asymptomatic infections.

Main Methods:

  • Development of a dynamic compartmental model for multiple serotypes with ADE.
  • Application of center manifold techniques to reduce model dimensionality.
  • Numerical analysis of both deterministic and stochastic model versions.
  • Investigation of model applicability to noisy systems and cross-immunity.

Main Results:

  • The complex multistrain dynamics rapidly collapse to a lower-dimensional system.
  • The reduced model successfully explains previously observed synchrony between primary and secondary infectives.
  • Center manifold equations remain valid in noisy systems.
  • Both model versions predict asymptomatic individuals, crucial for epidemic tracking.

Conclusions:

  • Center manifold techniques provide a powerful tool for analyzing and simplifying multistrain disease dynamics with ADE.
  • The model offers valuable insights into disease synchrony and the prediction of asymptomatic cases.
  • This approach is potentially applicable to other multistrain diseases, including those with cross-immunity.

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