Bulletin of Mathematical Biology

, Volume 77, Issue 7, pp 1437–1455

A Framework for Inferring Unobserved Multistrain Epidemic Subpopulations Using Synchronization Dynamics

Original Article

DOI: 10.1007/s11538-015-0091-7

Cite this article as:
Forgoston, E., Shaw, L.B. & Schwartz, I.B. Bull Math Biol (2015) 77: 1437. doi:10.1007/s11538-015-0091-7

Abstract

A new method is proposed to infer unobserved epidemic subpopulations by exploiting the synchronization properties of multistrain epidemic models. A model for dengue fever is driven by simulated data from secondary infective populations. Primary infective populations in the driven system synchronize to the correct values from the driver system. Most hospital cases of dengue are secondary infections, so this method provides a way to deduce unobserved primary infection levels. We derive center manifold equations that relate the driven system to the driver system and thus motivate the use of synchronization to predict unobserved primary infectives. Synchronization stability between primary and secondary infections is demonstrated through numerical measurements of conditional Lyapunov exponents and through time series simulations.

Keywords

Multistrain disease models Inferring unobserved populations Center manifolds Synchronization 

Funding information

Funder NameGrant NumberFunding Note
National Science Foundation
  • CMMI-1233397
National Institute of General Medical Sciences
  • R01GM090204
Office of Naval Research
  • N0001414WX20610
NRL Base Research Program
  • N0001414WX00023

Copyright information

© Society for Mathematical Biology (outside the USA) 2015

Authors and Affiliations

  • Eric Forgoston
    • 1
  • Leah B. Shaw
    • 2
  • Ira B. Schwartz
    • 3
  1. 1.Department of Mathematical SciencesMontclair State UniversityMontclairUSA
  2. 2.Department of Applied ScienceThe College of William & MaryWilliamsburgUSA
  3. 3.Nonlinear Systems Dynamics Section, Plasma Physics Division, Code 6792US Naval Research LaboratoryWashingtonUSA

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