Equation-free modelling of evolving diseases: Coarse-grained computations with individual-based models

Jaime Cisternas*, C. William Gear, Simon Levin, Ioannis G. Kevrekidis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


We demonstrate how direct simulation of stochastic, individual-based models can be combined with continuum numerical-analysis techniques to study the dynamics of evolving diseases. Sidestepping the necessity of obtaining explicit population-level models, the approach analyses the (unavailable in closed form) 'coarse' macroscopic equations, estimating the necessary quantities through appropriately initialized short 'bursts' of individual-based dynamic simulation. We illustrate this approach by analysing a stochastic and discrete model for the evolution of disease agents caused by point mutations within individual hosts. Building up from classical susceptible- infected recovered and susceptible infected-recovered-susceptible models, our example uses a one-dimensional lattice for variant space, and assumes a finite number of individuals. Macroscopic computational tasks enabled through this approach include stationary-state computation, coarse projective integration, parametric continuation and stability analysis.

Original languageEnglish
Pages (from-to)2761-2779
Number of pages19
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2050
StatePublished - 8 Oct 2004


  • Equation-free
  • Individual-based model
  • Influenza A drift
  • Multiscale analysis
  • Travelling wave


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