Modelling control of epidemics spreading by long-range interactions

Bartłomiej Dybiec, Adam Kleczkowski, Christopher A. Gilligan

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

We have studied the spread of epidemics characterized by a mixture of local and non-local interactions. The infection spreads on a two-dimensional lattice with the fixed nearest neighbour connections. In addition, long-range dynamical links are formed by moving agents (vectors). Vectors perform random walks, with step length distributed according to a thick-tail distribution. Two distributions are considered in this paper, an a-stable distribution describing self-similar vector movement, yet characterized by an infinite variance and an exponential power characterized by a large but finite variance. Such long-range interactions are hard to track and make control of epidemics very difficult. We also allowed for cryptic infection, whereby an infected individual on the lattice can be infectious prior to showing any symptoms of infection or disease. To account for such cryptic spread, we considered a control strategy in which not only detected, i.e. symptomatic, individuals but also all individuals within a certain control neighbourhood are treated upon the detection of disease. We show that it is possible to eradicate the disease by using such purely local control measures, even in the presence of long-range jumps. In particular, we show that the success of local control and the choice of the optimal strategy depend in a non-trivial way on the dispersal patterns of the vectors. By characterizing these patterns using the stability index of the a-stable distribution to change the power-law behaviour or the exponent characterizing the decay of an exponential power distribution, we show that infection can be successfully contained using relatively small control neighbourhoods for two limiting cases for long-distance dispersal and for vectors that are much more limited in their dispersal range.

Original languageEnglish
Pages (from-to)941-950
Number of pages10
JournalJournal of the Royal Society Interface
Volume6
Issue number39
DOIs
Publication statusPublished - 6 Oct 2009

Keywords

  • disease spread
  • dispersal patterns
  • epidemiological control
  • epidemiological modelling
  • stochastic modelling
  • stochastic control systems
  • infection control
  • mathematical model

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