Extinction of an infectious disease: a large fluctuation in a nonequilibrium system.

We develop a theory of first passage processes in stochastic nonequilibrium systems of birth-death type using two closely related epidemiological models as examples. Our method employs the probability generating function technique in conjunction with the eikonal approximation. In this way the problem is reduced to finding the optimal path to extinction: a heteroclinic trajectory of an effective multidimensional classical Hamiltonian system. We compute this trajectory and mean extinction time of the disease numerically and uncover a nonmonotone, spiral path to extinction of a disease. We also obtain analytical results close to a bifurcation point, where the problem is described by a Hamiltonian previously identified in one-species population models.

• Publication year

  2008

• Venue

  Physical review. E, Statistical, nonlinear, and soft matter physics

• Publication date

  2008-01-31

• Fields of study

  Biology, Mathematics, Physics, Medicine

• Identifiers
  DOI 10.1103/PhysRevE.77.061107arXiv 0801.4900PMID 18643217
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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