Extinction of an infectious disease: a large fluctuation in a non-equilibrium system

Details Extinction of an infectious disease: a large fluctuation in a non-equilibrium system Extinction of an infectious disease: a large fluctuation in a non-equilibrium system

2008-01-31

arxiv.org/abs/0801.4900v2

Physics

Condensed Matter

Statistical Mechanics

4 pages

Scientific paper

10.1103/PhysRevE.77.061107

We develop a theory of first passage processes in stochastic non-equilibrium 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 multi-dimensional classical Hamiltonian system. We compute this trajectory and mean extinction time of the disease numerically and uncover a non-monotone, 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.

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