Author/Authors :
Worden, Lee University of California - San Francisco - San Francisco, USA , Schwartz, Ira B Nonlinear Systems Dynamics Section - Plasma Physics Division - U.S. Naval Research Laboratory - Washington, USA , Bianco, Simone Department of Industrial and Applied Genomics - IBM Accelerated Discovery Lab - IBM Almaden Research Center - 650 Harry Rd - San Jose, USA , Ackley, Sarah F Department of Epidemiology and Biostatistics - University of California - San Francisco - San Francisco, USA , Lietman, Thomas M Department of Epidemiology and Biostatistics - University of California - San Francisco - San Francisco, USA , Porco, Travis C Department of Epidemiology and Biostatistics - University of California - San Francisco - San Francisco, USA
Abstract :
We extend a technique of approximation of the long-term behavior of a supercritical stochastic epidemic model, using the WKB
approximation and a Hamiltonian phase space, to the subcritical case. The limiting behavior of the model and approximation are
qualitatively different in the subcritical case, requiring a novel analysis of the limiting behavior of the Hamiltonian system away from
its deterministic subsystem. This yields a novel, general technique of approximation of the quasistationary distribution of stochastic
epidemic and birth-death models and may lead to techniques for analysis of these models beyond the quasistationary distribution.
For a classic SIS model, the approximation found for the quasistationary distribution is very similar to published approximations
but not identical. For a birth-death process without depletion of susceptibles, the approximation is exact. Dynamics on the phase
plane similar to those predicted by the Hamiltonian analysis are demonstrated in cross-sectional data from trachoma treatment
trials in Ethiopia, in which declining prevalences are consistent with subcritical epidemic dynamics.
