TY - JOUR
T1 - Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction
AU - Forgoston, Eric
AU - Bianco, Simone
AU - Shaw, Leah B.
AU - Schwartz, Ira B.
PY - 2011/3
Y1 - 2011/3
N2 - Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of extinction. We show that the optimal path is also directly related to the finite-time Lyapunov exponents of the underlying dynamical system in that the optimal path displays maximum sensitivity to initial conditions. We consider several stochastic epidemic models, and examine the extinction process in a dynamical systems framework. Using the dynamics of the finite-time Lyapunov exponents as a constructive tool, we demonstrate that the dynamical systems viewpoint of extinction evolves naturally toward the optimal path.
AB - Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of extinction. We show that the optimal path is also directly related to the finite-time Lyapunov exponents of the underlying dynamical system in that the optimal path displays maximum sensitivity to initial conditions. We consider several stochastic epidemic models, and examine the extinction process in a dynamical systems framework. Using the dynamics of the finite-time Lyapunov exponents as a constructive tool, we demonstrate that the dynamical systems viewpoint of extinction evolves naturally toward the optimal path.
KW - Optimal path to extinction
KW - Stochastic dynamical systems and Lyapunov exponents
UR - http://www.scopus.com/inward/record.url?scp=79952575263&partnerID=8YFLogxK
U2 - 10.1007/s11538-010-9537-0
DO - 10.1007/s11538-010-9537-0
M3 - Article
C2 - 20352495
AN - SCOPUS:79952575263
SN - 0092-8240
VL - 73
SP - 495
EP - 514
JO - Bulletin of Mathematical Biology
JF - Bulletin of Mathematical Biology
IS - 3
ER -