Eric A. Cator

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Since the Susceptible-Infected-Susceptible (SIS) epidemic threshold is not precisely defined in spite of its practical importance, the classical SIS epidemic process has been generalized to the ε-SIS model, where a node possesses a self-infection rate ε, in addition to a link infection rate β and a curing rate δ. The exact Markov equations are derived, from(More)
We show that, for a stationary version of Hammersley’s process, with Poisson “sources” on the positive x-axis, and Poisson “sinks” on the positive y-axis, an isolated second class particle, located at the origin at time zero, moves asymptotically, with probability one, along the characteristic of a conservation equation for Hammersley’s process. This allows(More)
We study the last-passage growth model on the planar integer lattice with exponential weights. With boundary conditions that represent the equilibrium exclusion process as seen from a particle right after its jump we prove that the variance of the last-passage time in a characteristic direction is of order t. With more general boundary conditions that(More)
Since mean-field approximations for susceptible-infected-susceptible (SIS) epidemics do not always predict the correct scaling of the epidemic threshold of the SIS metastable regime, we propose two novel approaches: (a) an ε-SIS generalized model and (b) a modified SIS model that prevents the epidemic from dying out (i.e., without the complicating absorbing(More)
Given the adjacency matrix A of a network, we present a second-order mean-field expansion that improves on the first-order N-intertwined susceptible-infected-susceptible (SIS) epidemic model. Unexpectedly, we found that, in contrast to first-order, second-order mean-field theory is not always possible: the network size N should be large enough. Under the(More)
In Cator and Lopuhaä [3] an asymptotic expansion for the MCD estimators is established in a very general framework. This expansion requires the existence and non-singularity of the derivative in a first-order Taylor expansion. In this paper, we prove the existence of this derivative for multivariate distributions that have a density and provide an explicit(More)
The classical, continuous-time susceptible-infected-susceptible (SIS) Markov epidemic model on an arbitrary network is extended to incorporate infection and curing or recovery times each characterized by a general distribution (rather than an exponential distribution as in Markov processes). This extension, called the generalized SIS (GSIS) model, is(More)
We define the minimum covariance determinant functionals for multivariate location and scatter through trimming functions and establish their existence at any multivariate distribution. We provide a precise characterization including a separating ellipsoid property and prove that the functionals are continuous. Moreover we establish asymptotic normality for(More)