Nodal infection in Markovian susceptible-infected-susceptible and susceptible-infected-removed epidemics on networks are non-negatively correlated

By invoking the famous Fortuin, Kasteleyn, and Ginibre (FKG) inequality, we prove the conjecture that the correlation of infection at the same time between any pair of nodes in a network cannot be negative for (exact) Markovian susceptible-infected-susceptible (SIS) and susceptible-infected-removed (SIR) epidemics on networks. The truth of the...

Susceptible-infected-susceptible epidemics on networks with general infection and cure times

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)...

Epidemics in networks with nodal self-infection and the epidemic threshold

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 ??SIS model, where a node possesses a self-infection rate ?, in addition to a link infection rate ? and a curing rate ?. The exact Markov equations are...

Second-order mean-field susceptible-infected-susceptible epidemic threshold

Busemann functions and equilibrium measures in last passage percolation models

The interplay between two-dimensional percolation growth models and one-dimensional particle processes has been a fruitful source of interesting mathematical phenomena. In this paper we develop a connection between the construction of Busemann functions in the Hammersley last-passage percolation model with i.i.d. random weights, and the...

Semiparametric shift estimation based on the cumulated periodogram for non-regular functions

The problem of estimating the center of symmetry of a symmetric signal in Gaussian white noise is considered. The underlying nuisance function f is not assumed to be differentiable, which makes a new point of view to the problem necessary. We investigate the well-known sieve maximum likelihood estimators based on the cumulated periodogram, and...

Engine Management: A Decision Support Tool for Strategic Engine Maintenance Planning

This paper presents a model that helps engine management make cost saving decisions. The model is developed around airline-influenced factors that have an impact on engine Maintenance Repair & Overhaul (MRO): Operations, maintenance philosophy, contract type, and fleet age. Within the model a decision support tool is developed to analyze the...