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- Luı́s M.A. Bettencourt, Ariel Cintrón-Arias, David I. Kaiser, Carlos Castillo-Chavez
- 2006

The population dynamics underlying the diffusion of ideas hold many qualitative similarities to those involved in the spread of infections. In spite of much suggestive evidence this analogy is hardly ever quantified in useful ways. The standard benefit of modeling epidemics is the ability to estimate quantitatively population average parameters, such as… (More)

- Ariel Cintrón-Arias, Carlos Castillo-Chavez, Luís M. A. Bettencourt, Alun L. Lloyd, Harvey Thomas Banks
- Mathematical biosciences and engineering : MBE
- 2009

We consider a single outbreak susceptible-infected-recovered (SIR) model and corresponding estimation procedures for the effective reproductive number R(t). We discuss the estimation of the underlying SIR parameters with a generalized least squares (GLS) estimation technique. We do this in the context of appropriate statistical models for the measurement… (More)

We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that correspond to sensitivity matrices with full rank. Second, the algorithm involves uncertainty quantification by using the… (More)

We discuss methods for a priori selection of parameters to be estimated in inverse problem formulations (such as Maximum Likelihood, Ordinary and Generalized Least Squares) for dynamical systems with numerous state variables and an even larger number of parameters. We illustrate the ideas with an in-host model for HIV dynamics which has been successfully… (More)

The use of network models to describe the impact of local spatial structure on the spread of infections is discussed. In particular, we focus on small-world networks, within which the pattern of interactions can be varied from being entirely local to being entirely global as a single parameter is changed. Analysis approaches from graph theory, statistical… (More)

- Gerardo Chowell, Ariel Cintrón-Arias, +5 authors Carlos Castillo-Chavez
- 2005

Efforts to anticipate, prevent, or control deliberate releases of biological agents are critical components of homeland security research. The lack of data on deliberately induced epidemics naturally leads to the use of mathematical models (capable of simulating realistic scenarios) in the evaluation of policies that ensure our security. Modeling single… (More)

- Ariel Cintrón-Arias, Norman D. Curet, +4 authors Patrick Quillen
- 2000

This paper is concerned with analyzing the susceptibility of a communications network to a specific type of attack. Attacks may consist of physically disabling communication links or flooding links with information in order to prevent legitimate communications. Large-scale denial of service attacks have been prevalent in recent years, affecting many… (More)

Relapse, the recurrence of a disorder following a symptomatic remission, is a frequent outcome in substance abuse disorders. Some of our prior results suggested that relapse, in the context of abusive drinking, is likely an “unbeatable” force as long as recovered individuals continue to interact in the environments that lead to and/or reinforce the… (More)

- Ariel Cintrón-Arias, Carlos Barrera-Rodriguez
- 2009

The population vaccination effectiveness (PVE) is defined as the fraction of disease cases prevented by a vaccination campaign. We use occupancy urn models to estimate the PVE, and compare results for leaky, all-or-nothing and VEl (vaccine efficacy for infectiousness) vaccines using data of a measles outbreak and San Francisco current AIDS epidemic. This… (More)

- Sharon R. Lubkin, Mette S. Olufsen, +12 authors Jasmine Zhou
- 2008

Tracking vehicles in flight with range capable sensors can provide very precise position and velocity estimates. If the sensor is only capable of making angular measurements, the estimates will not be as accurate. It is desired to have a bound on the estimates of the position and velocity under the relatively modest assumption that the vehicle is flying… (More)