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Romulus Breban

Publications and source records attributed to Romulus Breban.

6 recordsLinked to original sources
PubMed2006

Role of parametric resonance in virological failure during HIV treatment interruption therapy.

We present a novel hypothesis that could explain virological failure to structured treatment interruptions (STI). We analysed a classic mathematical model of HIV within-host viral dynamics and found that non-linear parametric resonance occurs when STI are added to the model; resonance is observed as virological failure. We simulated clinical trial data and calculated patient-specific resonant spectra. We gained two important insights. First, within an STI trial, patients who begin with similar viral loads can be expected to show very different virological responses as a result of resonance. Second, and more importantly, virological failure is not simply due to STI or patients' characteristics; instead it is the result of complex interaction between STI and the patient's viral dynamics. Hence, our analyses show that no universal regimen with periodic interruptions will be effective for all patients.

CD4 Lymphocyte Count↗
PubMed2005

Linking population-level models with growing networks: a class of epidemic models.

We introduce a class of growing network models that are directly applicable to epidemiology. We show how to construct a growing network model (individual-level model) that generates the same epidemic-level outcomes as a population-level ordinary differential equation (ODE) model. For concreteness, we analyze the susceptible-infected (SI) ODE model of disease invasion. First, we give an illustrative example of a growing network whose population-level variables are compatible with those of this ODE model. Second, we demonstrate that a growing network model can be found that is equivalent to the Crump-Mode-Jagers (CMJ) continuous-time branching process of the SI ODE model of disease invasion. We discuss the computational advantages that our growing network model has over the CMJ branching process.

Animals↗
PubMed2003

Scaling properties of saddle-node bifurcations on fractal basin boundaries.

We analyze situations where a saddle-node bifurcation occurs on a fractal basin boundary. Specifically, we are interested in what happens when a system parameter is slowly swept in time through the bifurcation. Such situations are known to be indeterminate in the sense that it is difficult to predict the eventual fate of an orbit that tracks the prebifurcation node attractor as the system parameter is swept through the bifurcation. In this paper we investigate the scaling of (1) the fractal basin boundary of the static (i.e., unswept) system near the saddle-node bifurcation, (2) the dependence of the orbit's final destination on the sweeping rate, (3) the dependence of the time it takes for an attractor to capture a swept orbit on the sweeping rate, and (4) the dependence of the final attractor capture probability on the noise level. With respect to noise, our main result is that the effect of noise scales with the 5/6 power of the parameter drift rate. Our approach is to first investigate all these issues using one-dimensional map models. The simplification of treatment inherent in one dimension greatly facilitates analysis and numerical experiment, aiding us in obtaining the new results listed above. Following our one-dimensional investigations, we explain that these results can be applied to two-dimensional systems. We show, through numerical experiments on a periodically forced second-order differential equation example, that the scalings we have found also apply to systems that result in two-dimensional maps.

Journal Article↗
PubMed2003

Phase synchronization of chaotic attractors with prescribed periodic signals.

Given a chaotic attractor in a dynamical system with dense periodic windows (i.e., structurally unstable), is it possible to find a periodic driver that will phase synchronize the chaotic attractor? We conjecture that the answer is typically yes, and we give an example for a funneling chaotic attractor in the Roessler system.

Journal Article↗
PubMed2002

Phase synchronization of chaotic attractors in the presence of two competing periodic signals.

We discuss the situation where two periodic signals compete to phase synchronize a chaotic attractor. Depending on the relative position of the periods with respect to the synchronization tongue for a single frequency signal, we distinguish several different cases. We find that, depending on parameters, it is possible that one or the other signal will entrain exclusively, or that they will entrain alternately, at their average frequency, or not at all.

Journal Article↗