arXiv subjects

A. Nunes

Publications and source records attributed to A. Nunes.

10 recordsLinked to original sources

arXiv2012

Stochastic oscillations in models of epidemics on a network of cities

We carry out an analytic investigation of stochastic oscillations in a susceptible-infected-recovered model of disease spread on a network of $n$ cities. In the model a fraction $f_{jk}$ of individuals from city $k$ commute to city $j$, where they may infect, or be infected by, others. Starting from a continuous time Markov description of the model the deterministic equations, which are valid in the limit when the population of each city is infinite, are recovered. The stochastic fluctuations about the fixed point of these equations are derived by use of the van Kampen system-size expansion. The fixed point structure of the deterministic equations is remarkably simple: a unique non-trivial fixed point always exists and has the feature that the fraction of susceptible, infected and recovered individuals is the same for each city irrespective of its size. We find that the stochastic fluctuations have an analogously simple dynamics: all oscillations have a single frequency, equal to that found in the one city case. We interpret this phenomenon in terms of the properties of the spectrum of the matrix of the linear approximation of the deterministic equations at the fixed point.

nlin.AO↗

arXiv2012

Phase lag in epidemics on a network of cities

We study the synchronisation and phase-lag of fluctuations in the number of infected individuals in a network of cities between which individuals commute. The frequency and amplitude of these oscillations is known to be very well captured by the van Kampen system-size expansion, and we use this approximation to compute the complex coherence function that describes their correlation. We find that, if the infection rate differs from city to city and the coupling between them is not too strong, these oscillations are synchronised with a well defined phase lag between cities. The analytic description of the effect is shown to be in good agreement with the results of stochastic simulations for realistic population sizes.

q-bio.PE↗

arXiv2008

Reheating induced by competing decay modes

We address the problem of studying the decay of the inflaton field $ϕ$ to another scalar field $χ$ through parametric resonance in the case of a coupling that involves several decay modes. This amounts to the presence of extra harmonic terms in the perturbation of the $χ$ field dynamics. For the case of two frequencies we compute the geometry of the resonance regions, which is significantly altered due to the presence of non-cuspidal resonance regions associated to higher harmonics and to the emergence of instability `pockets'. We discuss the effect of this change in the efficiency of the energy transfer process for the simplest case of a coupling given by a combination of the two interaction terms of homogeneous degree usually considered in the literature. We find that the presence of higher harmonics has limited cosmological implications.

hep-ph↗

arXiv2007

Stochastic Fluctuations in Epidemics on Networks

The effects of demographic stochasticity in the long term behaviour of endemic infectious diseases have been considered for long as a necessary addition to an underlying deterministic theory. The latter would explain the regular behaviour of recurrent epidemics, and the former the superimposed noise of observed incidence patterns. Recently, a stochastic theory based on a mechanism of resonance with internal noise has shifted the role of stochasticity closer to the center stage, by showing that the major dynamic patterns found in the incidence data can be explained as resonant fluctuations, whose behaviour is largely independent of the amplitude of seasonal forcing, and by contrast very sensitive to the basic epidemiological parameters. Here we elaborate on that approach, by adding an ingredient which is missing in standard epidemic models, the 'mixing network' through which infection may propagate. We find that spatial correlations have a major effect in the enhancement of the amplitude and the coherence of the resonant stochastic fluctuations, providing the ordered patterns of recurrent epidemics, whose period may differ significantly from that of the small oscillations around the deterministic equilibrium. We also show that the inclusion of a more realistic, time correlated, recovery profile instead of exponentially distributed infectious periods may, even in the random-mixing limit, contribute to the same effect.

q-bio.PE↗

arXiv2007

Scalar field phase dynamics in preheating

We study the model of a massive inflaton field $ϕ$ coupled to another scalar filed $χ$ with interaction term $g^2ϕ^2χ^2$ for the first stage of preheating. We obtain the the behavior of the phase in terms of the iteration of a simple family of circle maps. When expansion of the universe is taken into account the qualitative behavior of the phase and growth number evolution is reminiscent of the behavior found in the case without expansion.

hep-ph↗

arXiv2005

Does host contact structure reduce pathogen diversity?

We investigate the dynamics of a simple epidemiological model for the invasion by a pathogen strain of a population where another strain circulates. We assume that reinfection by the same strain is possible but occurs at a reduced rate due to acquired immunity. The rate of reinfection by a distinct strain is also reduced due to cross-immunity. Individual based simulations of this model on a `small-world' network show that the host contact network structure significantly affects the outcome of such an invasion, and as a consequence will affect the patterns of pathogen evolution. In particular, host populations interacting through a 'small-world' network of contacts support lower prevalence of infection than well-mixed populations, and the region in parameter space for which an invading strain can become endemic and coexist with the circulating strain is smaller, reducing the potential to accommodate pathogen diversity. We discuss the underlying mechanisms for the reported effects, and we propose an effective mean-field model to account for the contact structure of the host population in 'small-world' networks.

q-bio.PE↗

arXiv2005

Epidemics in small world networks

For many infectious diseases, a small-world network on an underlying regular lattice is a suitable simplified model for the contact structure of the host population. It is well known that the contact network, described in this setting by a single parameter, the small-world parameter $p$, plays an important role both in the short term and in the long term dynamics of epidemic spread. We have studied the effect of the network structure on models of immune for life diseases and found that in addition to the reduction of the effective transmission rate, through the screening of infectives, spatial correlations may strongly enhance the stochastic fluctuations. As a consequence, time series of unforced Susceptible-Exposed-Infected-Recovered (SEIR) models provide patterns of recurrent epidemics with realistic amplitudes, suggesting that these models together with complex networks of contacts are the key ingredients to describe the prevaccination dynamical patterns of diseases such as measles and pertussis. We have also studied the role of the host contact strucuture in pathogen antigenic variation, through its effect on the final outcome of an invasion by a viral strain of a population where a very similar virus is endemic. Similar viral strains are modelled by the same infection and reinfection parameters, and by a given degree of cross immunity that represents the antigenic distance between the competing strains. We have found, somewhat surprisingly, that clustering on the network decreases the potential to sustain pathogen diversity.

q-bio.PE↗

arXiv2005

Phase dynamics and particle production in preheating

We study a simple model of a massive inflaton field $ϕ$ coupled to another scalar filed $χ$ with interaction term $g^2ϕ^2χ^2$. We use the theory developed by Kofman {\em et al.} (Phys. Rev. D {\bf 56} (1997) 3258 [arXiv:hep-ph/9704452])for the first stage of preheating to give a full description of the dynamics of the $χ$ field modes, including the behaviour of the phase, in terms of the iteration of a simple family of circle maps. The parameters of this family of maps are a function of time when expansion of the universe is taken into account. With this more detailed description, we obtain a systematic study of the efficiency of particle production as a function of the inflaton field and coupling parameters, and we find that for $g \lesssim 3 \times 10^{-4}$ the broad resonance ceases during the first stage of preheating.

hep-ph↗

arXiv2005

The Go model revisited: Native structure and the geometric coupling between local and long-range contacts

Monte Carlo simulations show that long-range interactions play a major role in determining the folding rates of 48-mer three-dimensional lattice polymers modelled by the Go potential. For three target structures with different native geometries we found a sharp increase in the folding time when the relative contribution of the long-range interactions to the native state's energy is decreased from ~50% towards zero. However, the dispersion of the simulated folding times depends strongly on the native geometry and Go polymers folding to one of the target structures exhibit folding times spanning three orders of magnitude. We have also found that, depending on the target geometry, a strong geometric coupling may exist between local and long-range contacts meaning that, when this coupling exists, the formation of long-range contacts is forced by the previous formation of local contacts. The absence of a strong geometric coupling leads to kinetics that are more sensitive to the interaction energy parameters; in this case the formation of local contacts is not sufficient to promote the establishment of long-range ones when these are strongly penalized energetically, leading to longer folding times.

q-bio.BM↗

arXiv2004

Recurrent epidemics in small world networks

The effect of spatial correlations on the spread of infectious diseases was investigated using a stochastic SIR (Susceptible-Infective-Recovered) model on complex networks. It was found that in addition to the reduction of the effective transmission rate, through the screening of infectives, spatial correlations may have another major effect through the enhancement of stochastic fluctuations. As a consequence large populations will have to become even larger to 'average out' significant differences from the solution of deterministic models. Furthermore, time series of the (unforced) model provide patterns of recurrent epidemics with slightly irregular periods and realistic amplitudes, suggesting that stochastic models together with complex networks of contacts may be sufficient to describe the long term dynamics of some diseases. The spatial effects were analysed quantitatively by modelling measles and pertussis, using a SEIR (Susceptible-Exposed-Infective-Recovered) model. Both the period and the spatial coherence of the epidemic peaks of pertussis are well described by the unforced model for realistic values of the parameters.

q-bio.PE↗