Jordi Ripoll

A multiple failure propagation model in GMPLS-based networks

In this article, a new model to simulate different failure propagation scenarios in GMPLS-based networks is proposed. Several types of failures and malfunctions may spread along the network following different patterns (hardware failures, natural disasters, accidents, configuration errors, viruses, software bugs, etc.). The current literature presents several models for the spreading of failures in general networks. In communication networks, a failure affects not only nodes but also the connections passing through those nodes. The model in this article takes into account GMPLS node failures, affecting both data and control planes. The model is tested by simulation using different types of network topologies. In addition, a new method for the classification of network robustness is also introduced.

OPTIMAL LATENT PERIOD IN A BACTERIOPHAGE POPULATION MODEL STRUCTURED BY INFECTION-AGE

We study the lysis timing of a bacteriophage population by means of a continuously infection-age-structured population dynamics model. The features of the model are the infection process of bacteria, the death process, and the lysis process which means the replication of bacteriophage viruses inside bacteria and the destruction of them. The time till lysis (or latent period) is assumed to have an arbitrary distribution. We have carried out an optimization procedure, and we have found that the latent period corresponding to maximal fitness (i.e. maximal growth rate of the bacteriophage population) is of fixed length. We also study the dependence of the optimal latent period on the amount of susceptible bacteria and the number of virions released by a single infection. Finally, the evolutionarily stable strategy of the latent period is also determined as a fixed period taking into account that super-infections are not considered.

Evolution of age-dependent sex-reversal under adaptive dynamics.

We investigate the evolution of the age (or size) at sex-reversal in a model of sequential hermaphroditism, by means of the function-valued adaptive dynamics. The trait is the probability law of the age at sex-reversal considered as a random variable. Our analysis starts with the ecological model which was first introduced and analyzed by Calsina and Ripoll (Math Biosci 208(2), 393–418, 2007). The structure of the population is extended to a genotype class and a new model for an invading/mutant population is introduced. The invasion fitness functional is derived from the ecological setting, and it turns out to be controlled by a formula of Shaw–Mohler type. The problem of finding evolutionarily stable strategies is solved by means of infinite-dimensional linear optimization. We have found that these strategies correspond to sex-reversal at a single particular age (or size) even if the set of feasible strategies is considerably broader and allows for a probabilistic sex-reversal. Several examples, including in addition the population-dynamical stability, are illustrated. For a special case, we can show that an unbeatable size at sex-reversal must be larger than 69.3% of the expected size at death.

On the Reproduction Number of a Gut Microbiota Model

A spatially structured linear model of the growth of intestinal bacteria is analysed from two generational viewpoints. Firstly, the basic reproduction number associated with the bacterial population, i.e. the expected number of daughter cells per bacterium, is given explicitly in terms of biological parameters. Secondly, an alternative quantity is introduced based on the number of bacteria produced within the intestine by one bacterium originally in the external media. The latter depends on the parameters in a simpler way and provides more biological insight than the standard reproduction number, allowing the design of experimental procedures. Both quantities coincide and are equal to one at the extinction threshold, below which the bacterial population becomes extinct. Optimal values of both reproduction numbers are derived assuming parameter trade-offs.

Epidemic and cascading survivability of complex networks

Our society nowadays is governed by complex networks, examples being the power grids, telecommunication networks, biological networks, and social networks. It has become of paramount importance to understand and characterize the dynamic events (e.g. failures) that might happen in these complex networks. For this reason, in this paper, we propose two measures to evaluate the vulnerability of complex networks in two different dynamic multiple failure scenarios: epidemic-like and cascading failures. Firstly, we present epidemic survivability (ES), a new network measure that describes the vulnerability of each node of a network under a specific epidemic intensity. Secondly, we propose cascading survivability (CS), which characterizes how potentially injurious a node is according to a cascading failure scenario. Then, we show that by using the distribution of values obtained from ES and CS it is possible to describe the vulnerability of a given network. We consider a set of 17 different complex networks to illustrate the suitability of our proposals. Lastly, results reveal that distinct types of complex networks might react differently under the same multiple failure scenario.

Impact of density-dependent migration flows on epidemic outbreaks in heterogeneous metapopulations

We investigate the role of migration patterns on the spread of epidemics in complex networks. We enhance the SIS-diffusion model on metapopulations to a nonlinear diffusion. Specifically, individuals move randomly over the network but at a rate depending on the population of the departure patch. In the absence of epidemics, the migration-driven equilibrium is described by quantifying the total number of individuals living in heavily or lightly populated areas. Our analytical approach reveals that strengthening the migration from populous areas contains the infection at the early stage of the epidemic. Moreover, depending on the exponent of the nonlinear diffusion rate, epidemic outbreaks do not always occur in the most populated areas as one might expect.

Density-Dependent Diffusion and Epidemics on Heterogeneous Metapopulations

Systems with many components (individuals or local populations as cities, or metropolitan areas, or regions, …) connected by non-trivial associations or relationships can be statistically described by means of the formalism of complex networks which is based on descriptors like degree distributions, degree-degree correlations, etc. In the last years, many researchers from different fields have been using different approaches to model processes taking place on complex networks.

Monte Carlo Simulations of a SIS‐Diffusion Model in Heterogeneous Metapopulations

We present a model for the spread of infectious diseases in heterogeneous metapopulations. The equations governing the epidemic dynamics have been recently proposed as an alternative formulation in a continuous‐time framework. In the model, the reaction process (i.e. the disease transmission and the recovery of the individuals) and the migration/diffusion process are considered to take place simultaneously. Several Monte Carlo simulations of the system are implemented using uncorrelated networks with scale‐free or exponential degree distribution. The numerical data of the simulations are consistent with the predictions of the continuous‐time equations.