Marcelo N. Kuperman

Small world effect in an epidemiological model.

A model for the spread of an infection is analyzed for different population structures. The interactions within the population are described by small world networks, ranging from ordered lattices to random graphs. For the more ordered systems, there is a fluctuating endemic state of low infection. At a finite value of the disorder of the network, we find a transition to self-sustained oscillations in the size of the infected subpopulation.

Effects of immunization in small-world epidemics

The propagation of model epidemics on a small-world network under the action of immunization is studied. Although the connectivity in this kind of networks is rather uniform, a vaccination strategy focused on the best connected individuals yields a considerable improvement of disease control. The model exhibits a transition from disease localization to propagation as the disorder of the underlying network grows. As a consequence, for fixed disorder, a threshold immunization level exists above which the disease remains localized.

Associative memory on a small-world neural network

Abstract.We study a model of associative memory based on a neural network with small-world structure. The efficacy of the network to retrieve one of the stored patterns exhibits a phase transition at a finite value of the disorder. The more ordered networks are unable to recover the patterns, and are always attracted to non-symmetric mixture states. Besides, for a range of the number of stored patterns, the efficacy has a maximum at an intermediate value of the disorder. We also give a statistical characterization of the spurious attractors for all values of the disorder of the network.

Stochastic resonance in a model of opinion formation on small-world networks

Abstract:We analyze the phenomenon of stochastic resonance in an Ising-like system on a small-world network. The system, which is subject to the combined action of noise and an external modulation, can be interpreted as a stylized model of opinion formation by imitation under the effects of a “fashion wave”. Both the amplitude threshold for the detection of the external modulation and the width of the stochastic-resonance peak show considerable variation as the randomness of the underlying small-world network is changed.

Evolution of reaction-diffusion patterns in infinite and bounded domains

We introduce a semi-analytical method to study the evolution of spatial structures in reaction-diffusion systems. It consists in writing an integral equation for the relevant densities, from the propagator of the linear part of the evolution operator. In order to test the method, we perform an exhaustive study of a one-dimensional reaction-diffusion model associated to an electrical device - the ballast resistor. We consider the evolution of step and bubble-shaped initial density profiles in free space as well as in a semi-infinite domain with Dirichlet and Neumann boundary conditions. The piecewise-linear form of the reaction term, which preserves the basic ingredients of more complex nonlinear models, makes it possible to obtain exact wave-front solutions in free space and stationary solutions in the bounded domain. Short and long-time behaviour can also be analytically studied, whereas the evolution at intermediate times is analyzed by numerical techniques. We paid particular attention to the features introduced in the evolution by boundary conditions.

The social behavior and the evolution of sexually transmitted diseases

We introduce a model for the evolution of sexually transmitted diseases, in which the social behavior is incorporated as a determinant factor for the further propagation of the infection. The system may be regarded as a society of agents where in principle, anyone can sexually interact with any other one in the population, indeed, in this contribution only the homosexual case is analyzed. Different social behaviors are reflected in a distribution of sexual attitudes ranging from the more conservative to the more promiscuous. This is measured by what we call the promiscuity parameter. In terms of this parameter, we find a critical behavior for the evolution of the disease. There is a threshold below which the epidemic does not occur. We relate this critical value of promiscuity to what epidemiologists call the basic reproductive number, connecting it with the other parameters of the model, namely the infectivity and the infective period in a quantitative way. We consider the possibility of subjects to be grouped in couples.

Social Learning in Vespula Germanica Wasps: Do They Use Collective Foraging Strategies?

Vespula germanica is a social wasp that has become established outside its native range in many regions of the world, becoming a major pest in the invaded areas. In the present work we analyze social communication processes used by V. germanica when exploiting un-depleted food sources. For this purpose, we investigated the arrival pattern of wasps at a protein bait and evaluated whether a forager recruited conspecifics in three different situations: foragers were able to return to the nest (full communication), foragers were removed on arrival (communication impeded), or only one forager was allowed to return to the nest (local enhancement restricted). Results demonstrated the existence of recruitment in V. germanica, given that very different patterns of wasp arrivals and a higher frequency of wasp visits to the resource were observed when communication flow between experienced and naive foragers was allowed. Our findings showed that recruitment takes place at a distance from the food source, in addition to local enhancement. When both local enhancement and distant recruitment were occurring simultaneously, the pattern of wasp arrival was exponential. When recruitment occurred only distant from the feeder, the arrival pattern was linear, but the number of wasps arriving was twice as many as when neither communication nor local enhancement was allowed. Moreover, when return to the nest was impeded, wasp arrival at the bait was regular and constant, indicating that naive wasps forage individually and are not spatially aggregated. In conclusion, this is the first study to demonstrate recruitment in V. germanica at a distance from the food source by modelling wasps’ arrival to a protein-based resource. In addition, the existence of correlations when communication was allowed and reflected in tandem arrivals indicates that we were not in the presence of random processes.

An exact analytical solution of a three-component model for competitive coexistence.

A three-component competition system is modeled as a reaction-diffusion process. An exact analytical solution has been found that indicates that in certain situations the classical results on extinction and coexistence of Lotka-Volterra-type equations are no longer valid. Cases with one or both predators diffuse are analyzed, and the stability question is discussed.

Space use by foragers consuming renewable resources

We study a simple model of a forager as a walk that modifies a relaxing substrate. Within it simplicity, this provides an insight on a number of relevant and non-intuitive facts. Even without memory of the good places to feed and no explicit cost of moving, we observe the emergence of a finite home range. We characterize the walks and the use of resources in several statistical ways, involving the behavior of the average used fraction of the system, the length of the cycles followed by the walkers, and the frequency of visits to plants. Preliminary results on population effects are explored by means of a system of two non directly interacting animals. Properties of the overlap of home ranges show the existence of a set of parameters that provides the best utilization of the shared resource.

Competitive Coexistence in Biological Systems: Exact Analytical Results Through a Quantum Mechanical Analogy

We have studied an ecological system of two species (called strongandweak)competing for a single food resource, modelled as a reaction diffusion process. A whole family of exact analytical solutions has been found resorting to a quantum mechanical analogy. Such solutions indicate that in certain situations (and essentially as a consequence of the weakspecies mobility), the classical results on extinction and coexistence of Lotka-Volterra type equations are no longer valid. We have analyzed the stability of these solutions and discussed different possibilities for extending our results.