BackgroundDengue is a disease of great complexity, due to interactions between humans, mosquitoes and various virus serotypes as well as efficient vector survival strategies. Thus, understanding the factors influencing the persistence of the disease has been a challenge for scientists and policy makers. The aim of this study is to investigate the influence of various factors related to humans and vectors in the maintenance of viral transmission during extended periods.Methodology/Principal FindingsWe developed a stochastic cellular automata model to simulate the spread of dengue fever in a dense community. Each cell can correspond to a built area, and human and mosquito populations are individually monitored during the simulations. Human mobility and renewal, as well as vector infestation, are taken into consideration. To investigate the factors influencing the maintenance of viral circulation, two sets of simulations were performed: (1st) varying human renewal rates and human population sizes and (2nd) varying the house index (fraction of infested buildings) and vector per human ratio. We found that viral transmission is inhibited with the combination of small human populations with low renewal rates. It is also shown that maintenance of viral circulation for extended periods is possible at low values of house index. Based on the results of the model and on a study conducted in the city of Recife, Brazil, which associates vector infestation with Aedes aegytpi egg counts, we question the current methodology used in calculating the house index, based on larval survey.Conclusions/SignificanceThis study contributed to a better understanding of the dynamics of dengue subsistence. Using basic concepts of metapopulations, we concluded that low infestation rates in a few neighborhoods ensure the persistence of dengue in large cities and suggested that better strategies should be implemented to obtain measures of house index values, in order to improve the dengue monitoring and control system.

We consider the N-vortex problem on an ellipsoid of revolution. Applying standard techniques of classical perturbation theory, we construct a sequence of conformal transformations from the ellipsoid into the complex plane. Using these transformations, the equations of motion for the N-vortex problem on the ellipsoid are written as a formal series on the eccentricity of the ellipsoid's generating ellipse. First order equations are obtained explicitly. We show numerically that the truncated first order system for the three vortex system on the symmetric ellipsoid is nonintegrable.

In this paper we study the motion of a charged particle on a Riemmanian surface under the influence of a positive magnetic field B. Using Moser's Twist Theorem and ideas from classical pertubation theory we find sufficient conditions to perpetually trap the motion of a particle with a sufficient large charge in a neighborhood of a level set of the magnetic field. The conditions on the level set of the magnetic field that guarantee the trapping are local and hold near all non-degenerate critical local minima or maxima of B. Using symplectic reduction we apply the results of our work to certain S 1 -invariant magnetic fields on R 3 .

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