Moacyr A. H. B. da Silva

A Fast Marching Method for the Area Based Affine Distance

Abstract In a previous paper, it was proved that the area based affine distance of a convex region in the plane satisfies a non-homogeneous Monge-Ampère differential equation. Based on this equation, in this paper we propose a fast marching method for the computation of this distance. The proposed algorithm has a lower computational complexity than the direct method and we have proved its convergence. And since the algorithm allows one to obtain a connection from any point of the region to the boundary by a path of decreasing distance, it offers a dynamic point of view for the area based affine distance.

Ensuring successful introduction of Wolbachia in natural populations of Aedes aegypti by means of feedback control

The control of the spread of dengue fever by introduction of the intracellular parasitic bacterium Wolbachia in populations of the vector Aedes aegypti, is presently one of the most promising tools for eliminating dengue, in the absence of an efficient vaccine. The success of this operation requires locally careful planning to determine the adequate number of individuals carrying the Wolbachia parasite that need to be introduced into the natural population. The introduced mosquitoes are expected to eventually replace the Wolbachia-free population and guarantee permanent protection against the transmission of dengue to human. In this study, we propose and analyze a model describing the fundamental aspects of the competition between mosquitoes carrying Wolbachia and mosquitoes free of the parasite. We then use feedback control techniques to devise an introduction protocol that is proved to guarantee that the population converges to a stable equilibrium where the totality of mosquitoes carry Wolbachia.

Polygons with Parallel Opposite Sides

In this paper we consider convex planar polygons with parallel opposite sides. These polygons can be regarded as discretizations of closed convex planar curves by taking tangent lines at samples with pairwise parallel tangents. For such polygons, we define discrete versions of the area evolute, central symmetry set, equidistants, and area parallels and show that they behave quite similarly to their smooth counterparts.

Global stabilizing feedback law for a problem of biological control of mosquito-borne diseases

The control of the spread of dengue fever by introduction of the intracellular parasitic bacterium Wolbachia in populations of the vector Aedes aegypti, is presently one of the most promising tools for eliminating dengue, in the absence of an efficient vaccine. The success of this operation requires locally careful planning to determine the adequate number of mosquitoes carrying the Wolbachia parasite that need to be introduced into the natural population. The latter are expected to eventually replace the Wolbachia-free population and guarantee permanent protection against the transmission of dengue to human. In this paper, we propose and analyze a model describing the fundamental aspects of the competition between mosquitoes carrying Wolbachia and mosquitoes free of the parasite. We then introduce a simple feedback control law to synthesize an introduction protocol, and prove that the population is guaranteed to converge to a stable equilibrium where the totality of mosquitoes carry Wolbachia. The techniques are based on the theory of monotone control systems, as developed after Angeli and Sontag. Due to bistability, the considered input-output system has multivalued static characteristics, but the existing results are unable to prove almost-global stabilization, and ad hoc analysis has to be conducted.

Affine Skeletons and Monge-Ampère Equations

An important question about affine skeletons is the existence of differential equations that are related to the “affine distance” and the “area distance” (hence to affine skeletons) in the same way the Eikonal equation is related to the “Euclidean distance” (and the medial axis). We show a surprisingly simple nonlinear second order PDE of Monge-Ampere type that relates to the affine skeletons (and extends the Eikonal equation for the medial axis). We also discuss some consequences and ideas that this new PDE formulation suggests.

How Public Transport affected the Propagation of Zika and Microcephaly within Rio de Janeiro early in 2015

From mid-2015 to the end of January 2016, 47 cases of microcephaly were observed in the city of Rio de Janeiro, that were not due to other viral infections (syphilis, toxoplasmosis, herpes & cytomegalovirus). These children were conceived from Dec 2014 to April 2015, far too early to be explained by the officially recorded cases from October 2015 onward. Zika must have been rampant in the city from late 2014 onward. In the first half of the paper we study how the geographic spread of microcephaly cases evolved from mid-2015 to January 2016 (and hence Zika 6-9 months earlier). Cases were not evenly spread in proportion to the number of births; they were preferentially located in the northern suburbs apparently following the public transport routes, with virtually no cases in favelas and none in the southern suburbs (Zona Sul). One key difference between the transport systems in the northern and southern suburbs is that the metro & rail system in the north is above ground in the north whereas in the southern part the metro is underground with air-conditioning in carriages and forced ventilation on the platforms. The train system does not extend to Zona Sul. In the second half of the paper we postulate that the air-conditioning and ventilation prevent mosquitos from biting people who are waiting on platforms in Zona Sul. Agent-based simulations are used to test this hypothesis. After confirming this, we postulate that providing air-conditioning and/or forced ventilation on the rail-metro transport hub in the city center (Centro) would significantly delay the propagation of arboviruses in the city, possibly preventing epidemics. One advantage of this proposal is that it does not require the use of insecticides.