From mid-2015 to the end of January 2016, 47 cases of microcephaly were observed in the city of R... more 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...
In this paper we consider the problem of computing the area-based affine distance for a convex do... more In this paper we consider the problem of computing the area-based affine distance for a convex domain in the plane. Since this affine distance satisfies a non-homogeneous Monge-Ampère differential equation, we propose a fast marching method for its computation. The proposed algorithm is efficient and the obtained results are quite precise. We have also proved the convergence of the algorithm.
We present a model of infection by Wolbachia of an Aedes aegypti population. This model is design... more We present a model of infection by Wolbachia of an Aedes aegypti population. This model is designed to take into account both the biology of this infection and any available experimental data obtained in the field. The objective is to use this model for predicting the sustainable introduction of this bacteria. We provide a complete mathematical analysis of the model proposed and give the basic reproduction ratio R0 for Wolbachia. We observe a bistability phenomenon. Two equilibria are asymptotically stable : an equilibrium where all the population is uninfected and an equilibrium where all the population is infected. A third unstable equilibrium exists. We provide an lower bound for the basin of attraction of the desired infected equilibrium. We are in a backward bifurcation situation. The bistable situations occurs with natural biological values for the parameters.
The use of bacteria Wolbachia is a promising method presently considered to block the transmissio... more The use of bacteria Wolbachia is a promising method presently considered to block the transmission of dengue and chikungunya viruses. Systematic procedures for introduction of mosquitos infected by the bacteria in a healthy population are still to be studied. This is a central question, with heavy impact on the cost and efficiency. The aim of the present study is the synthesis of a method allowing the reduction of the number of introduced mosquitos, and consequently the cost, without putting at risk the success of the infestation (something that could happen e.g. if the initial size of the population has been underestimated). Using the fact that measurements are completed during the whole release process, techniques from the theory of control of dynamical systems are used to define the quantity to be introduced. The original system is shown to have two stable equilibria, corresponding to Wolbachia-free and complete infestation situations. A simple feedback law is proposed and shown ...
Transportation Research Record: Journal of the Transportation Research Board
This paper presents the utilization of mobile phone data for transport models, with spatial model... more This paper presents the utilization of mobile phone data for transport models, with spatial modeling of the study region in geographical units that allows the integration of aggregated call detail records (CDR) with demographic data and other sources. The algorithm used for the estimation of the origin–destination matrices obtained a distribution of the number of trips compatible with those of a household survey conducted in 2013. With the use of a one-year dataset, two mobility patterns were identified in Rio de Janeiro: home–work and weekend trips. Changes in mobility patterns because of an important road modification were also detected, demonstrating that the use of CDR for urban planning and monitoring is a robust and low-cost option.
Defining and measuring spatial inequalities across the urban environment remains a complex and el... more Defining and measuring spatial inequalities across the urban environment remains a complex and elusive task which has been facilitated by the increasing availability of large geolocated databases. In this study, we rely on a mobile phone dataset and an entropy-based metric to measure the attractiveness of a location in the Rio de Janeiro Metropolitan Area (Brazil) as the diversity of visitors’ location of residence. The results show that the attractiveness of a given location measured by entropy is an important descriptor of the socioeconomic status of the location, and can thus be used as a proxy for complex socioeconomic indicators.
We study the effect of human circulation and host/vector heterogeneities on the onset of epidemic... more We study the effect of human circulation and host/vector heterogeneities on the onset of epidemics of arboviruses. From a meta-population dynamics based on the classical Bailey-Dietz model, we derive a multi-group model under three assumptions: (i) fast host sojourn timescale ; (ii) mosquitoes do not move; (iii) time homogeneity and strong connectivity of human circulation. Within this modelling framework, three different kinds of R 0 appear: (i) the "true" or "global" R 0-derived from the corresponding next generation matrix; (ii) the uniform R 0-obtained if the patches are taken homogeneous; (iii) the local R 0 s-obtained if the patches are disconnected. We show that there is relevant epidemiological information associated to all of them. In particular, they can be used to understand the effects of changing the circulation on the value of the global R 0. We also present additional results on the effects on R 0 of different vector control policies, and a simulation with data from the city of Rio de Janeiro, Brazil.
2015 54th IEEE Conference on Decision and Control (CDC), 2015
The control of the spread of dengue fever by introduction of the intracellular parasitic bacteriu... more 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 inputoutput system has multivalued static characteristics, but the existing results are unable to prove almost-global stabilization, and ad hoc analysis has to be conducted.
Given a pair of planar curves, one can define its generalized area distance, a concept that gener... more Given a pair of planar curves, one can define its generalized area distance, a concept that generalizes the area distance of a single curve. In this paper, we show that the generalized area distance of a pair of planar curves is an improper indefinite affine spheres with singularities, and, reciprocally, every indefinite improper affine sphere in R 3 is the generalized distance of a pair of planar curves. Considering this representation, the singularity set of the improper affine sphere corresponds to the area evolute of the pair of curves, and this fact allows us to describe a clear geometric picture of the former. Other symmetry sets of the pair of curves, like the affine area symmetry set and the affine envelope symmetry set can be also used to describe geometric properties of the improper affine sphere.
In this paper we consider planar polygons with parallel opposite sides. This type of polygons can... more In this paper we consider planar polygons with parallel opposite sides. This type of polygons can be regarded as discretizations of closed convex planar curves by taking tangent lines at samples with pairwise parallel tangents. For this class of 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.
The control of the spread of dengue fever by introduction of the intracellular parasitic bacteriu... more 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...
ABSTRACT This paper presents an architecture for historical archives maintenance based on Open Li... more ABSTRACT This paper presents an architecture for historical archives maintenance based on Open Linked Data technologies and open source distributed development model and tools. The proposed architecture is being implemented for the archives of the Centro de Pesquisa e Documentação de História Contemporânea do Brasil (Center for Research and Documentation of Brazilian Contemporary History) of the Fundação Getulio Vargas (Getulio Vargas Foundation). We discuss the benefits of this initiative and suggest ways of implementing it, as well as describing the preliminary milestones already achieved. We also present some of the possibilities for extending the accessibility and usefulness of the data archives information using semantic web technologies, natural language processing, image analysis tools, and audio-textual alignment, both in progress and planned.
An important question about ane skeletons is the existence of dierential equations that are relat... more An important question about ane skeletons is the existence of dierential equations that are related to the Ane Distance and the Area Distance (hence to ane 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-Ampère type that relates to the ane skeletons (and extends the Eikonal equation for the medial axis). We also discuss some consequences and ideas that this new PDE formulation suggests.
The area distance to a convex plane curve is an important concept in computer vision. In this pap... more The area distance to a convex plane curve is an important concept in computer vision. In this paper we describe a strong link between area distances and improper affine spheres. This link makes possible a better understanding of both theories. The concepts of the theory of affine spheres lead to a new definition of an area distance on the outer part of a convex plane arc. Also, based on the theory of discrete affine spheres, we propose fast algorithms to compute the area distances. On the other hand, area distances provide a good geometrical understanding of improper affine spheres.
Background: Visceral leishmaniasis belongs to the list of neglected tropical diseases and is cons... more Background: Visceral leishmaniasis belongs to the list of neglected tropical diseases and is considered a public health problem worldwide. Spatial correlation between the occurrence of the disease in humans and high rates of canine infection suggests that in the presence of the vector, canine visceral leishmaniasis is the key factor for triggering transmission to humans. Despite the control strategies implemented, such as the sacrifice of infected dogs being put down, the incidence of American visceral leishmaniasis remains high in many Latin American countries. Methodology/Principal Findings: Mathematical models were developed to describe the transmission dynamics of canine leishmaniasis and its control by culling. Using these models, imperfect control scenarios were implemented to verify the possible factors which alter the effectiveness of controlling this disease in practice. Conclusions/Significance: A long-term continuous program targeting both asymptomatic and symptomatic dogs should be effective in controlling canine leishmaniasis in areas of low to moderate transmission (R 0 up to 1.4). However, the indiscriminate sacrifice of asymptomatic dogs with positive diagnosis may jeopardize the effectiveness of the control program, if tests with low specificity are used, increasing the chance of generating outrage in the population, and leading to lower adherence to the program. Therefore, culling must be planned accurately and implemented responsibly and never as a mechanical measure in large scale. In areas with higher transmission, culling alone is not an effective control strategy.
In this paper we consider the problem of computing the area-based affine distance for a convex do... more In this paper we consider the problem of computing the area-based affine distance for a convex domain in the plane. Since this affine distance satisfies a non-homogeneous Monge-Amp ` ere differential equation, we propose a fast marching method for its computation. The proposed algorithm is efficient and the obtained results are quite precise. We have also proved the convergence of
From mid-2015 to the end of January 2016, 47 cases of microcephaly were observed in the city of R... more 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...
In this paper we consider the problem of computing the area-based affine distance for a convex do... more In this paper we consider the problem of computing the area-based affine distance for a convex domain in the plane. Since this affine distance satisfies a non-homogeneous Monge-Ampère differential equation, we propose a fast marching method for its computation. The proposed algorithm is efficient and the obtained results are quite precise. We have also proved the convergence of the algorithm.
We present a model of infection by Wolbachia of an Aedes aegypti population. This model is design... more We present a model of infection by Wolbachia of an Aedes aegypti population. This model is designed to take into account both the biology of this infection and any available experimental data obtained in the field. The objective is to use this model for predicting the sustainable introduction of this bacteria. We provide a complete mathematical analysis of the model proposed and give the basic reproduction ratio R0 for Wolbachia. We observe a bistability phenomenon. Two equilibria are asymptotically stable : an equilibrium where all the population is uninfected and an equilibrium where all the population is infected. A third unstable equilibrium exists. We provide an lower bound for the basin of attraction of the desired infected equilibrium. We are in a backward bifurcation situation. The bistable situations occurs with natural biological values for the parameters.
The use of bacteria Wolbachia is a promising method presently considered to block the transmissio... more The use of bacteria Wolbachia is a promising method presently considered to block the transmission of dengue and chikungunya viruses. Systematic procedures for introduction of mosquitos infected by the bacteria in a healthy population are still to be studied. This is a central question, with heavy impact on the cost and efficiency. The aim of the present study is the synthesis of a method allowing the reduction of the number of introduced mosquitos, and consequently the cost, without putting at risk the success of the infestation (something that could happen e.g. if the initial size of the population has been underestimated). Using the fact that measurements are completed during the whole release process, techniques from the theory of control of dynamical systems are used to define the quantity to be introduced. The original system is shown to have two stable equilibria, corresponding to Wolbachia-free and complete infestation situations. A simple feedback law is proposed and shown ...
Transportation Research Record: Journal of the Transportation Research Board
This paper presents the utilization of mobile phone data for transport models, with spatial model... more This paper presents the utilization of mobile phone data for transport models, with spatial modeling of the study region in geographical units that allows the integration of aggregated call detail records (CDR) with demographic data and other sources. The algorithm used for the estimation of the origin–destination matrices obtained a distribution of the number of trips compatible with those of a household survey conducted in 2013. With the use of a one-year dataset, two mobility patterns were identified in Rio de Janeiro: home–work and weekend trips. Changes in mobility patterns because of an important road modification were also detected, demonstrating that the use of CDR for urban planning and monitoring is a robust and low-cost option.
Defining and measuring spatial inequalities across the urban environment remains a complex and el... more Defining and measuring spatial inequalities across the urban environment remains a complex and elusive task which has been facilitated by the increasing availability of large geolocated databases. In this study, we rely on a mobile phone dataset and an entropy-based metric to measure the attractiveness of a location in the Rio de Janeiro Metropolitan Area (Brazil) as the diversity of visitors’ location of residence. The results show that the attractiveness of a given location measured by entropy is an important descriptor of the socioeconomic status of the location, and can thus be used as a proxy for complex socioeconomic indicators.
We study the effect of human circulation and host/vector heterogeneities on the onset of epidemic... more We study the effect of human circulation and host/vector heterogeneities on the onset of epidemics of arboviruses. From a meta-population dynamics based on the classical Bailey-Dietz model, we derive a multi-group model under three assumptions: (i) fast host sojourn timescale ; (ii) mosquitoes do not move; (iii) time homogeneity and strong connectivity of human circulation. Within this modelling framework, three different kinds of R 0 appear: (i) the "true" or "global" R 0-derived from the corresponding next generation matrix; (ii) the uniform R 0-obtained if the patches are taken homogeneous; (iii) the local R 0 s-obtained if the patches are disconnected. We show that there is relevant epidemiological information associated to all of them. In particular, they can be used to understand the effects of changing the circulation on the value of the global R 0. We also present additional results on the effects on R 0 of different vector control policies, and a simulation with data from the city of Rio de Janeiro, Brazil.
2015 54th IEEE Conference on Decision and Control (CDC), 2015
The control of the spread of dengue fever by introduction of the intracellular parasitic bacteriu... more 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 inputoutput system has multivalued static characteristics, but the existing results are unable to prove almost-global stabilization, and ad hoc analysis has to be conducted.
Given a pair of planar curves, one can define its generalized area distance, a concept that gener... more Given a pair of planar curves, one can define its generalized area distance, a concept that generalizes the area distance of a single curve. In this paper, we show that the generalized area distance of a pair of planar curves is an improper indefinite affine spheres with singularities, and, reciprocally, every indefinite improper affine sphere in R 3 is the generalized distance of a pair of planar curves. Considering this representation, the singularity set of the improper affine sphere corresponds to the area evolute of the pair of curves, and this fact allows us to describe a clear geometric picture of the former. Other symmetry sets of the pair of curves, like the affine area symmetry set and the affine envelope symmetry set can be also used to describe geometric properties of the improper affine sphere.
In this paper we consider planar polygons with parallel opposite sides. This type of polygons can... more In this paper we consider planar polygons with parallel opposite sides. This type of polygons can be regarded as discretizations of closed convex planar curves by taking tangent lines at samples with pairwise parallel tangents. For this class of 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.
The control of the spread of dengue fever by introduction of the intracellular parasitic bacteriu... more 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...
ABSTRACT This paper presents an architecture for historical archives maintenance based on Open Li... more ABSTRACT This paper presents an architecture for historical archives maintenance based on Open Linked Data technologies and open source distributed development model and tools. The proposed architecture is being implemented for the archives of the Centro de Pesquisa e Documentação de História Contemporânea do Brasil (Center for Research and Documentation of Brazilian Contemporary History) of the Fundação Getulio Vargas (Getulio Vargas Foundation). We discuss the benefits of this initiative and suggest ways of implementing it, as well as describing the preliminary milestones already achieved. We also present some of the possibilities for extending the accessibility and usefulness of the data archives information using semantic web technologies, natural language processing, image analysis tools, and audio-textual alignment, both in progress and planned.
An important question about ane skeletons is the existence of dierential equations that are relat... more An important question about ane skeletons is the existence of dierential equations that are related to the Ane Distance and the Area Distance (hence to ane 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-Ampère type that relates to the ane skeletons (and extends the Eikonal equation for the medial axis). We also discuss some consequences and ideas that this new PDE formulation suggests.
The area distance to a convex plane curve is an important concept in computer vision. In this pap... more The area distance to a convex plane curve is an important concept in computer vision. In this paper we describe a strong link between area distances and improper affine spheres. This link makes possible a better understanding of both theories. The concepts of the theory of affine spheres lead to a new definition of an area distance on the outer part of a convex plane arc. Also, based on the theory of discrete affine spheres, we propose fast algorithms to compute the area distances. On the other hand, area distances provide a good geometrical understanding of improper affine spheres.
Background: Visceral leishmaniasis belongs to the list of neglected tropical diseases and is cons... more Background: Visceral leishmaniasis belongs to the list of neglected tropical diseases and is considered a public health problem worldwide. Spatial correlation between the occurrence of the disease in humans and high rates of canine infection suggests that in the presence of the vector, canine visceral leishmaniasis is the key factor for triggering transmission to humans. Despite the control strategies implemented, such as the sacrifice of infected dogs being put down, the incidence of American visceral leishmaniasis remains high in many Latin American countries. Methodology/Principal Findings: Mathematical models were developed to describe the transmission dynamics of canine leishmaniasis and its control by culling. Using these models, imperfect control scenarios were implemented to verify the possible factors which alter the effectiveness of controlling this disease in practice. Conclusions/Significance: A long-term continuous program targeting both asymptomatic and symptomatic dogs should be effective in controlling canine leishmaniasis in areas of low to moderate transmission (R 0 up to 1.4). However, the indiscriminate sacrifice of asymptomatic dogs with positive diagnosis may jeopardize the effectiveness of the control program, if tests with low specificity are used, increasing the chance of generating outrage in the population, and leading to lower adherence to the program. Therefore, culling must be planned accurately and implemented responsibly and never as a mechanical measure in large scale. In areas with higher transmission, culling alone is not an effective control strategy.
In this paper we consider the problem of computing the area-based affine distance for a convex do... more In this paper we consider the problem of computing the area-based affine distance for a convex domain in the plane. Since this affine distance satisfies a non-homogeneous Monge-Amp ` ere differential equation, we propose a fast marching method for its computation. The proposed algorithm is efficient and the obtained results are quite precise. We have also proved the convergence of
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