A stochastic SIR model with contact-tracing: large population limits and statistical inference

A stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease is studied. Precisely, individuals identified as infected may contribute to detecting other infectious individuals by providing information related to persons with whom they have had possibly infectious contacts. The population evolves through demographic, infection and detection processes, in a way that its temporal evolution is described by a stochastic Markov process, of which the component accounting for the contact-tracing feature is assumed to be valued in a space of point measures. For adequate scalings of the demographic, infection and detection rates, it is shown to converge to the weak deterministic solution of a PDE system, as a parameter n, interpreted as the population size roughly speaking, becomes large. From the perspective of the analysis of infectious disease data, this approximation result may serve as a key tool for exploring the asymptotic properties of standard inference methods such as maximum likelihood estimation. We state preliminary statistical results in this context. Eventually, relation of the model to the available data of the HIV epidemic in Cuba, in which country a contact-tracing detection system has been set up since 1986, is investigated and numerical applications are carried out

Modeling secondary level of HIV contact tracing: its impact on HIV intervention in Cuba

<p>Abstract</p> <p>Background</p> <p>Universal HIV testing/treatment program has currently been suggested and debated as a useful strategy for elimination of HIV epidemic in Africa, although not without practical issues regarding the costs and feasibility of a fully implemented program.</p> <p>Methods</p> <p>A mathematical model is proposed which considers two levels of detection of HIV-infectives through contact tracing of known infectives in addition to detections through other means such as random screening. Simulations based on Cuban contact tracing data were performed to ascertain the potential impact of the different levels of contact tracing.</p> <p>Results</p> <p>Simulation studies illustrate that: (1) contact tracing is an important intervention measure which, while less effective than random screening, is perhaps less costly and hence ideal for large-scale intervention programs in developing countries with less resources; (2) the secondary level of contact tracing could significantly change the basic disease transmission dynamics, depending on the parameter values; (3) the prevalence of the epidemic at the time of implementation of contact tracing program might be a crucial factor in determining whether the measure will be effective in preventing disease infections and its eventual eradication.</p> <p>Conclusions</p> <p>Our results indicate that contact tracing for detection of HIV infectives could be suitably used to remedy inadequacies in a universal HIV testing program when designing timely and effective intervention measures.</p

A non linear model for a sexually transmitted disease with contact tracing.

International audienceA non-linear model is developed for an epidemic with contact tracing, and its dynamic is studied. We present the data for the Cuban HIV/AIDS epidemic and fit the non-linear model, we obtain estimates for the size of the Cuban HIV epidemic, and for the mean time for detecting a person that is infected with HIV

Adapted wavelets for pattern detection

Dans cette thèse, nous sommes intéressés à la conception d'ondelettes à support compact adaptées pour la détection de motifs dans les signaux 1-D. Abry et al. ont proposé des méthodes utilisant des combinaisons linéaires et des projections. Cependant, elles peuvent conduire à des filtres très longs approchant des filtres infinis. Nous proposons d'abord ici une technique basée sur le lifting pour construire des ondelettes adaptées à une forme donnée. Les ondelettes construites peuvent être aussi régulières que désiré et avoir plusieurs moments nuls. Nous étudions la stabilité de la méthode par rapport aux petites variations du motif ainsi que trois possibilités d'extension. Notre méthode est, en outre, comparée a celle proposé par Abry et al. dans le cas unidimensionnel. Trois applications sont ensuite développées dans ce travail. Toutes les trois sont liées aux problèmes de reconnaissance ou de détection de motifs. Nous proposons une méthodologie pour résoudre ce type de problèmes avec des ondelettes adaptées en décrivant l'intérêt de les utiliser au lieu de choisir l'une des ondelettes classiques. Les deux premières applications sont en relation avec la médecine, plus précisément avec les neurosciences. Elles consistent en le traitement des électroencéphalogrammes (EEG) : la première porte sur la détection des épis épileptiques et la seconde est liée a l'étude des potentiels évoqués. La troisième et dernière application présentée concerne la détection automatique de deux types des défauts dans la caténaire à partir des mesures de la force de contact avec le pantographe des trains. Pour finir, un chapitre décrit les outils logiciels créés lors de ce travail.In this thesis, we are interested in efficient design of compactly supported adapted wavelets for pattern detection in the 1-D case. Interesting schemes have been developed by Abry et al. using projections and linear combinations. Nevertheless, they may lead to very long filters in order to approximate IIR filters. We first propose a lifting based technique to construct adapted wavelets starting from the function to approximate. This procedure allows to constructconstructing wavelets as smooth as wanted with several vanishing moments. We study the stability of this construction method for small variations of the given pattern and three extension possibilities. We also compare the proposed approach to the one based on projection and linear combinations. Then we examine then three applications where we used adapted wavelets with satisfactory results. All of them are related to pattern recognition or detection problems so we start by proposing a methodology to solve this kind of problems with pattern adapted wavelets, describing the interest of using them instead of the classical ones. The two first applications are related with medicine, more precisely with neurosciences. They consist of the processing of electroencephalogram (EEG) signals: The first one is the detection of epileptic spikes and the second is related to the study of evoked potentials. The third and last application consists of the automatic detection of two kinds of defects in the catenary lines of trains. To end the thesis, a chapter describes some of the software tools that were implemented during this thesis.ORSAY-PARIS 11-BU Sciences (914712101) / SudocORSAY-PARIS 11-Bib. Maths (914712203) / SudocSudocFranceF

Hierarchical clustering for graph visualization

Abstract. This paper describes a graph visualization methodology based on hierarchical maximal modularity clustering, with interactive and significant coarsening and refining possibilities. An application of this method to HIV epidemic analysis in Cuba is outlined.

Deterministic modeling of the size of the HIV/AIDS epidemic in Cuba

The objective is to model the contact tracing aspect of the HIV detection system, to try to obtain some information that could be useful to the Health System in Cuba in evaluating the way the program is working, and to ascertain its usefulness in terms of intervention and treatment of HIV. Other models have been used to study the effect of contact tracing with this objective in mind . However, these were essentially linear models. We will now introduce non-linearity to model contact tracing. We will also discuss the implications of our results for the purpose of intervention and treatment of HIV/AIDS in Cuba, and to estimate the size of the epidemic in Cuba