Deterministic modeling for transmission of Human Papillomavirus 6/11: impact of vaccination.

International audienceThis paper is devoted to assess the impact of quadrivalent Human Papillomavirus (HPV) vaccine on prevalence of non-oncogenic HPV 6/11 types in French males and females. For this purpose, a non-linear dynamic model of heterosexual transmission for HPV 6/11 types infection is developed, which accounts for immunity due to vaccination in particular. The vaccinated reproduction number Rv is derived using the approach described by Diekmann (2010) called the Next Generation Operator approach. The model proposed is analyzed, with regard to existence and uniqueness of the solution, steady-state stability. Precisely, the stability of the model is investigated depending on the sign of Rv − 1. Prevalence data are used to fit a numerical HPV model, so as to assess infection rates. Our approach suggests that 10 years after introducting vaccination, the prevalence of HPV 6/11 types in females will be halved and that in males will be reduced by one quarter, assuming a sustained vaccine coverage of 30% among females. Using the formula we derived for the vaccinated reproduction number, we show that the non-oncogenic HPV 6/11 types would be eradicated if vaccine coverage in females is kept above 12%. Human Papillomavirus, deterministic epidemic model, equilibrium, stability, reproduction number, vaccination

Modélisation déterministe de la transmission des infections à Papillomavirus Humain (Impact de la vaccination)

Les infections à Papillomavirus Humain (HPV) sont des infections sexuellement transmissibles très fréquentes. La persistance de ces infections est un facteur causal du cancer du col de l utérus et est aussi à l origine d autres cancers de la zone ano-génitale et de verrues génitales chez les femmes et chez les hommes. Depuis l introduction de deux vaccins bivalent et quadrivalent permettant de prévenir certains types d HPV, de nombreux modèles mathématiques ont été développés afin d estimer l impact potentiel de différentes stratégies de vaccination. L objectif de ce travail de thèse a été d estimer l impact potentiel de la vaccination en France sur l incidence de certains cancers liés à l HPV, notamment le cancer du col de l utérus et le cancer anal chez les femmes françaises ; ainsi que sur la prévalence des infections à HPV 6/11/16/18. Différents modèles dynamiques de type déterministe ont été développés. Ils sont représentés par des systèmes d équations différentielles ordinaires. Une étude théorique du comportement asymptotique d un premier modèle comportant peu de strates a été réalisée. Le nombre de reproduction de base R0 et le nombre de reproduction avec vaccination Rv ont été estimés. Des modèles plus complexes ont intégré une structure d âge et de comportement sexuel. Les modélisations réalisées permettent de conclure à l impact important de la vaccination sur la prévalence des infections à HPV et sur l incidence des cancers du col de l utérus et de la zone anale chez les femmes françaises dans un délai de quelques décennies, si l on prend en compte les taux de vaccination observés en France au début de la campagne de vaccinationHuman Papillomavirus infection (HPV) is the most frequent sexually transmitted disease. Epidemiological studies have established a causal relationship between HPV infections and occurence of cervical cancer. These infections have also been incriminated in anogenital cancers and anogenital warts among women and men. Since the introduction of bivalent and quadrivalent vaccines which offer protection against some HPV genotypes, many mathematical models have been developed in order to assess the potential impact of vaccine strategies. The aim of this thesis work was to assess the potential impact of HPV vaccination in France on the incidence of some cancers linked with HPV, particularly cervical cancer and anal cancer in French women, and on the prevalence of HPV 6/11/16/18 infections. Different deterministic dynamic models have been developped. They are represented by systems of ordinary differential equations. A theoretical analysis of the asymptotic behavior for a first model with few strata is realized. The basic reproduction number R0 and the vaccinated reproduction number Rv are assessed. More complex models taking into account age and sexual behavior have been developed. Using vaccination rates observed in France at the launch of the vaccination campaign, our modeling shows the large impact of vaccination on HPV prevalences, on cervical cancer and anal cancer incidences among French women within a few decadesPARIS5-Bibliotheque electronique (751069902) / SudocSudocFranceF

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

The HIV/AIDS epidemic in Cuba: description and tentative explanation of its low HIV prevalence

<p>Abstract</p> <p>Background</p> <p>The Cuban HIV/AIDS epidemic has the lowest prevalence rate of the Caribbean region. The objective of this paper is to give an overview of the HIV/AIDS epidemic in Cuba and to explore the reasons for this low prevalence.</p> <p>Methods</p> <p>Data were obtained from the Cuban HIV/AIDS programme established in 1983. This programme has an extensive adult HIV testing policy, including testing of all pregnant women. HIV and AIDS cases have been recorded since 1986. Persons found to be HIV-positive are interviewed on their sexual behaviour and partners. Tracing and voluntary testing of these partners are organised. Epidemiological description of this epidemic was obtained from analysis of this data set. Using elementary mathematical analyses, we estimated the coverage of the detection system (percentage of HIV-positive adults detected) and the average period between HIV infection and detection. Estimated HIV prevalence rates were corrected to account for the coverage.</p> <p>Results</p> <p>HIV prevalence has increased since 1996. In 2005, the prevalence among pregnant women was 1.2 per 10,000 (16/137000). Estimated HIV prevalence among 15- to 49-year-olds was 8.1 per 10,000 (4913/6065000; 95%CI: 7.9 per 10,000 – 8.3 per 10,000). Most (77%) of the HIV-positive adults were men, most (85.1%) of the detected HIV-positive men were reported as having sex with men (MSM), and most of the HIV-positive women reported having had sex with MSM. The average period between HIV infection and detection was estimated to be 2.1 years (IQR = 1.7 – 2.2 years). We estimated that, for the year 2005, 79.6% (IQR: 77.3 – 81.4%) of the HIV-positive persons were detected.</p> <p>Conclusion</p> <p>MSM drive the HIV epidemic in Cuba. The extensive HIV testing policy may be an important factor in explaining the low HIV prevalence. To reduce the HIV epidemic in Cuba, the epidemic among MSM should be addressed. To understand this epidemic further, data on sexual behaviour should be collected. Now that antiretroviral therapy is more widely available, the Cuban policy, based on intensive HIV testing and tracing of partners, may be considered as a possible policy to control HIV/AIDS epidemics in other countries.</p

Bayesian analysis for detecting a change in exponential family

We propose a bayesian analysis of detection of a change of parameter in a sequence of independent random variables from exponential family. The test uses the highest posterior density credible set

Deux procédures de détection de rupture pour des observations poissonniennes groupées

National audienceWe consider two tests with regard to detection of change of parameter in a sequence of independent Poisson random variables. The first test considered is based on the likelihood ratio appropriately adapted for a change point problem. The limiting distribution of the test statistics, under the null hypothesis is evaluated by asymptotical techniques. Under the null hypothesis the distribution of the test statistic obtained by maximization of the likelihood ratio converges to the supremum of an square function of the Brownian bridge process. The second test use Bayes technic, and is based on the marginal posterior density of the change. Finaly, we apply the results for a set of data from the Liverpool Registry during 1960 to 1982, and compare the two procedures

Bayesian analysis for detecting a change in exponential family

We propose a bayesian analysis of detection of a change of parameter in a sequence of independent random variables from exponential family. The test uses the highest posterior density credible set

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

Efficacy of Vaccination against HPV Infections to Prevent Cervical Cancer in France: Present Assessment and Pathways to Improve Vaccination Policies

Background: Seventy percent of sexually active individuals will be infected with Human Papillomavirus (HPV) during their lifetime. These infections are incriminated for almost all cervical cancers. In France, 3,068 new cases of cervical cancer and 1,067 deaths from cervical cancer occurred in 2005. Two vaccines against HPV infections are currently available and vaccination policies aim to decrease the incidence of HPV infections and of cervical cancers. In France, vaccine coverage has been reported to be low. Methods: We developed a dynamic model for the heterosexual transmission of Human Papillomavirus types 16 and 18, which are covered by available vaccines. A deterministic model was used with stratification on gender, age and sexual behavior. Immunity obtained from vaccination was taken into account. The model was calibrated using French data of cervical cancer incidence. Results: In view of current vaccine coverage and screening, we expected a 32 % and 83 % reduction in the incidence of cervical cancers due to HPV 16/18, after 20 years and 50 years of vaccine introduction respectively. Vaccine coverage and screening rates were assumed to be constant. However, increasing vaccine coverage in women or vaccinating girls before 14 showed a better impact on cervical cancer incidence. On the other hand, performing vaccination in men improves the effect on cervical cancer incidence only moderately, compared to strategies in females only

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