[Show abstract][Hide abstract] ABSTRACT: OBJECTIVES: To investigate the temporal and regional variability of the 2001-2002 dengue outbreak in Havana City where 12 889 cases, mostly of DENV-3 type, were reported over a period of 7 months. METHODS: A simple mathematical model, the Richards model, was used to fit the weekly reported dengue case data by municipality, in order to quantify the transmissibility and temporal changes in the epidemic in each municipality via the basic reproduction number R0 . RESULTS: Model fits indicate either a 2-wave or 3-wave outbreak in all municipalities. Estimates for R0 varied greatly, from 1.97 (95% CI: 1.94, 2.01), for Arroyo Naranjo, to 61.06 (60.44, 61.68), for Boyeros, most likely due to heterogeneity in community structure, geographical locations and social networking. CONCLUSIONS: Our results illustrate the potential impact of climatological events on disease spread, further highlighting the need to be well prepared for potentially worsening disease spread in the aftermath of natural disasters such as hurricanes/typhoons.
Tropical Medicine & International Health 04/2013; · 2.94 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This paper is devoted to assess the impact of quadrivalent human papillomavirus (HPV) vaccine on the 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 et al. (2010) called the next generation operator approach. The model proposed is analysed, 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 introducing 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%.
Mathematical Medicine and Biology 03/2013; · 2.41 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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.
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.
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.
While current vaccination policies may significantly decrease cervical cancer incidence, other supplementary strategies in females could be considered in order to improve vaccination efficacy.
PLoS ONE 01/2012; 7(3):e32251. · 3.53 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A nonlinear compartmental model is developed for the HIV detection system in Cuba with different types of detections, some
random and others non-random. We analyze the dynamics of this system, compute the reproduction numbers, and use the data from
the Cuban HIV/AIDS epidemic between 1986-2008 to fit the model. We obtain estimates for the detection-related parameters during
two separate time periods to reflect the timeline of the implementation of various types of searches. The reproduction numbers
for each time period are also computed from the sets of values of the parameters. We found that random screening is most important
as a mean of surveillance. Moreover, local asymptotic stability for the Disease Free Equilibrium can be achieved if (i) random
screening is sufficiently effective and (ii) infection by detected HIV-positive individuals is minimal. Our results highlight
the importance of education for the known infectious for the purpose of preventing further infection. Fitting the 1986-2008
HIV data to obtain the model parameter estimates indicates that the HIV epidemic in Cuba is currently approaching an endemic
equilibrium. A Genetic Algorithm is used.
Advances in Computational Intelligence - 11th International Work-Conference on Artificial Neural Networks, IWANN 2011, Torremolinos-Málaga, Spain, June 8-10, 2011, Proceedings, Part II; 01/2011
[Show abstract][Hide abstract] ABSTRACT: Les infections à Papillomavirus Humain sont incriminées dans la quasi-totalité des cancers du col de l'utérus chez la femme. En France, 3400 nouveaux cas de cancer du col utérin et 1000 décès par cancer du col ont été estimés pour l'année 2000. Depuis la mise sur le marché récente de deux vaccins, une réduction de l'incidence de ces infections et des cancers du col de l'utérus est attendue. L'utilisation de modèles mathématiques permet de comparer différentes stratégies vaccinales et de retenir celles qui ont un rapport coût/efficacité optimal. Nous avons développé un modèle dynamique de transmission hétérosexuelle des infections à Papillomavirus Humain pour les sérotypes 6/11/16/18 qui sont couverts par le vaccin quadrivalent. Un modèle déterministe de type Susceptible-Infecté-Susceptible a été utilisé avec stratification selon le genre et le sérotype. L'immunité procurée par la vaccination est prise en compte. La sensibilité des prédictions du modèle a été évaluée par rapport à l'incertitude des paramètres. Trois scénarios de vaccination ont été comparés en considérant les prévalences des infections à Papillomavirus obtenues. L'analyse de sensibilité a mis en évidence l'importance de l'imprécision des durées d'infection des différents sérotypes d'infection à HPV sur les prédictions du modèle. La modélisation de la transmission des infections à HPV a permis de comparer l'efficacité potentielle de 3 scénarios de vaccination. La vaccination de la moitié des hommes entrant chaque année dans la population sexuellement active donne les mêmes résultats qu'une large couverture vaccinale (90%) des femmes entrant dans la population sexuellement active. Nos résultats montrent que l'introduction de la vaccination des jeunes garçons peut être motivée par une faible couverture vaccinale atteinte pour les jeunes femmes.
Revue d Épidémiologie et de Santé Publique 09/2010; · 0.69 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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.
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.
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.
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.
[Show abstract][Hide abstract] ABSTRACT: 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.
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.
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.
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.
[Show abstract][Hide abstract] ABSTRACT: Underreporting of HIV/AIDS cases is a common problem in HIV epidemiology which often skews epidemiologic projections on which public health policy decisions are often based, especially in the cases of low HIV prevalence countries or in early phases of an emerging epidemic when the HIV incidence is still low, but might be growing rapidly. In this work, we propose a simple mathematical model with groups of known and undetected HIV-positives. Using this model with the annual HIV incidence data of new HIV cases and new AIDS cases detected at onset of symptoms, we are able to obtain an estimate for the number of undetected HIV-positives. Moreover, using Taiwan data of 1993–2000, we are able to predict the number of new cases in the next two years within 5% accuracy. We also give an approximate ratio of underreporting which approximates the magnitude of underreporting of HIV cases in low HIV prevalence settings. The procedure is illustrated with the HIV data of Taiwan and Cuba. The result shows that underreporting in Cuba is low, probably due to its intense contact tracing program. For Taiwan, the level of underreporting is higher, but has improved slightly since 1999. The method is useful as a simple tool to gauge the immediate impact of an emerging epidemic, as well as for the purpose of public health policy planning and short-term future projections.
Journal of Biological Systems 01/2005; 13(04). · 0.73 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The data for the Cuban HIV-AIDS epidemic from 1986 to 2000 were presented. With the purpose of evaluating the efficiency of the HIV detection system, two methods were used to estimate the size of the HIV-infected population, backcalculation and a dynamical model. From these models it can be estimated that in the worst scenario 75% of the HIV-infected persons are known and in the best case 87% of the total number of persons that have been infected with HIV have been detected by the National Program. These estimates can be taken as a measure of the efficiency of the detection program for HIV-infected persons.
Revista cubana de medicina tropical 01/2003; 55(1):30-7.
[Show abstract][Hide abstract] ABSTRACT: A 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.
IMA journal of mathematics applied in medicine and biology 10/2002; 19(3):221-34.
[Show abstract][Hide abstract] ABSTRACT: 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.
Applied Mathematics and Computation 01/2001; 124(1). · 1.35 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A nonlinear model is developed for an epidemic with contact tracing, and its dynamic is studied. A linear version of the model is presented in both deterministic and stochastic versions. We present the data for the cuban HIV/AIDS epidemic and fit the linear model to the data, we obtain estimates for the size of the Cuban HIV epidemic.
[Show abstract][Hide abstract] ABSTRACT: We study deterministic and stochastic versions of a birth and death process for a two-type population with immigration for both types. For the stochastic model we consider the case where the rates are time dependent, and also when they are constant, as is the case in our AIDS application. We derive the probability generating function of the bivariate process and the expectations of the marginal processes. We also study the marginal behaviour of the bivariate process in a particular case where we suppose that the first event is an immigration, and examine the behaviour of the marginal processes divided by their expectations. Finally, we apply some of these results to a sexual-partner notification system, as in the Cuban national programme on HIV/AIDS.
IMA journal of mathematics applied in medicine and biology 07/1999; 16(2):143-54.
[Show abstract][Hide abstract] ABSTRACT: We 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 technics, 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.
[Show abstract][Hide abstract] ABSTRACT: A model for the AIDS program in Cuba is proposed, based on two classes of individuals, ‘known seropositives to HIV’ and ‘known AIDS cases’. The equations for this situation are stated, and solutions for the expectation for the variables of the two classes are calculated. Using the data from the Cuban National Program on HIV-AIDS some of the not known coefficients are found. These coefficients can be used to estimate the size of the population of the ‘unknown HIV seropositives’.
Revista Investigación Operacional. 01/1996; 17(1).
[Show abstract][Hide abstract] ABSTRACT: Human Papillomavirus is the most frequent sexually transmitted infection. Human Papillomavirus (HPV) is the primary cause of cervical cancer and its precursor lesions. Two prophylactic vaccines against HPV infections are available. Mathematical models can be used to compare several vaccine strategies. Consequently, most effective vaccine strategy can be enlightened and selected. Nevertheless, proposed HPV transmission models in the litterature have become very complex while some input values remain unknown or badly estimated. Our aim was to assess the variability in the outcome variable that is due to the uncertainty in estimating the input values. We carried out and calibrated a Susceptible-Infected-Susceptible model of heterosexual transmission of Human Papillomavirus infections for serotypes 6/11/16/18 which are covered by the quadrivalent vaccine. Immunity obtained from vaccination was considered. The basic and vaccinated basic reproduction numbers were expressed. Model prediction sensitivity to parameters uncertainty has been assessed using the Partial Rank Correlation Coefficients. Three scenarios of vaccination have been compared considering estimated HPV infection prevalences. Six posterior parameter sets among one million combination tested best fitted epidemiologic data. Sensitivity analysis showed that the significiance level of uncertainty was linked to the length of different serotype HPV infections in model predictions. Deterministic modeling of HPV infection transmission allowed us to compare potential efficiency of 3 vaccination scenarios. Additional vaccination of the half of men who enter annually in the sexually active population led to the same results when compared to an exclusive large vaccination rate of women (who enter annually in the sexually active population). Sensitivity analysis showed the importance of clearance rate in the precision of model predictions, therefore efforts have to been made to focus data collection concerning duration of HPV infections. Furthermore, usefulness of men's vaccination depends on women's vaccination rate.
[Show abstract][Hide abstract] ABSTRACT: A class of four linear and nonlinear differential equations models is given to describe the detection of HIV-positive individuals in Cuba through random screening and contact tracing. The basic reproduction number is obtained for each of the four models. Cuban HIV data from 1986 to 2002 are used to fit the models for the purpose of comparison. We also use the models to gauge the difference in detection time through random screening and contact tracing. Remarks on the implications for intervention measures and treatment of people living with HIV in Cuba are also given.
[Show abstract][Hide abstract] ABSTRACT: Human Papillomavirus (HPV) infections are the primary cause of cervical cancer and its precursor lesions. Two prophylactic vaccines against HPV infections are available. Mathematical models can be used to compare several vaccine strategies. A Susceptible-Infected-Susceptible model of heterosexual transmission of Human Papillomavirus infections is developed. Immunity obtained from vaccination is taken into account. The basic and vaccinated reproduction number are derived using the Next Generation Matrice. We find that if the vaccinated reproduction number is greater than unity, the disease free equilibrium (DFE) is unstable and we prove the existence and uniqueness of endemic equilibrium. If the vaccinated reproduction number is less than unity, there is a locally stable DFE and HPV will be eliminated.
[Show abstract][Hide abstract] ABSTRACT: Human papillomavirus (HPV) 16 and 18 are found to be involved in 80% of anal cancers. Two vaccines against HPV infections are currently available, and vaccination policies aim to decrease mainly, incidence of cervical cancers. Moreover, an impact of HPV vaccination on the incidence of anal cancer can also be expected. Our aim was to assess the potential benefits of HPV vaccination on the occurrence of female anal cancer in France. We developed a dynamic model for the heterosexual transmission of HPV and its progression to anal cancer in women. The model was calibrated using French data of anal cancer incidence. Considering vaccine coverage observed at the launch of vaccination campaign in France, reductions of 55 and 85% in the incidence of anal cancers due to HPV 16/18 are to be expected in French women 30 and 50 years after vaccine introduction, respectively. In case of a significant decrease in vaccine coverage, a dramatic reduction in the impact of HPV vaccination on female anal cancers would be observed. The number of anal cancer cases in French women is therefore expected to decrease significantly in 30 years, assuming sustained HPV vaccine coverage.