[Show abstract][Hide abstract] ABSTRACT: Human papillomavirus (HPV) types 16 and 18 cause 70% of cervical cancers, and currently two vaccines protecting against these types are available. In a previous paper, we estimated the long-term effect of HPV vaccination on the risk of cervical cancer in the French population using mathematical modeling. Several vaccination scenarios were tested, including different vaccination coverage rates of females alone or in conjunction with males. In the first scenario, which is based on the vaccination campaign initiated in France in 2007, 30% of females aged 14 to 19 years were vaccinated annually, resulting in a 60% cumulative vaccination coverage rate among 14 to 19 year old females 6 years after the beginning of the vaccination campaign. A catch-up program was also included with an annual vaccination rate of 10% among females aged 20 to 24 years. Using this scenario, the model predicted an 83% reduction in cervical cancer incidence 50 years after vaccination initiation. The following scenarios were also considered: extending vaccination: (1) to males, (2) to females under 14; and scenarios with (3) vaccination among 14 to 24 year-old females (annual rate of 80%), (4) vaccination among 14 to 24 year-old females and males (annual rate of 80%). Greater reductions in cervical cancer incidence of 92% to 98% were predicted.
Public Health 12/2014; 129(1). DOI:10.1016/j.puhe.2014.11.005 · 1.43 Impact Factor
[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.
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 .
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.
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; 18(7). DOI:10.1111/tmi.12105 · 2.33 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; 31(2). DOI:10.1093/imammb/dqt001 · 1.66 Impact Factor
[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.
[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 03/2012; 7(3):e32251. DOI:10.1371/journal.pone.0032251 · 3.23 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; 06/2011
[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: 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; 58. DOI:10.1016/j.respe.2010.06.110 · 0.59 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: From the beginning of the HIV/AIDS epidemic in Cuba a system for detection of persons living with HIV was put in place,. A nonlinear model is developed for the detection system considering different types of searches, some random and others non-random, the model is based on another one studied before by some of the present authors. We study the dynamics of the system. Using the data from the Cuban HIV/AIDS epidemic, we fit the model to the data. For this, as not all types of searches were introduced at the same time, we consider the parameters of the system to be step functions. 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. Also the basic reproduction number is computed for each set of values of the parameters.
[Show abstract][Hide abstract] ABSTRACT: Dengue fever is a disease transmitted through mosquitoes. In Cuba the transmission vector is the Aedes Aegipty mosquito. Dengue fever is endemic in many areas in Central America and the Caribbean, but in Cuba it is always an imported disease, it is not endemic. One of the problems confronted by the Health System is finding the size of the mosquito population during an outbreak of dengue fever. There are indices studied by the surveillance system, and there are indicators that point to a possible outbreak, if a case is introduced by some traveler that is unaware of its condition as a carrier of one of the dengue viruses. Since the first papers (Esteva and Vargas, J. Math Biol, 1999) modeling dengue fever has been a priority in the countries where it is endemic.In our work using a mathematical model with ODE adapted from (Coutinho and all, Bull. Math. Biol, 2006), we fit the epidemic curve given by the model to the known cases of a dengue fever outbreak in the city of Havana, using as parameters the carrying capacity for mosquito eggs, larvae and pupa. This carrying capacity depends on the actions the Health System takes to eliminate areas where the mosquito can breed. Once we have the parameters that fit the part of the full blown outbreak, we use these values to estimate the efficiency of the system in eliminating the mosquito and its breeding grounds. We present these results using the same epidemic outbreak in the city of Havana.
[Show abstract][Hide abstract] ABSTRACT: From the beginning of the HIV/AIDS epidemic in Cuba a system for detection of persons living with HIV was put in place. A nonlinear model is developed for the detection system considering different types of searches, some random and others non-random, the model is based on another one studied before by some of the present authors. We study the dynamics of the system. Using the data from the Cuban HIV/AIDS epidemic, we fit the model to the data. For this, as not all types of searches were introduced at the same time, we consider the parameters of the system to be step functions. 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. Also the basic reproduction number is computed for each set of values of the parameters.
[Show abstract][Hide abstract] ABSTRACT: 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.
Mathematical Methods in Survival Analysis, Reliability and Quality of Life, 01/2010: pages 315 - 332; , ISBN: 9780470610985
[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 12/2005; 13(04). DOI:10.1142/S0218339005001616 · 0.38 Impact Factor
[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: 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. DOI:10.1093/imammb19.3.221