Background: 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.

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.

A nonlinear model is developed for an epidemic with contact tracmg, 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 HIVIAIDS epidemic and fit the linear model to the data, we obtain estimates for the size of the Cuban HIV epidemic.

ObjectivesTo investigate the temporal and regional variability of the 2001-2002 d engue outbreak in Havana City, when 12,889 cases, mostly of DENV-3 type, were reported over a period of 7 months. MethodsA simple mathematical model, the Richards model, is utilized to fit the weekly reported dengue case data by municipality, in order to quantify the transmissibility and temporal changes of the epidemic in each municipality via the basic reproduction number R 0 . ResultsModel fits indicate either a 2-wave or 3-wave outbreak in all municipalities. Estimates for R 0 vary greatly, from 1.97 (95% CI: 1.94, 2.01), for Arroyo Naranjo to 61.06 (60.44, 61.68) for Boyeros. ConclusionsWide regional variability in our estimates of R 0 for dengue is consistent with studies from various regions of the world, most likely due to heterogeneity in community structure, geographical locations, and social networking. The epidemic had initially started to ease around late October (e-week 43). However, infections spread once again after e-week 45, perhaps due to Hurricane Michelle, one of the most destructive and wettest tropical cyclones ever in Cuba that may have contributed to a protracted and more severe epidemic. For all municipalities with 3 waves, model fit indicates a new third wave occurred after Christmas/New Year, mostly likely attributable to a decrease in reporting during the holidays. Our results illustrate the potential impact of climatological events on disease spread, further highlighting the need to be wellprepared for potentially worsening disease spread in the aftermath of natural disasters such as hurricanes/typhoons.

BackgroundSeventy 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.MethodsWe 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.ResultsIn 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.ConclusionWhile current vaccination policies may significantly decrease cervical cancer incidence, other supplementary strategies in females could be considered in order to improve vaccination efficacy.

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%.

BackgroundUniversal 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.MethodsA 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.ResultsSimulation 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.ConclusionsOur 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.

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