The Human papillomaviruses (HPV) vaccine induces a herd immunity effect in genital warts when a large number of the population is vaccinated. This aspect should be taken into account when devising new vaccine strategies, like vaccination at older ages or male vaccination. Therefore, it is important to develop mathematical models with good predictive capacities. We devised a sexual contact network that was calibrated to simulate the Spanish epidemiology of different HPV genotypes. Through this model, we simulated the scenario that occurred in Australia in 2007, where 12–13 year-old girls were vaccinated with a three-dose schedule of a vaccine containing genotypes 6 and 11, which protect against genital warts, and also a catch-up program in women up to 26 years of age. Vaccine coverage were 73% in girls with three doses and with coverage rates decreasing with age until 52% for 20–26 year-olds. A fast 59% reduction in the genital warts diagnoses occurred in the model in the first years after the start of the program, similar to what was described in the literature.

Taking into account the public health importance of the human papillomavirus (HPV) control in the future, it is mandatory to assess the effect of the vaccination campaigns on the control of HPV spread and the associated diseases using reliable mathematical models. We propose a computational random network model with the aim of studying the transmission dynamics of HPV infections. This model reflects the herd immunity effect in the heterosexual network more accurately than the classical models. We perform a sensitivity analysis of the sexual behavior changes consisting of increasing the number of men who have sex with men (MSM), increasing the frequency of the intercourses and increasing the number of sexual partners. We find that large changes in the sexual behavior, in some extent, only have minor effects on the decline of the HPV infections in women and men in the current vaccination campaign in Spain (vaccination of young girls with a coverage of 70%). Therefore, the current vaccination program in Spain is robust for the heterosexuals. However, we cannot say the same for MSM, where they do not benefit by the herd immunity effect of the vaccination of girls, and consequently, the circulation of the virus among them remains unchanged. A consequence of the present study is that the effect of other external factors that may affect the transmission dynamics of the HPV, for instance, the tourism or the immigration, does not influence the protection provided by the current Spanish vaccination program.

Working in large networks applied to epidemiological-type models has led us to design a simple but effective computed distributed environment to perform a large amount of model simulations in a reasonable time in order to study the behavior of these models and to calibrate them. Finding the model parameters that best fit the available data in the designed distributed computing environment becomes a challenge and it is necessary to implement reliable algorithms for model calibration. In this article, we have adapted the random particle swarm optimization algorithm to our distributed computing environment to be applied to the calibration of a papillomavirus transmission dynamics model on a lifetime sexual partners network. And we have obtained a good fitting saving time and calculations compared with the exhaustive searching strategy we have been using so far.

A major challenge in human papillomavirus (HPV) vaccine programs is the universal gender-neutral recommendation, as well as estimation of its long-term effect. The objective of this study is to predict the added benefit of male vaccination, especially in men who have sex with men (MSM), and to analyze the impact of the program on society. We propose a mathematical model of the HPV infection based on a network paradigm. Data from Spain allowed constructing the sexual network. HPV force of infection was taken from literature. Different scenarios using variable vaccine coverage in both males and females were studied. Strong herd immunity is shown in the heterosexual population, with an important decrease of HPV 6/11 infections both in men and in unvaccinated women with an only-women vaccination at 14 years of age. No impact of this program occurred in the infection incidence in MSM. This group would only benefit from a vaccination program that includes males. However, the impact at short term would be lower than in heterosexual men. The protection of MSM can only be achieved by direct vaccination of males. This may have important consequences for public health.

HPV vaccine induces a herd immunity effect in genital warts when a large number of the population is vaccinated. That aspect should be taken into account when devising new vaccine strategies, like vaccination at older ages or male vaccination. Therefore it is important to develop mathematical models with good predictive capacities. We devised a sexual contact network that was calibrated to simulate the Spanish epidemiology of different HPV genotypes. Through this model we simulated the scenario that occurred in Australia in 2007, where 12-13 year-old girls where vaccinated with a three-dose schedule of a vaccine containing genotypes 6 and 11, that protect against genital warts, and also a catch-up program in women up to 26 years of age. Vaccine coverage were 73% in girls with three doses and with coverage rates decreasing with age until 52% for 20 − 26 year-olds. A fast 59% reduction in the genital warts diagnoses occurred in the model in the first years after the start of the program, similar to what was described in the literature.