Modeling and analysis of a human papilloma virus transmission model with impact of media

The human papillomavirus (HPV) is threatening human health as it spreads globally in varying degrees. On the other hand, the speed and scope of information transmission continues to increase, as well as the significant increase in the number of HPV-related news reports, it has never been more important to explore the role of media news coverage in the spread and control of the virus. Using a decreasing factor that captures the impact of media on the actions of people, this paper develops a model that characterizes the dynamics of HPV transmission with media impact, vaccination and recovery. We obtain global stability of equilibrium points employing geometric method, and further yield effective methods to contain the HPV pandemic by sensitivity analysis. With the center manifold theory, we show that there is a forward bifurcation when R0=1. Our study suggested that, besides controlling contact between infected and susceptible populations and improving effective vaccine coverage, a better intervention would be to strengthen media coverage. In addition, we demonstrated that contact rate and the effect of media coverage result in multiple epidemics of infection when certain conditions are met, implying that interventions need to be tailored to specific situations.

Mathematical analysis of a two-sex Human Papillomavirus (HPV) model

A two-sex deterministic model for Human Papillomavirus (HPV) that assesses the impact of treatment and vaccination on its transmission dynamics is designed and rigorously analyzed. The model is shown to exhibit the phenomenon of backward bifurcation, caused by the imperfect vaccine as well as the re-infection of individuals who recover from a previous infection, when the associated reproduction number is less than unity. Analysis of the reproduction number reveals that the impact of treatment on effective control of the disease is conditional, and depends on the sign of a certain threshold unlike when preventive measures are implemented (i.e. condom use and vaccination of both males and females). Numerical simulations of the model showed that, based on the parameter values used therein, a vaccine (with 75% efficacy) for male population with about 40% condom compliance by females will result in a significant reduction in the disease burden in the population. Also, the numerical simulations of the model reveal that with 70% condom compliance by the male population, administering female vaccine (with 45% efficacy) is sufficient for effective control of the disease.

MODELING VACCINE PREVENTABLE VECTOR-BORNE INFECTIONS: YELLOW FEVER AS A CASE STUDY

In this paper, we propose and simulate a deterministic model for a vector-borne disease in the presence of a vaccine. The model allows the assessment of the impact of an imperfect vaccine with various characteristics, which include waning protective immunity, incomplete vaccine-induced protection and adverse events. We find three threshold parameters which govern the existence and stability of the equilibrium points. Our stability analysis suggests that the reduction in the mosquito fertility theoretically is the most effective factor of reducing disease prevalence in both low and high transmission areas. To illustrate the theoretical results, the model is simulated by the example of yellow fever. We also perform sensitivity analyses to determine the importance of both vaccine-induced mortality rate and disease-induced mortality rate for determining a control strategy. We found that there is an optimum vaccination rate, above which people die by the vaccination and below which people die by the disease.