Narrow Results

In this paper, a model describing the transmission of Human Papilloma Virus (HPV) in a bisexually active human host community is presented. We analyze the model in a feasible region where the model is realistic in the sense of HPV transmission. Since the trivial equilibrium does not exist, we obtain the HPV-free equilibrium solutions and make use of the next generation matrix method to compute the basic reproduction number $R_{hpv}$, which governs HPV extinction and persistence whenever it is less or greater than unity, respectively. We perform the sensitivity analysis of the model parameters of $R_{hpv}$ as to HPV prevalence and found that parameters ${\beta }_1,{\beta }_2,{\gamma }_o$ and ${\gamma }_1$, which are the effective HPV transmission and progression to recovery parameters, are positively sensitive to $R_{hpv}$. In order to minimize the increasing effect of $R_{hpv}$ as regards the positive sensitive parameters, we re-construct the model via optimal control theory to incorporate controls of condom usage $u_1$, vaccination $u_2$ and medical counseling $u_3$ respectively. With these controls, we characterize and discuss the existence and uniqueness of the control model and solve the optimality system using the forward–backward Runge–Kutta fourth-order technique via the Matlab computational software. Simulations show that each of the control strategies is potent in combating HPV but the combination of the three controls proved more efficient in minimizing HPV infection in the human bisexual host community.

A new deterministic model for the transmission dynamics of human papillomavirus (HPV) and related cancers, in the presence of the Gardasil vaccine (which targets four HPV types), is presented. In the absence of routine vaccination in the community, the model is shown to undergo the phenomenon of backward bifurcation. This phenomenon, which has important consequences on the feasibility of effective disease control in the community, arises due to the re-infection of recovered individuals. For the special case when backward bifurcation does not occur, the disease-free equilibrium (DFE) of the model is shown to be globally-asymptotically stable (GAS) if the associated reproduction number is less than unity. The model with vaccination is also rigorously analyzed. Numerical simulations of the model with vaccination show that, with the assumed 90% efficacy of the Gardasil vaccine, the effective community-wide control of the four Gardasil-preventable HPV types is feasible if the Gardasil coverage rate is high enough (in the range 78–88%).

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Mathematical models are increasingly being used in the evaluation of control strategies for infectious disease such as the vaccination program for the Human Papillomavirus (HPV). Here, an ordinary differential equation (ODE) transmission dynamic model for HPV is presented and analyzed. Parameter values for a gender and risk structured model are estimated by calibrating the model around the known prevalence of infection. The effect on gender and risk sub-group prevalence induced by varying the epidemiological parameters are investigated. Finally, the outcomes of this model are applied using a classical mathematical method for calculating R₀ in a heterogeneous mixing population. Estimates for R₀ under various gender and mixing scenarios are presented.