Multiple control strategies against human papilloma virus spread: A mathematical model

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 Rhpv, 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 Rhpv as to HPV prevalence and found that parameters β1,β2,γo and γ1, which are the effective HPV transmission and progression to recovery parameters, are positively sensitive to Rhpv. In order to minimize the increasing effect of Rhpv as regards the positive sensitive parameters, we re-construct the model via optimal control theory to incorporate controls of condom usage u1, vaccination u2 and medical counseling u3 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.