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

Department of Mathematics, Faculty of Science, Ekiti State University, Ado — Ekiti, Ekiti State, P. O. Box 5363, Nigeria

E-mail Address: oluwatayo.ogunmiloro@eksu.edu.ng

Corresponding author.

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Kayode James Adebayo

Department of Mathematics, Faculty of Science, Ekiti State University, Ado — Ekiti, Ekiti State, P. O. Box 5363, Nigeria

E-mail Address: akj7070@yahoo.com

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https://doi.org/10.1142/S0129183123500080Cited by:0 (Source: Crossref)

Abstract

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 $R_{h p v}$ , 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 $R_{h p v}$ as to HPV prevalence and found that parameters $β_{1}, β_{2}, γ_{o}$ and $γ_{1}$ , which are the effective HPV transmission and progression to recovery parameters, are positively sensitive to $R_{h p v}$ . In order to minimize the increasing effect of $R_{h p v}$ 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.

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