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Sensitivity Analysis and Modeling the Impact of Screening on the Transmission Dynamics of Human Papilloma Virus (HPV)
American Journal of Applied Mathematics
Volume 7, Issue 3, June 2019, Pages: 70-79
Received: Jun. 21, 2019; Accepted: Jul. 22, 2019; Published: Aug. 26, 2019
Authors
Eshetu Dadi Gurmu, Department of Mathematics, Wollega University, Nekemte, Ethiopia
Purnachandra Rao Koya, Department of Mathematics, Wollega University, Nekemte, Ethiopia
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Abstract
In this paper, a mathematical model on the Human Papilloma Virus (HPV) governed by a system of ordinary differential equations is developed. The aim of this study is to investigate the role of screening as a control strategy in reducing the transmission of the disease. It is shown that a solution for the system of model equations exists and is unique. Further, it is shown that the solution is both bounded and positive. Hence, it is claimed that the model developed and presented in this paper is biologically meaningful and mathematically valid. The model is analyzed qualitatively for verifying the existence and stability of disease free and endemic equilibrium points using threshold parameter that governs the disease transmission. Furthermore, sensitivity analysis is performed on the key parameters driving Human Papilloma Virus and to determine their relative importance and potential impact on the dynamics of Human Papilloma Virus. Numerical result shows that Human Papilloma Virus infection is reduced using screening strategies. Due to the presence of interventions, the number of susceptible cells decreases implying that, most of the susceptible cells are screened. Similarly, the number of unaware infected cells decreases. This happens because unaware cells become aware after screening. The screened infected cells initially increase and then start to diminish after the equilibrium point. This is because many people from screened class recovered through treatment. Also, the number of cells with cancer decreases and this may be due to disease induced death. Furthermore, the number of recovered cells increases because there are two ways of recovering, through immune system or treatment. With =0.5677, implies that screening can reduce the transmission of the disease in the population when <1.
Keywords
HPV Infection, Sensitivity Analysis, Screening, Basic Reproduction Number, Stability Analysis, Jacobian Matrix, Numerical Simulation
Eshetu Dadi Gurmu, Purnachandra Rao Koya, Sensitivity Analysis and Modeling the Impact of Screening on the Transmission Dynamics of Human Papilloma Virus (HPV), American Journal of Applied Mathematics. Vol. 7, No. 3, 2019, pp. 70-79. doi: 10.11648/j.ajam.20190703.11
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