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.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 uniq...Show More
Abstract: Moving boundary problems arise in many important applications to biology and chemistry. Comparing to the fixed boundary problem, moving boundary problem is more reasonable. To the best of our knowledge, there’s few results on the moving boundary for nonlinear first-order hyperbolic initial-boundary value problems. In the present paper, we mainly clarify the problem and show the existence and uniqueness of the solution for such kind of problems. We take a classical transform to straighten the moving boundary and develop a monotone approximation, based on upper and lower solutions technique, for solving a class of first-order hyperbolic initial-boundary value problems of moving boundary. Such an approximation results in the existence and uniqueness of the solution for the problem. The idea behind such a method is to replace the actual solution in all the nonlinear and nonlocal terms with some previous guess for the solution, then solve the resulting linear model to obtain a new guess for the solution. Iteration of such a procedure yields the solution of the original problem upon passage to the limit. A novelty of such a technique is that an explicit solution representation for each of these iterates is obtained, and hence an efficient numerical scheme can be developed. The key step is a comparison principle between consecutive guesses.Abstract: Moving boundary problems arise in many important applications to biology and chemistry. Comparing to the fixed boundary problem, moving boundary problem is more reasonable. To the best of our knowledge, there’s few results on the moving boundary for nonlinear first-order hyperbolic initial-boundary value problems. In the present paper, we mainly cl...Show More
=0.5677, implies that screening can reduce the transmission of the disease in the population when