Computational modelling
Eshetu Dadi Gurmu; Boka Kumsa Bole; Purnachandra Rao Koya
Abstract
In this paper, optimal control problem is applied to Human Papillomavirus (HPV) and Herpes Simplex Virus type 2 (HSV-2) coinfection model formulated by a system of ordinary differential equations. Optimal control strategy is employed to study the effect of combining different intervention strategy on ...
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In this paper, optimal control problem is applied to Human Papillomavirus (HPV) and Herpes Simplex Virus type 2 (HSV-2) coinfection model formulated by a system of ordinary differential equations. Optimal control strategy is employed to study the effect of combining different intervention strategy on the transmission dynamics of HPV-HSV-II coinfection diseases. The necessary conditions for the existence of the optimal controls are established using Pontryagin’s Maximum Principle. Optimal control systems were performed with help of Runge-Kutta forward-backward sweep numerical approximation method. Finally, numerical simulation illustrated that a combination of all controls is the most effective strategy to minimize the disease from the community. The results shows that the size of infectious population are minimized by using different control strategies.
Eshetu Dadi Gurmu; Boka Kumsa Bole; Purnachandra Rao Koya
Abstract
The aim of study is to formulate and analyze a mathematical model for coinfection of sexually transmitted diseases HPV, HIV, and HSV-II. The well possedness of the developed model equations was proved and the equilibrium points of the model have been identified. Qualitative analysis of the formulated ...
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The aim of study is to formulate and analyze a mathematical model for coinfection of sexually transmitted diseases HPV, HIV, and HSV-II. The well possedness of the developed model equations was proved and the equilibrium points of the model have been identified. Qualitative analysis of the formulated model equations was proved and the equilibrium points of the model have been identified. Qualitative analysis of the formulated model was established using basic reproduction number. The results show that the disease free equilibrium is locally asymptotically stable if the basic reproduction is less than one. The endemic states are considered to exist when the basic reproduction number for each disease is greater than one. Finally, numerical simulations of the model equations are carried out using the software MATLAB R2015b with ODE45 solver. Numerical simulations illustrated that all infection solutions converge to zero when the basic reproduction number is less than unity.