Mathematical model of human papillma virus (Hpv) With Optimal control

Abstract

In this thesis work, a deterministic mathematical model has been formulated to describe the transmission dynamic of human papilloma virus (HPV) using a system of non-linear ordinary differential equations with optimal control. The system has two equilibrium points, namely the disease free equilibrium point and the endemic equilibrium point which exists conditionally. The basic reproduction number R0 was calculated using the next-generation matrix and the stability of the equilibrium points were analyzed. From the qualitative analysis the disease free equilibrium point is both locally and globally stable if R0 < 1, and the endemic equilibrium point is also both locally and globally stable under some conditions on the system parameters. Furthermore, sensitivity analysis of the model equation was performed on the key parameters to find out their relative significance and potential impact on thetransmissiondynamicofHPV.Finallynumericalsimulationsofthemodelequationswere carriedoutusingMATLAB R2015b with ode45solver. Thesimulationsresultillustratedthat applyingcontrolstrategycansuccessfullyreducesthetransmissiondynamicofHPVdisease.