PHYSICOCHEMICAL PROPERTIES AND BIOLOGICAL ACTIVITIES OF PEPPERMINT (Mentha piperita L.) LEAF OIL EXTRACT

Abstract

The main purpose of this study was to propose and analyze a nonlinear mathematical model for the transmission dynamics of cervical cancer due to human papillomavirus with vaccination. The aim of this study is to investigate the dynamics of cervical cancer and analyze a deterministic mathematical model for the spread of cervical cancer due to HPV dynamics with vaccination. To conduct the study, a deterministic mathematical model system of ordinary differential equation and numerical simulation were used. The total population (or sample size) of this model is sub-divided in to five compartments, namely; Susceptible (S), Vaccinated (V), Infected (I), permanently Recovered () and temporary Recovered (). Data of the study was collected through document analysis of recorded data and used to estimate the most influential parameters such as infection rate, vaccination rate and recovery rate. The model is studied qualitatively using stability theory of differential equations and the basic reproductive number that represents the epidemic indicator is obtained from the largest Eigen value of the next-generation matrix. Both local and global asymptotic stability conditions for disease-free and endemic equilibrium are determined. We used Maple 18 software in order to check the effect of some parameters in the expansion as well as in the control of cervical cancer dynamics. From the numerical simulation results we concluded that increasing the recovery rate has a great contribution to eradicate cervical cancer infection in the community and decreasing the contact rate can also have a great contribution to eliminate the cervical cancer. Moreover, our numerical simulation results indicated that increasing vaccination rate and decreasing contact rate is vital to eradicate the cervical cancer disease.