An Age Structure Mathematical Model Analysis on the Dynamics of Chronic and Hyper Toxic Forms of Hepatitis B Virus by SVEA_1 A_2 CR Model with Vaccination Intervention Control Strategy in Ethiopia

Abstract

In our work we considered nonlinear ordinary differential equations to study the dynamics of hepatitis B virus (HBV) epidemics in Ethiopia. We proved that the invariant and bounded ness of the solution of the dynamical system. We used a nonlinear stability analysis method for proving the local and global stability of the existing equilibrium points. We have got that the diseases free equilibrium point and endemic equilibrium point exist for some conditions. We proved that the disease free equilibrium point is locally asymptotically stable and also globally asymptotically stable. We found that the effective reproduction number for the system is   which depends on fifteen parameters. On the other hand, the basic reproduction number is   Using standard parameter estimation we found that the numerical value of the effective reproduction number is and   From this numerical value we conclude that the disease spreads in the community and vaccination intervention strategy reduces the spread. Out of these fifteen parameters we identified five parameters which contribute significant role in control of the disease; and these are the rate of moving from exposed to acutely infected class with age below or equal to 5 years , the rate of moving from exposed to acutely infected class with age above 5 years the proportion of leaving acutely infected class with age below or equal to 5 years and progressing to chronically infected class ,the proportions of vaccinated newborns  and the ratio of vaccinated newborn  to total population H; which influence the effective reproduction number. We also conduct numerical simulations which support the finding in the sensitivity analysis.