THE SPREAD OF THE HEPATITIS B DISEASE WITH VACCINATION AND TREATMENT FACTORS - Wahyuni, Tri
Hepatitis b is an infectious disease caused by the hepatitis b virus or HBV. Transmissions of this disease can occur both vertically and horizontally in all age groups. This disease is one of the leading causes of death in the world. Therefore, it is necessary to analyze the spread of hepatitis b. One way that is done by making a mathematical model of the spread of this disease. The mathematical model that will be used is the SEICR model. The SEICR model divides the population in to five compartements, namely susceptible, exposed, infected, carriers, and recovered. The five compartements are distinguished based on individual body resistance to viruses. Derivation of mathematical models used will involve differential equations. From the differential equation we will get fixed points obtained can be divided into two, namely the disease-free fixed point and endemic fixed point. Endemic fixed points are divided into four cases, namely fixed points for cases without vaccination and treatment control, without vaccination with treatment, with vaccination without treatment, as well as with vaccination and treatment. The fixed points obtained will then be analyzed its stability and existence of a fixed point is determined by the parameter values used. In addition to the fixed point, we also get the basic reproduction number or ????0. Basic reproduction numbers show the spread of disease in population. If ????0<1 is obtained, the spread of HBV will cease so that disease will disappear and the population be free from disease. Meanwhile if ????0>1, the disease will spread to the population. Therefore, vaccination and treatment control will be observed the effect on the model.