Abstract

Ismail Husein, Herman Mawengkang, Saib Suwilo, Mardiningsih.

The model of spread of infectious diseases is research that must be done continuously as the development of infectious diseases. Although medical measures can reduce the consequences of infectious diseases, preventing the spread of infectious diseases is the main action that must be taken. Vaccination is a method commonly used to control the spread of communicable diseases today. This study aims to develop an epidemic model that warts proposed by Kermark and Mc Kendrick in 1927 in the form of S, I and R. compartments. The method used was an experiment by adding V compartment which is a vaccination. The results show that the point remains disease free to become asymptotically stable when the number of basic reproduction is less than one which means that the disease will not spread in the population and eventually the disease will disappear from the population. Whereas the endemic point will be asymptotically stable when the number of basic reproduction is more than one which means that the disease Exists. This study can be concluded that based on the stability analysis shows that the vaccination process is entirely dependent on the basic reproduction rate.