3rd International Conference on Pure and Applied Mathematics-2020, Van, Turkey, 3 - 05 September 2020, pp.51
In this paper we introduce a vaccination model as mathematically in a population in which spread of a disease. This is a SVEIR model but it has some different aspcets to the class S. We assume that the susceptible individuals consist of two separate subgroups: susceptible individuals with high
risk and other susceptible individuals. Also these subgroups are vaccinated at different rates. This model considering the incubation period too, consists of a delay differential equation system.
We firstly present the equilibrium points and the reproduction number R_0 which is a vital threshold in spread of diseases. Then we give some results about the local and global stabilities of the equilibrium points according that R_0 is greater than one or not. To do these we use Lyapunov
function and LaSalle Invariance Principle . Finaly we present an example to show the effect of vaccination rate of high risk group to spread of the disease.