Since first time introduced by Kermack and McKendrick in 1927, Various models of epidemic models have been introduced, such as SIR, SIS, SEIR, SVIR, SVEIR, and so on. The existence and stability analysis of the equilibria is a routine things that is done by various authors. Furthermore, basic reproductive number is constructed to show the endemic level of the model.

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Here in this talk, we will discuss a Susceptible-Vaccinated-Infected-Recovered (SVIR) model to understand how a disease might spread among closed population. We include the awareness of population into the model. This awareness effect will make susceptible people become more aware to the danger of the disease. To construct the model, we divide human population based on their health status and their awareness status specially in susceptible population.

The model developed as 6 dimensional nonlinear ordinary differential equation. Existence and local stability criteria of equilibrium point analyzed analytically and numerically. Basic reproduction number also constructed to show how the disease might behave for long time period. Some numerical simulations will be shown for a better interpretation of previous analytical results.