Stability analysis and optimal vaccination of an SIR epidemic model

作者：Zaman Gul; Kang Yong Han; Jung Il Hyo^*

来源：Biosystems, 2008, 93(3): 240-249.

DOI：10.1016/j.biosystems.2008.05.004

• population models
• stability
• optimization
• vaccination
• numerical simulation
• smoking dynamics

Almost all mathematical models of diseases start from the same basic premise: the population can be subdivided into a set of distinct classes dependent upon experience with respect to the relevant disease. Most of these models classify individuals as either a susceptible individual S, infected individual I or recovered individual R. This is called the susceptible-infected-recovered (SIR) model. In this paper, we describe an SIR epidemic model with three components; S, I and R. We describe Our study of stability analysis theory to find the equilibria for the model. Next in order to achieve control of the disease, we consider a control problem relative to the SIR model. A percentage of the susceptible populations is vaccinated in this model. We show that an optimal control exists for the control problem and describe numerical simulations using the Runge-Kutta fourth order procedure. Finally, we describe a real example showing the efficiency of this optimal control.

• 出版日期2008-9