A feedback vaccination law for an SIR epidemic model: A case study

An SIR (Susceptible-Infected-Removed) epidemic model is mathematically analyzed while obtaining its equilibrium points and analyzing their stability. A feedback-infection dependent vaccination control law is proposed and studied. Finally, the mathematical model is applied to study the evolution of the common influenza in the Autonomous Community of the Basque Country (Spain). The infection has been parametrized using experimental data published by the medical services. With the obtained parameters different simulations are made to visualize the effects of a proportional vaccination in the number of infected individuals. It is seen that the vaccination decreases the overshoots compared to the vaccination-free case.