Partial stability of controlled SEIR epidemic models

This paper proposes to use the concept of partial stability instead of that of global stability to analyze the dynamic behavior of epidemic models. The rationale behind this is that it is only needed, from a practical point of view, to ensure the boundedness of the infectious and infected subpopulations in order to get the disease under control. Thus, the partial stability of a controlled SEIR epidemic model is studied in the vaccination-free case. It will be proved that the infectious and infected subpopulations may still be bounded when the total population increases and global stability is not achieved. In addition, a feedback-based vaccination policy is designed based on the concept of partial stability of the closed-loop system. Some numerical simulations illustrating the usefulness of the designed control law along with a comparison with previous vaccination laws complete the paper.