A State Feedback Vaccination Strategy Applied to a SISV Epidemic Model for Avoiding Endemic Equilibrium Points

A vaccination strategy based on the state feedback control theory is proposed. The objective is to fight against the propagation of an infectious disease within a host population. Such a propagation is modelled by means of a SISV (susceptible-infectious-susceptible-vaccinated) epidemic model with a time varying whole population and with a mortality directly associated with the disease. This model contains some free-design parameters, namely, the feedback gains of the vaccination control law. The paper analyses the positivity of such a model under the proposed vaccination strategy as well as the conditions for the existence of the equilibrium points of its normalized model. In this context, it is proved that an appropriate adjustment of the control gains avoids the existence of endemic equilibrium points in the normalized SISV model while guaranteeing the existence of a unique disease-free equilibrium point being globally asymptotically stable.