Nonlinear switching control for suppressing the spread of avian influenza

Abstract

This paper proposes a novel method of killing birds and applying vaccines for suppressing the spread of avian influenza via a nonlinear switching control approach. The switching strategy is based on the population of the susceptible birds and the population of the susceptible humans. There are four switching cases. For the first three switching cases, the elimination control force and the quarantine control force are equal to either zero or one. For the last switching case, they are equal to one minus a scalar divided by the population of the susceptible birds and one minus another scalar divided by the population of the susceptible humans, respectively. The system state vectors of the avian influenza model are guaranteed to reach the desirable equilibrium point. Also, the positivity requirements on the system states as well as the constraints on both the lower bounds and the upper bounds of both the elimination control force and the quarantine control force are guaranteed to be satisfied. Computer numerical simulation results show that the proposed control strategy is very effective and efficient.