On a Class of Decentralized Feedback Controllers for the Networked Bivirus SIS Model

Recent work has established many properties of systems modeling the spread of two competing viruses in a population, and for networks with multiple connected populations with different spreading properties (e.g. men and women). This work considers the introduction of a class of nonlinear decentralized feedback controls aimed at reducing the fractions of populations infected at an endemic equilibrium. One surprising conclusion is that in some circumstances, new types of equilibria can arise. They can be viewed as an outcome of a transcritical bifurcation which is never observed for uncontrolled systems. In addition, we show that the controlled system is strongly monotone, and an unstable boundary equilibrium of the uncontrolled system cannot be stabilized using the class of decentralized state feedback controllers considered in this paper.