Summary: Monotone systems are those systems whose solutions preserve an order on the initial conditions. Such systems are considered one of the most important classes of dynamical systems used in the analysis and control of mathematical biology models. This paper suggests a control approach for monotone input-output systems with multi-valued static characteristics. This class of monotone systems reveals multiple equilibrium points when constant inputs are applied. The design procedure, derived from a ‘generalized monotone small gain theorem’, results in a negative feedback law that guarantees the boundedness of the solutions and the output regulation at desired constant set-points. In addition, the proposed control method is generalized to the problems with the input and state constraints. This approach achieves control objectives without knowing or using the precise model of the system, but only through limited amount of qualitative and quantitative data provided from relatively simple experiments. To investigate the applicability of the proposed control technique, a model for the spread of Ebola virus disease is exploited. By means of the constrained control laws, the treatment aims to eventually regulate the system at the disease-free equilibrium point, at which the disease is completely eradicated.