Global dynamics of a Filippov epidemic system with nonlinear thresholds

Abstract

Due to the intermittency of prevention and control measures, the right-hand function of the dynamic model describing the spread of infectious disease is often induced to be nonsmooth, which can be formulated by employing Filippov systems and have been widely studied recently. Note that these systems only consider the number of infected individuals as the switching threshold. However, infectious disease control depends not only on the number of infected individuals, but also on the change rate of infected individuals. To address this, we propose a Filippov system with media-influenced nonlinear thresholds which integrate the change rate of infected individuals into the threshold strategy. The main results reveal that the proposed threshold strategy can induce the complex dynamic behavior, including multiple sliding segments and pseudo-equilibrium. Furthermore, our main results show that variations of threshold (ET) and the nonlinear threshold control strategy not only lead to rich dynamics including bistability, but also have important implications for disease control.