A Filippov Model Describing the Effect of Social Distancing in Controlling Infectious Diseases

Social distancing is now a familiar strategy for managing disease outbreaks, but it is important to understand the interaction between disease dynamics and social behaviour. We distinguished the fully susceptibles from the social-distancing susceptibles and proposed a Filippov epidemic model to study the effect of social distancing on the spread and control of infectious diseases. The threshold policy is defined as follows: once the number of infected individuals exceeds the threshold value, social-distancing susceptibles take more stringent social-distancing practices, resulting in a decreasing infection rate. The target model exhibits novel dynamics: in addition to the coexistence of two attractors, it also demonstrates the coexistence of three attractors. In particular, bistability of the regular endemic equilibrium and the disease-free equilibrium occurs for the system; multistability of the regular endemic equilibrium, a pseudo-equilibrium and the disease-free equilibrium also occurs for the system. Discontinuity-induced bifurcations, including boundary-node, focus and saddle-node bifurcations, occur for the proposed model, which reveals that a small change in threshold values would significantly affect the outcome. Our findings indicate that for a proper threshold value, the infections can be ruled out or contained at the previously given level if the initial infection is relatively small.