Stability and bifurcations for a 3D Filippov SEIS model with limited medical resources

In this paper, a three-dimensional (3D) Filippov SEIS epidemic model is proposed to characterize the impact of limited medical resources on disease transmission with discontinuous treatment functions. Qualitative analysis of non-smooth dynamical behaviors are performed on two subsystems and sliding modes. Criteria on the stability of various kinds of feasible equilibria and bifurcations, e.g., saddle-node bifurcation, transcritical bifurcation, and boundary equilibrium bifurcation, are established. The theoretical results are illustrated by numerical simulation, from which we find there could exist bistable phenomena, e.g., endemic and pseudo-equilibria, endemic equilibria of the two subsystems, or endemic and disease-free equilibria, even the basic reproduction numbers of two subsystems are less than 1. The disease spread is dependent both on the limited medical resources and latent compartment, which are more beneficial to effective disease control than planar Filippov and smooth models.