Stability behavior of a two-susceptibility SHIR epidemic model with time delay in complex networks

Taking two susceptible groups into account, we formulate a modified subhealthy-healthy-infected-recovered (SHIR) model with time delay and nonlinear incidence rate in networks with different topologies. Concretely, two dynamical systems are designed in homogeneous and heterogeneous networks by utilizing mean field equations. Based on the next-generation matrix and the existence of a positive equilibrium point, we derive the basic reproduction numbers R-0(1) and R-0(2) which depend on the model parameters and network structure. In virtue of linearized systems and Lyapunov functions, the local and global stabilities of the disease-free equilibrium points are, respectively, analyzed when R-0(1) < 1 in homogeneous networks and R-0(2) < 1 in heterogeneous networks. Besides, we demonstrate that the endemic equilibrium point is locally asymptotically stable in homogeneous networks in the condition of R-0(1) > 1. Finally, numerical simulations are performed to conduct sensitivity analysis and confirm theoretical results. Moreover, some conjectures are proposed to complement dynamical behavior of two systems.

Automated summary

This study proposes a modified SHIR model with time delay and nonlinear incidence rate for two susceptible groups in networks with different topologies. By analyzing the basic reproduction numbers and stability of equilibrium points, the study examines disease spread in homogeneous and heterogeneous networks. Numerical simulations and theoretical analysis are used to study the dynamics of two systems and propose conjectures.