Stability analysis and optimal control of avian influenza model on complex networks

In this paper, an avian influenza model with saturation and psychological effect on heterogeneous complex networks is proposed. Firstly, the basic reproduction number Script capital R0 is given through mathematical analysis, which is a threshold to determine whether or not the disease spreads. Secondly, the locally and globally asymptotical stability of the disease-free equilibrium point and the endemic equilibrium point are investigated by using Lyapunov functions and Kirchhoff's matrix tree theorem. If Script capital R0<1, the disease-free equilibrium is globally asymptotically stable and the disease will die out. If Script capital R0>1, the endemic equilibrium is globally asymptotically stable. Thirdly, an optimal control problem is established by taking slaughter rate and cure rate as control variables. Finally, numerical simulations are given to demonstrate the main results.

Automated summary

This paper presents an avian influenza model for heterogeneous complex networks, with analyses on the basic reproduction number, stability of equilibrium points, and an optimal control problem. Numerical simulations are used to demonstrate the main results, including the conditions for disease spread and control strategies for the outbreak.