Stability analysis and optimal control of avian influenza model on complex networks
• keguo ren,
• zhang qimin,
• Ting Kang
keguo ren
North Minzu University
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zhang qimin
School Mathematics and Computer Science, Ningxia University,
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Ting Kang
Ningxia University
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## Abstract

In this paper, an avian influenza model with saturation and psychological effect on heterogeneous complex networks is proposed. Firstly, the basic reproduction number $\mathscr{R}_{0}$ 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 $\mathscr{R}_{0}<1$, the disease-free equilibrium is globally asymptotically stable and the disease will die out. If $\mathscr{R}_{0}>1$, 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.

#### Peer review status:Published

25 Sep 2020Submitted to Mathematical Methods in the Applied Sciences
26 Sep 2020Submission Checks Completed
26 Sep 2020Assigned to Editor
06 Oct 2020Reviewer(s) Assigned
19 Feb 2021Review(s) Completed, Editorial Evaluation Pending
23 Feb 2021Editorial Decision: Revise Minor