Dynamical behavior and optimal control of a vector-borne diseases model on bipartite networks

•Propose a novel vector-borne diseases model with vaccination and quarantine control strategies on bipartite networks.•Prove global stability of the disease-free equilibrium and the endemic equilibrium.•Analyze the optimal control problem for reducing control cost.•Numerical model based on real data...

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Bibliographic Details
Published in:Applied Mathematical Modelling 2022-02, Vol.102, p.540-563
Main Authors: Zhao, Rundong, Liu, Qiming
Format: Article
Language:English
Subjects:
Bipartite networks
Control theory
Dynamical model
Global stability
Infectious diseases
Liapunov functions
Mathematical models
Optimal control
Vector-borne diseases
Vectors (Biology)
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Summary:•Propose a novel vector-borne diseases model with vaccination and quarantine control strategies on bipartite networks.•Prove global stability of the disease-free equilibrium and the endemic equilibrium.•Analyze the optimal control problem for reducing control cost.•Numerical model based on real data verifies the analysis results and the efficiency of the optimal control. For better application of vaccination control and quarantine control, a novel vector-borne diseases model with two control strategies on bipartite networks is proposed. By using complex network theory and Lyapunov function method, the basic reproduction number is obtained, and the global stability of disease-free equilibrium and endemic equilibrium are proved. Then the time-varying optimal control problem for reducing control cost is investigated. Using the optimal control theory, the existence and uniqueness of the optimal control and the model’s optimal solution are both studied. Finally, numerical simulations are carried out to verify the analysis results and the efficiency of the optimal control.
ISSN:0307-904X
1088-8691
0307-904X
DOI:10.1016/j.apm.2021.10.011