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

Abstract

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.