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In this paper, an avian influenza model with saturation and psychological effect on heterogeneous complex networks is proposed. Firstly, the basic reproduction number 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 ℛ0<1, the disease‐free equilibrium is globally asymptotically stable and the disease will die out. If 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.

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In this paper, we consider an optimal control model governed by a class of delay differential equation, which describe the spread of avian influenza virus from the poultry to human. We take three control variables into the optimal control model, namely: slaughtering to the susceptible and infected poultry (u 1 (t)), educational campaign to the susceptible human population (u 2 (t)) and treatment to infected population (u 3 (t)). The model involves two time delays that stand for the incubation periods of avian influenza virus in the infective poultry and human populations. We derive first order necessary conditions for existence of the optimal control and perform several numerical simulations. Numerical results show that different control strategies have different effects on controlling the outbreak of avian influenza. At the same time, we discuss the influence of time delays on objective function and conclude that the spread of avian influenza will slow down as the time delays increase.