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.

中文翻译：

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状态和控制变量具有多个时间延迟的禽流感模型的最优控制

在本文中，我们考虑了由一类时滞微分方程控制的最优控制模型，该模型描述了禽流感病毒从家禽到人的传播。我们将三个控制变量纳入最优控制模型，即：对易感和感染的家禽进行屠宰（$ u_ {1}（t）$），对易感人群进行教育运动（$ u_ {2}（t）$）和对感染人群的治疗（$ u_ {3}（t）$）。该模型涉及两个时间延迟，代表了禽流感病毒在感染家禽和人群中的潜伏期。我们得出存在最优控制的一阶必要条件，并进行几个数值模拟。数值结果表明，不同的控制策略对禽流感暴发的控制效果不同。