Optimal control of an avian influenza model with multiple time delays in state and control variables

In this paper, we consider an optimal control model governed by a class of delay differential equation, which describe the spread avian influenza virus from poultry to human. We take three variables into model, namely: slaughtering susceptible and infected (\begin{document}$ u_{1}(t) $\end{document}), educational campaign human population id="M2">\begin{document}$ u_{2}(t) $\end{document}) treatment id="M3">\begin{document}$ u_{3}(t) $\end{document}). The involves two time delays that stand for incubation periods in infective populations. derive first order necessary conditions existence perform several numerical simulations. Numerical results show different strategies have effects on controlling outbreak influenza. At same time, discuss influence objective function conclude will slow down as increase.