Hopf bifurcation and optimal control studies for avian-influenza virus with multi-delay model

A mathematical model employing logistic growth is formulated to explore the dynamics of the avian influenza virus disease with multiple delays. Additionally, the stability of the system is explored, showing that Hopf bifurcation leads to oscillatory and periodic solutions when any combination of two time-delays is used as the bifurcation parameter. Our analysis covers the local stability of the disease-free and endemic equilibrium points considering all delay cases. Furthermore, the basic reproduction number has been analyzed for sensitivity with respect to the model parameters. The impact of slaughter intensity and an educational campaign are considered as control measures. To minimize disease outbreaks and control costs, the optimization problem is proposed and discussed the control strategy. Numerical simulations are provided to illustrate the analytical findings.