Abstract
In this research article we have developed a mathematical model to describe the spread of avian influenza A (H7N9) virus from the birds to human. We also consider the incubation periods of avian influenza A (H7N9) virus in this model with different time delay in the infective avian and human populations. By analyzing behaviour of the model, we calculate the basic reproduction number and investigate the local and global stability of equilibria of the system. Here we also set up an optimal control problem and used a quadratic control to reduce the spread of the disease and the cost of treatment. Computer simulations are carried out to explain the analytical findings.
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