Transmission dynamics and optimal control of H7N9 in China

H7N9 avian influenza is a highly pathogenic zoonotic disease. In order to control the disease, many strategies have been adopted in China such as poultry culling, the closure of live poultry markets (LPMs), the vaccination of poultry, and the treatment for humans. Due to the limited resource, it is of paramount significance to achieve the optimal control. In this paper, an epidemic model incorporating the selective culling rate is formulated to investigate the transmission mechanism of H7N9. The threshold dynamics and bifurcation analyses of the model are well investigated. Furthermore, the problem of optimal control is explored in line with Pontryagin's Maximum Principle, with consideration given to the comprehensive measures. The numerical simulations suggest that the vaccination of poultry and the closure of LPMs are the two most economical and effective measures.