Near-optimal control of a stochastic avian influenza model with multi-time delays and spatial diffusion on complex networks

Avian influenza commonly called “bird flu” is a viral infectious disease of global public health concern. To investigate the impact of control strategies on avian and human populations, we formulate a stochastic avian influenza model with multi-time delays and spatial diffusion on complex networks, which considers the high variability of highly pathogenic avian influenza viruses and the effect of the incubation period on infected individuals. The well-posedness of the model is proved by constructing some suitable Lyapunov functions. Regarding the slaughter of birds and some treatments of human populations infected with avian and mutated avian viruses as control measures, the near-optimal control problem of stochastic model is developed to minimize expenses as much as possible with the limited resource allocation. Utilizing Ekeland’s variational principle and the Pontryagin random maximum principle, conditions that are both necessary and sufficient are derived for achieving near-optimality, which is supported by preliminary estimates of the state equations along with the adjoint processes. Theoretical results are validated through the presentation of numerical simulations.