Optimal Vaccination and Treatment Schedules in a Deterministic Avian influenza Model

In this study, a transmission model of the Avian influenza disease was developed and analyzed in view of optimization of vaccination and medical treatment. The model is a host-vector model. We focussed on control of Avian influenza , where a vaccination is given to susceptible poultry, while medical treatment is given to infected humans. In the model, the human population is divided into four compartments: susceptible humans, infected humans, recovered humans, and treated humans. Meanwhile, the poultry population is divided into three compartments: susceptible poultry, infected poultry, and vaccinated poultry. To analyze the dynamical behavior of the model, we obtained the disease-free equilibrium, the endemic equilibrium, and the basic reproduction ratio. Furthermore, a model of the optimal vaccination and medical treatment schedule was constructed to know the optimal strategy for controlling Avian influenza . The model can be used to determine the minimal cost of controlling the disease. The model is solved by a genetic algorithm method. Numerical simulations showed that effective control of Avian influenza can be achieved with a combination of vaccination and medical treatment. Likewise, the optimal schedule and strategy for controlling Avian influenza are shown.