Modeling Filippov Control And Quarantine On Avian-Influenza Transmission

As an important zoonosis,avian influenza has been widely concerned.Avian influenza virus can accompany the migration of migratory birds and spread widely,resulting in huge losses.Therefore,prevention and control of avian influenza virus has become a major problem.From the epidemiological point of view,we propose two Filippov systems with threshold policies,and study different dynamic behaviors of the two systems under different threshold values.Firstly,we establish a Filippov system taking the number of infected birds as the index:if the number of infected birds does not exceed the threshold level I_c,no control measures will be taken;once the number of infected birds exceeds the threshold level I_c,the infected birds must be culled to prevent the further transmission of the disease.By constructing suitable Dulac function and Lyapunov functions,we obtain the global asymptotic stabilities of the real equilibria and pseudo-equilibrium.According to the theoretical results and numerical simulations,the solution of the model can either stablize at the endemic equilibrium of the two subsystems or at the pseudo equilibrium point of the sliding mode depending on different threshold levels.Secondly,we consider the impact of avian influenza on humans,and establish an SI-SIR avian influenza model with culling of infected birds,isolating infected hu-mans and reallocating of medical resources as control measures.The total number of infected birds and humans is taken as the index:if the number does not exceed the threshold I_T,no control will be taken;otherwise,if the number exceeds the threshold I_T,control measures are applied.Based on the threshold strategy,the SI-SIR avian influenza model is a three-dimensional Filippov system.According to the threshold level I_T,the solution of the model finally stabilizes at an endemic equilibrium or a pseudo-equilibrium.The numerical simulations show that a good threshold strategy can effectively control the transmission of the disease,so as to keep avian influenza in an acceptable or desired level.