Dynamic Behavior Of Avian Influenza Models On Complex Networks

Avian influenza is an animal disease caused by avian influenza A virus.Avian influenza generally targets specific species,but the virus can infect humans by crossing species barriers in rare cases.In recent decades,avian influenza viruses have become widespread all over the world,threatening public safety and causing huge enormous economic losses.Therefore,it is of great value to study the spreading rules and control measures of avian influenza.We concerns the dynamic behavior of avian influenza models with saturation on heterogeneous complex networks in this paper,the main contents are as follows:1.In order to reflect the heterogeneity of contacting between individuals,an avian in-fluenza model with saturation and psychological effect on heterogeneous complex networks is proposed.Firstly,the basic reproduction number R₀is given through mathematical analy-sis,which is a threshold to determine whether or not the disease spreads.Secondly,the local-ly and globally asymptotical stability of the disease-free equilibrium point and the endemic equilibrium point are investigated by using Lyapunov functions and Kirchhoff's matrix tree theorem.If R₀<1,the disease-free equilibrium is globally asymptotically stable and the disease will die out.If R₀>1,the endemic equilibrium is globally asymptotically stable.Thirdly,an optimal control problem is established by taking slaughter rate and cure rate as control variables.Finally,numerical simulations are given to demonstrate the main results.2.For a complex system,it is difficult to find the optimal solution,and optimal control even does not exist in many cases.So we concerns the near-optimal control of an avian influenza model with saturation on heterogeneous complex networks.Firstly,the basic re-production number R₀is defined for the model,which can be used to govern the threshold dynamics of influenza disease.Secondly,the near-optimal control problem was formulat-ed by slaughtering poultry and treating infected humans while keeping the loss and cost to a minimum.Thanks to the maximum condition of the Hamiltonian function and the Eke-land's variational principle,we establish both necessary and sufficient conditions for the near-optimality by several delicate estimates for the state and adjoint processes.Finally,a number of examples presented to illustrate our theoretical results.