Cotton Bollworm-cotton Modeling And Dynamics Analysis With Disease Transmission

Cotton is China's most important cash crop,and it is the most important agricultural product and strategic material besides food.Cotton production has an irreplaceable position in the development of the national economy.With the rapid development of China's economy and the improvement of people's living standards,cotton has a great impact on people's lives.The cotton bollworm is dependent on cotton growth.The cotton bollworm grows by eating cotton.It is an important drill borer in the cotton bud and boll stage,which caused huge losses to cotton production.The control of cotton bollworm is of great significance.First,based on the characteristic that cotton bollworm attaches to the growth of cotton,combined with the theory of infectious disease model,the bilinear incidence rate of cotton bollworm-cotton SIS infectious disease model is established.And find the positive equilibrium point and basic regeneration number of the system of equations.Prove the asymptotic stability at the equilibrium point using Hurwitz's theorem,and simulate it by numerical simulation.Secondly,considering that the action of the cotton bollworm is slow and the contact rate with other cotton bollworms will become smaller,and there is a certain distance between cotton and cotton,based on the original model,we have constructed a disease with the saturation incidence of cotton bollworm-cotton SIS infectious disease model,Proving the global stability of the positive equilibrium point by constructing Lyapunov function.At the same time,it was concluded that the amount of bollworm and cotton reached a balance.Finally,considering the dynamic model of cotton and cotton bollworm is closer to real life.Based on the basic knowledge of complex networks and its propagation dynamics theory,this paper establishes a mathematical model of cotton bollworm-cotton under a non-uniform network.