Study On The Propagation Model Of Alien Species And Its Prediction

In this paper,we mainly use the mathematical modeling method to study the comprehensive treatment of invasive alien species.We establish differential equation models of invas ive alien species to discuss the existence and stability of the system equilibrium point.And also we carry out the numerical simulation according to the actual situation.It provides a strong theoretical basis for the comprehensive treatment of alien species.In the third chapter,based on the invas ion of Bursaphelenchus xylophilus,we divide the pine trees into three categories(Susceptible,Infectious and Remove)and establish a single population differential equation model species by using the method of population dynamics,considering the use chemical agents and other factors.The existence and stability of the positive equilibrium point of the system are discussed by using the first approximation method of stability.At the same time,the time-varying propagation rate of the insect pest was discussed according to the number of diseased trees.The fourth chapter uses the numerical analysis method.On the one hand,the theoretical results of the third chapter are numerically simulated to verify the correctness of the conclusion.On the other hand,according to the actual pests of Qiandao Lake,we forecast and predict the propagation of Bursaphelenchus xylophilus according to different propagation rate ? and different removal coeffic ient h.And the time-varying propagation rate is also calculated.The results show that reducing the effective propagation rate ? and increasing the removal coeffic ient h can play a positive role in the treatment of Bursaphelenchus xylophilus.In the fifth chapter,according to the case that Hainan Province introduces Eulophidae and Tetrastichus to control the alien species Brontispa longissima,we establish a differential equation of three groups considering the interrelationships of the three populations of Brontispa longissima,coconut tree and Brontispa longissima's natural enemies.Secondly,the existence and stability of the non-enemy equilibrium point and enemy equilibrium point are proved respectively.Finally,the numerical analysis shows that the effect of biocontrol using the natural enemies of Brontispa longissima is better than that of the chemical treatment alone.