Research On Foreign Biological Propagation And Diffusion Model

Alien invasive organisms have brought great harm to the ecosystems and even human health in some regions.Using mathematical models to study the prevention and control strategies of invasive alien organisms can provide the theoretical basis for the control and control of relevant departments.We mainly use the theory and methods of differential equation stability and functional differential equations to study the modeling and dynamic behavior of invasive organisms,and we have obtained many meaningful results.The first part studies the stage structure model of alien invasive organisms.Considering plant species that carry pests and disease stages,a model of plant infestation of organisms was established,and the system's non-invasive equilibrium balance points and intruder equilibrium points were given.The system intrusion was given using Lyapunov stability theory.A sufficient condition for the asymptotic stability of the equilibrium point.In the second part,the invasive biological model with the incidence of saturation and insecticide spraying was studied.When considering theinfection rate as the saturation occurrence rate,the basic reproduction number of the system was first obtained and the system's non-intrusion equilibrium point and intrusion equilibrium point were obtained by calculation.Secondly,the first approximation method of stability was used to prove that there was no intrusion equilibrium point.The local asymptotic stability and the second additive composite matrix theory are used to obtain the sufficient conditions for the global asymptotic stability of the intruder equilibrium.Finally,the consistent persistence of the system is proved.The numerical simulation is used to verify the conclusion.In the third part,we study the time-delay model of invasion of foreign organisms with the rate of saturation.One is to calculate and analyze the system's non-intrusion equilibrium point,intrusion equilibrium point,and basic regeneration number.The second is to discuss the stability of the equilibrium point using the Lyapunov stability theory to obtain sufficient conditions for the local asymptotic stability of the two types of equilibrium points;The principle of LaSalle invariant sets discusses the global stability of non-intrusive equilibrium points and intrusion equilibrium points,and proves that the system is consistent and persistent.