Research On Biological Population Model Based On Confounding Control

With the increasing quantification of biology,the application of mathematics in this field has become more and more inevitable.The mathematical model of population dynamics is a rapidly developing field,which plays a very important role in the study of population and their relationship.Among them,population and infectious disease dynamics models are mainly based on ordinary differential equations,which is an im?portant method for quantitative research.According to the growth characteristics of the population,the interaction among various groups,the occurrence,spread and de-velopment of infectious diseases,as well as the relevant social factors,it establishes a mathematical model that can reflect the dynamic characteristics of the population and infectious diseases.Through the qualitative,quantitative analysis and numerical simu-lation of the dynamic characteristics of the model,To show the development process of populations and diseases,to predict their development trends,and to analyze the causes and key factors,to find the optimal management control strategy.Qualitative analysis is basic and more important in the study of biomathematical models,mainly reflected in existence of solutions and local stability,etc.In addition,with the development of the economy,control systems have received more and more attention,and it has been widely used in various fields,such as ecosystems,disease treatment,genetic engineer-ing and pest control,especially the two hot topics of pest control of insecticides and the treatment of HIV infectious diseases in this era.This paper will proceed from these two directions.Differential equations with different control effects are used to describe its biological significance,and then a reasonable management scheme is proposed.In Chapter 2,we construct a population model of aphids based on drug resistance geno-types and controlled continuously.First,we verify the boundedness of the model.Then the existence and local stability of the equilibria of the model were discussed.Final-ly,based on the optimal algorithm,we not only obtained the optimal pesticide dose through numerical simulation,but also found that the number of aphids and insecticide resistance were reduced before and after the control,which achieves the desired effect.Both the quantity and insecticide resistance were reduced,which achieved the effect we wanted.In Chapter 3,we constructed a time-delayed response-diffusion virus im-mune model with threshold control under homogeneous Neumann boundary conditions.Here,the threshold level is designed to keep the number of viruses below a certain level.In this section,we first prove the existence and stability of the constant equilibria,and the Hopf branch value of the stability of the regular equilibria are obtained.Next,the direction,stability,and period of the Hopf branch are also studied.Furthermore,the complex dynamic behaviors such as the boundary node branch and the sliding domain are performed.At last,we give numerical simulation results and verify the correctness of the theoretical analysis.