Modeling And Research Of Two Kinds Of Aids Based On Data Driven

AIDS is an infectious disease with high fatality rate,which has caused great harm to human life and health.So,a great deal of research has been done on the dynamics of HIV transmission and prevention strategies by many scholars.The results show that the patients of different stages and ages have great influence on the spread of the disease.Based on this point,this paper establishes an AIDS model with different window periods and different age groups.By studying the stability,bifurcation and optimal control of the model,and according to the actual data of AIDS in Gansu Province,the parameters of the model are reasonably estimated,and the important parameters of the model are determined through uncertainty and sensitivity analysis.Finally,the suggestions and measures for disease prevention and control are given.In Chapter 1,we not only introduce the background knowledge of AIDS and the research status at home and abroad,but also give the preliminary knowledge related to this paper.In Chapter 2,a novel HIV/AIDS model with different window period and treatment is proposed.Window period individuals and latent individuals are divided into two types:treated and untreated in our model.When receiving antiretroviral treatment,the infected person will not transmit the disease to others.According to the World Health Organization,when infected people receive antiretroviral treatment,they are no longer infectious,that is,they do not transmit the disease to others.By using the next generation matrix,the basic reproduction number R₀ is obtained.At the same time,the stability of disease-free equilibrium is proved.Using the theory of central manifold,the generation of forward bifurcation is established.Existence of the optimal control pair is analyzed and the mathematical expression of the optimal control is also given by the Pontryagin maximum principle.The best-fit parameter values in our model are identified by the MCMC algorithm on the basis of the AIDS data in Gansu province of China from 2004 to 2019.We also estimate that the basic reproduction number R₀ is 2.1985(95%CI:(1.3535-3.0435)).Numerical simulation and sensitivity analysis of several parameters are also presented.Our results suggest that individuals who are in the stage of window period for AIDS should receive treatment,and this plays a key role in the prevention and control of HIV/AIDS.In Chapter 3,a discrete age-structured HIV/AIDS model with public health education is studied.The model focuses on the impact of education and publicity on disease transmission.In the model,the population is divided into n different age groups,and public health education is considered as a compartment.The basic regeneration number R₀ is obtained by calculation.By constructing the Lyapunov function,the stability of the equilibrium point is obtained.Then,based on the AIDS data of different age groups in Gansu Province from2005 to 2017,the AIDS patients are divided into three age groups: 0-19 years old,20-49 years old and over 50 years old.The corresponding parameter estimation is given.At the same time,the basic regeneration number R₀ is 3.1780(95%CI:(1.3535-3.0435)).Finally,the important parameters are determined by discussing the uncertainty and sensitivity.The results show that when more and more people are receiving public health education,the infection rate of all ages can be reduced,and the number of people infected with diseases can be reduced.