Dynamic Analysis And Optimal Control Of A HIV Model With The Influence Of Awareness And Treatment

Based on the transmission mechanism of AIDS,ODE model was constructed to the impact of latent infection,conscious infection,unconscious infection and ART infection on outbreaks.Among them,it is assumed that people with conscious infection have self-awareness,and the transmission power of AIDS in the model is mainly affected by latent infection and unconscious infection.This work mainly discusses the theoretical analysis,numerical simulation and optimal control of the AIDS model.In the theoretical analysis part,the stability of each equilibrium point is verified according to the basic regeneration number,Routh Hurwitz stability criterion and Lyapunov function.The results of analysis showed that when R₀<1 the infection-free equilibrium of the HIV model is locally asymptotically stable,and when R_n>1 the unique endemic equilibrium is globally asymptotically stable.In the numerical simulation part,combined with the analysis of various influencing factors,it is found that the strength of controlling influencing factors has an important impact on eliminating disease transmission.For example,the novel coronavirus pneumonia outbreak in 2020,the government took various measures to control the disease.From the control results,the intensity of government measures will affect the spread of disease.In the optimal control part,control the influencing factors such as screening,education and publicity,treatment,analyze the existence of optimal control,and calculate the optimal control,the Euler Lagrange necessary conditions of the optimal control are obtained,and finally the weight of the control variables is changed to analyze the change of the number of infected persons.