A Study Of Two Types Of Dynamic HIV Transmission Models With Media Influence

In this paper,the dynamics of two types of HIV transmission models under the influence of media were studied.The numerical simulation analyses were given to support the theoretical results obtained.In the second chapter,we discussed a class of HIV infection model with delay effects of media.The positive solution of the model was proved by using the theory of delay differential equations.The boundedness of the solution of the model was proved by the comparison theorem of the ordinary differential equations and exponential bounded definition of delay differential equations.Through the discussion of characteristic equations,the local asymptotic stability of the disease-free equilibrium and the local asymptotic stability of the media-absnet equilibrium were analyzed.The media-absnet equilibrium??is locally asymptotically stable for all??0.If the conditions?₁,?₂hold,then for all??0,the equilibrium point?^?was locally asymptotically stable.Numerical simulation results showed that the increase of delay of media would lead to an increase in HIV-infected population.Effectively strengthening the media's propaganda and reporting can reduce the number of HIV infections.Analysis through discussion of delay differential equations,we suggest that the media report HIV infection information to shorten the time delay as much as possible.We also suggest that health authorities release HIV epidemic information as soon as possible to reduce the increase in the number of infected people caused by delay.In the third chapter,we discussed the stability of a class of HIV model with media influence on the consciousness classification of key areas and key populations.Through the discussion of characteristic equations,the local asymptotic stability of the disease-free equilibrium and the local asymptotic stability of the media-absnet equilibrium were analyzed.The conditions for the local asymptotic stability of the disease-free equilibrium?₀,media-absnet equilibrium??,media-present endemic equilibrium?^?were given.With the increase of media transmission coefficient,the number of infected people decreases.We suggest that the media should report the spread of HIV infection or that the health authorities should strengthen the propaganda in key areas and key populations,and that the society should strengthen the construction of information infrastructure so that the healthy lifestyle can be popularized to the public,especially,in key areas and key populations,through the media at an early date.Actively promote sexual protection education in key areas and key populations,such as conducting safe sex,promoting condom penetration,and strengthening drug control to avoid the risk of disease transmission caused by repeated use of syringes,the media should strengthen the information dissemination of such measures.