Diversified Global HIV/AIDS Epidemic Model With The Intervention Of Vaccine And Drug Therapy

AIDS is called Acquired Immune Deficiency Syndrome, the acronym for AIDS, which spread rapidly with high mortality rate. By far human beings are still at a loss of AIDS. In addition, the spread of AIDS in the global trend became more and more fierce. According to Global Report from UNAIDS in 2008, almost three million people became newly infected with HIV. At the global level, the number of people living with HIV continues to grow - from 30 million in 2001 to 33 million in 2007. In the same year, almost three million were killed by AIDS; over 29,000,000 people, which is far more than the total number of people died in the war in 20th century, have died since the first cases of AIDS were identified in 1981.The research for epidemic spread of infectious diseases, especially AIDS, has been always the target of scholars and specialists. For the research of spread of HIV, some scholars may just adopt some simple observed and statistical data to make analysis and inference. This is not an effective way to reflect the nature of its epidemic.In fact, Mathematical models can be used as predictive and determining policy tools. Many scholars have made some valuable research. Hethcote [1,2] used to obtain the results for some simplest epidemiological models that the infectious disease spreads in a population which either is a fixed closed population or has a fixed size with balancing inflows and outflows. Gonzalez-Guzman analyzed an SIS model for the spread of typhoid by considering the direct as well as indirect transmission with the flow of bacteria from infective people into the environment without considering the explicit equation for bacteria. Blower S. [3, 4] made a great amount of contribution in this area, including some research on the estimate of the vaccine effect through some mathematical models. French scholars B.Cazelles [5] and N.P.Chau [5] used to use Kalman Filter models to access the changing HIV epidemic, but they adopt the method of functional analysis. Wang La-di [6] and Li Jian-quan [6] discussed an seis epidemic model with nonlinear incidence model. Apiradee Lim [10] uses a statistical method for forecasting demographic time series counts and applies to HIV/AIDS and other infectious disease mortality in Southern Thailand. Now there are many method discuss the problem of disease spread, such as traditional SIR model, SI model, and differential equation, dynamics, time series and so on.However, some domestic scholars just considered HIV/AIDS transmission as other common infectious diseases and lose sight of specific features for AIDS, while some others ignored some interventions like ARV drug therapy and preventative vaccine. Moreover, some international scholars made some really interesting thought, but most of them focus on the qualitative analysis of model theory, seldom we saw that some models give us some conspicuous, intuitionistic and trenchancy impression and figure through an example, especially for some concrete country.To make some more quantitative and more systematic analysis, in this paper, we established time series model, optimization model, grey model, and dynamics model to approximate the expected rate of change in the number of HIV/AIDS infections for these countries from 2008 to 2050 and contrasted these four different models in different background.In grey model, we first shortly introduced the method of Grey model first, especially for GM (1,1) model, and then estimated the number of HIV/AIDS infections of Haiti from 2008 to 2050. In optimization model, we found that the limited capital should be used to work on developing vaccine at first; after that, the surplus money will be for ARV drug therapy. We took more attention on time series model and dynamics model. In the time series models, we used sufficient data and ARIMA (p,d,q) to simulate the trend of HIV/AIDS epidemic of Russian Federation, China and some other countries. We draw the conclusion that AIDS case reports and AIDS deaths have been dramatically reduced in industrialized countries with the introduction of ARV drug therapy, like Russia, Germany, and France. Simultaneously, China and some other developing countries will face outburst of HIV/AIDS in few years, if the government will not take some urgent and positive measures.In the dynamics model we considered four different scenarios: (1) the absence of any additional interventions; (2) ARV drug therapy; (3) a preventative HIV/AIDS vaccine; (4) simultaneous ARV drug therapy and vaccine impact. Finally, we draw the conclusion that the vaccine makes great contributions in the reduction of HIV/AIDS infections and has several advantages while compare with the ARV drug therapy. Importantly, we should devote ourselves to actively promoting the funding the R&D and improvement of the vaccines. On the other hand, we should not neglect to assist in providing a significant amount of medication, as the medication treatment is still an indispensable way to control the spread of the disease before the new vaccine comes into being. That is, first we put our money into the medication areas to keep maintaining the transmission of the disease at a low level in 2008-2010, and then we go on to invest in HIV/AIDS preventative vaccine.