Statistical Model Based On Antiviral Therapy Associated With The AIDS Epidemic

As AIDS epidemic has become one of the most serious global public health and social event, HAART was used in AIDS patients in various degree for every country in the world. The present treatment policy can effectively suppress virus replication and rebuild the immune function of HIV-infected people, and also can improve quality of life and reduce morbidity and mortality of patients, however, HAART can not clear the virus completely. Patients need to take medicine for life. Drug adverse effects and resistance may appear with the long-term medicine-taking, which could reduce the living quality. Moreover, antiviral therapy can prolong the lifespan of HIV infected individuals, which consequently make them have more opportunities to infect others. So in terms of individual therapy and epidemic control, whether antiviral therapy is effective for infection control, or in what circumstance antiviral therapy is effective for infection control is still controversial and need a further study. Based on previous immune-virus dynamics and pharmacokinetic modeling,this study introduces the influence of virologic load variation on treatment effect and HIV epidemic with long-term treatment. Antiviral therapy can extend the life expectancy of HIV infected individuals, reduce the risk of clinical progression of disease, and ultimately produce a significant influence on the whole natural progression. In different long-term policies of HAART, what we focus on is how to keep the balance between drug adverse effects and the risk of HIV new infection.Section1:a virologic load model with individual antiviral therapy. In order to estimate side effect of antiviral therapy, disadvantages of continuous(or discontinuous) therapy, and simulate and predict the progression of disease, we improve the traditional virus dynamic model and introduce several variations like the life expectancy, treatment effect, drug resistance and sensibility. We use a series of ways, including different iterative dynamic models, to investigate optimal initial treatment time, the optimal time to switch therapy, the optimal CD4cell threshold value, the continuity, drug resistance and adherence of treatment policy, and simulate the model of the progression of virologic load under antiviral therapy and the model of different therapy policies. We study the relationship between individual drug concentration and effect in different medications through formulating the model combined virus dynamic model with pharmacokinetic model. Then we can analyze individual virus load, the change of well or infected CD4cell counts, and confirm pivotal parameters, finally on the base of which we formulate the complex model about microscopic virus dynamic model and macroscopical HIV epidemic. We use the way of theoretical analysis and numerical modeling to investigate dynamics of the complex model, the effectiveness of intervening measures and different therapy policies and predict the development tendency of HIV epidemic.Section2:The statistic model for estimating AIDS epidemic. This section mainly focused on the development of the epidemic of AIDS by a composite model, combining micro virus dynamics models with macro infectious disease dynamics models. In the macro dynamic modes, we introduced starting time, resistance, efficacy of the treatment and analyzed relations among them. This study established a bridge between these two modeling system, which is helpful to investigate the impact that antiviral therapy based on individuals has on HIV infected rate of China.In order to reduce the number of variables we introduced two factors to describe variation rate in infectiousness and disease progression rates respectively, used Latin Hypercube Sampling (LHS) and partial rank correlation coefficients (PRCCs) to examine the dependence and sensitivity of the reproduction number RO and the expected number of HIV-positive individuals in2015and got important influencing parameters. Meanwhile, according to the CD4+T cell counts in the blood, we divided the HIV-positive individuals to several stages and formulated a mathematical model with antiviral therapy. It proved that the disease-free equilibrium is globally asymptotically stable when Ro<1, whilst the system is uniformly persistence when R0>1.We studied the effect of antiviral therapy in two situations:antiviral therapy started immediately once diagnosed and started when CD4+T count is less than350cells per μL. There exists a critical value for the infectiousness below which immediate treatment once diagnosed is better than the current policy in terms of the reproduction number. Whereas, current policy exhibits better than immediate treatment if the infectiousness is greater than the critical level. The result also indicated when the infectiousness is relatively low (relatively good treatment efficacy) increasing treatment coverage will decrease the reproduction number and lead to new HIV infection decline, whilst increasing treatment coverage will result in an increase in new HIV infection for the relatively great infectiousness, which is in agreement with that for heterogeneous transmission. This indicates that if treatment efficacy is relatively good our conclusions suggest immediate treatment with high uptake rate, otherwise the current policy is reasonable.Using the data on the number of individuals living with HIV (not AIDS) or AIDS by year among MSM, we obtained estimates of the reproduction number, intervention parameter values and the high-risk population size. Our estimated reproduction number Ro is3.88(95%CI3.69-4.07). From the estimated parameters we know that the transmission coefficient β0is much larger than the estimation for heterosexual transmission and general high-risk population. Our estimation also shows that the diagnose rate among MSM is much lower than that for other high-risk population. Meanwhile, we estimated that the antiviral therapy coverage rate among MSM in2011is less than the estimation by China. Simulation results show that strengthening education to high-risk population and increasing surveillance and testing can slow down the spread of disease. Increasing treatment uptake rate may lead to HIV new infection decline, depending on infectiousness and behavior changes. Further, sensitivity analysis implies the most influential parameters are infection rate β0and disease related death rate for HIV-positive individuals α1. Note that high efficacy drug can reduce the transmission probability of HIV per high-risk behavior, and the education may reduce the contact rate and increase the condom use rate. This means that a high effective drug and timely education may effectively control HIV epidemic.In this study, we also applied trend surface analysis, spatial autocorrelation analysis and regression analysis to analysis and predict the epidemic of AIDS in Yunnan province, China, and found that many factors, such as the geographical distribution of railways, drug of abuse and commercial sexual actor, could contribute to different distribution of AIDS in different areas. Our modeling provided a further study to find the inducement of illness onset for gathering areas.The main original points in this study:First, in our statistic model we took into account the influence of individual virus progression with long-term therapy on the drug concentration, treatment effect and AIDS epidemic. Meanwhile, we tried to figure out the effect taking drugs in different ways on the evolution of HIV and the generation of resistance. Second, what influences the optimal initial treatment time, treatment courage, the change of individual or average virologic load have on the morbidity and mortality of patients were also discussed. Third, based on the data of high-risk groups queue, national AIDS epidemic and lab testing, Bayes statistic method was used to estimate the parameters of the model. At last, we estimated the HIV reproduction number(R0) of MSM systemically, evaluated the sensibility of Ro and got the influence that each parameter had on Ro, which could help us to make interventions.