基于基本再生率的流行病及其疫苗效果模型研究

发布时间：2019-05-05 16:53

【摘要】： 流行病是当今社会威胁人类最厉害的病种之一。由于其病毒的潜伏性,强感染性以及长存活性等特征,一直是困扰人类的一大难题。运用数学方法,对流行病的传播建立数学模型可以让我们对流行病传播机制有更好的理解。基本再生率R是对流行病表现形态的最直接的解释,若R 1,则表示流行病会逐渐消失,而当R 1,则表示流行病将会继续扩散。通过疫苗的使用能极大的影响到R值的大小,从而影响流行病,而疫苗的使用需要考虑费用和最优分配药剂量等问题。因此,围绕阈值理论或者基本再生率R的估计以及疫苗对流行病的抑制效果和相应的花费问题一直是诸多学者研究的重点。本文在Kermack-McKendrick、Batoszynski等人的研究基础上,给出了基本再生率的估计模拟,同时,在考虑疫苗注射花费的最优化模型上也对其他学者的研究做了推广。具体的工作概括如下: 1.基于家庭基本再生率估计模型及模拟。首先,我们给出了基于家庭的个体性差异的基本描述,通过对个体分布和传染概率等方面给出适当假设条件,利用似然方程的方法对这种模型的传播途径和感染概率进行描述,给出了基本再生率R和传染期参数分布的估计。最后用实验模拟了我们的估计方法。 2.考虑空间因素的基本再生率及模拟。首先,通过改变假设条件,我们给出了基于空间因素的家庭基本再生率模型,之后我们对这种模型的基本再生率和个体传染概率给出相应的估计,最后我们用实验模拟了考虑空间因素的流行病分布状态,并以实验的结果得出结论:当需要考虑距离因素时,在控制流行病时采取隔离小区域、家庭成员,关闭学校这些措施时应该可以达到更好的效果。 3.基于疫苗覆盖面的同特征个体的疫苗注射花费模型研究。在同特征人群中,我们以最优化疫苗费用为目标,建立线性规划模型,针对不同的疫苗覆盖面,求解最佳疫苗分配制度并给出一些数值例子做演示。
[Abstract]:Epidemics are one of the most dangerous diseases in society today. Because of its latent, strong infectivity and long-term activity, it has been a difficult problem for human beings. The mathematical model of epidemic transmission can help us to understand the mechanism of epidemic transmission better. The basic reproduction rate R is the most direct explanation of the epidemic pattern. If R 1, it indicates that the epidemic will gradually disappear, and when R 1, the epidemic will continue to spread. The size of R value can be greatly affected by the use of vaccines, thus affecting the epidemic, and the use of vaccines needs to consider the cost and the optimal distribution of drug dosage and other issues. Therefore, the estimation of threshold theory or the basic regeneration rate R, as well as the effect of vaccine on epidemic suppression and the corresponding cost have always been the focus of many scholars. Based on the research of Kermack-McKendrick,Batoszynski et al, this paper gives a simulation of the estimation of the basic regeneration rate, and also generalizes the research of other scholars on the optimization model considering the cost of vaccine injection. The specific work is summarized as follows: 1. Based on the family basic regeneration rate estimation model and simulation. First of all, we give a basic description of individual differences based on the family. By giving the appropriate assumptions on individual distribution and infection probability, we use likelihood equation to describe the transmission path and infection probability of this model, and make use of the method of likelihood equation to describe the transmission path and infection probability of this model. The estimation of the basic regeneration rate R and the parameter distribution of infection period are given. Finally, our estimation method is simulated experimentally. 2. The basic regeneration rate and simulation of space factors are considered. First of all, by changing the assumptions, we give a spatial factor-based family basic regeneration rate model, and then we give a corresponding estimate of the basic regeneration rate and individual infection probability of this model. Finally, we use experiments to simulate the distribution of epidemics taking into account spatial factors, and based on the results of the experiments, we conclude that when the distance factor needs to be taken into account, the epidemic should be controlled by isolating small areas and family members. These measures should achieve better results when closing schools. 3. Study on vaccine cost model of identical characteristic individuals based on vaccine coverage. In the same characteristic population, we set up linear programming model with the goal of optimizing vaccine cost, solve the optimal vaccine allocation system for different vaccine coverage, and give some numerical examples to illustrate it.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2010
【分类号】：R181.2;F416.72

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