在多个染病者群体中传播的血吸虫病模型的研究及分析

发布时间：2018-07-10 19:03

本文选题：血吸虫病 + 平衡点　；参考：《安徽大学》2017年硕士论文

【摘要】：本论文所要进行探讨的是关于血吸虫病在多个染病者群体中传播的数学模型,通过对模型稳定性分析及数值模拟,来推断不同发生率,不同感染度以及时滞对血吸虫病的影响.具体内容如下:1、研究了两种不同的发生率对这一类模型的影响,分别对采用双线性发生率和标准发生率产生的模型进行稳定性分析.求出模型的平衡点和疾病爆发的阈值,再分别讨论无病平衡点和地方病平衡点的稳定性情况,并通过数值模拟加以说明.2、在具有多个染病者群体的血吸虫病模型的基础上,考虑不同感染度对疾病的影响,着重考虑轻度感染者在一定条件下可以转化为重度感染者这一事实,我们对这一类模型进行修正,就不同感染度对病人数量和基本再生数的影响进行了讨论,发现轻度感染者转化为重度感染者会对疾病产生更加复杂的影响.3、引入时滞来讨论带时滞的血吸虫病模型,通过对此模型的稳定性分析及数值模拟发现时滞对此模型并无太大影响,但染病者的有效接触率对疾病有很大影响,尤其是轻度感染者的有效接触率对疾病有着深刻的影响.
[Abstract]:In this paper, the mathematical model of schistosomiasis transmission in multiple infected population is discussed. By analyzing the stability of the model and numerical simulation, we can infer the influence of different incidence, different infection degree and time delay on schistosomiasis. The specific contents are as follows: 1. The influence of two different incidence rates on this kind of model is studied. The stability of the model which is generated by bilinear rate and standard incidence is analyzed respectively. The equilibrium point of the model and the threshold of disease outbreak are obtained, and the stability of disease-free equilibrium point and endemic equilibrium point are discussed respectively. Considering the effects of different degrees of infection on the disease, and focusing on the fact that a mild infection can be converted into a severe infection under certain conditions, we have revised this type of model. The effects of different infection degrees on the number of patients and the number of basic regeneration were discussed. It was found that the transformation of mild infection to severe infection would have a more complex effect on the disease. The delay was introduced to discuss the schistosomiasis model with time delay. Through the stability analysis and numerical simulation of the model, it is found that the delay has no great influence on the model, but the effective contact rate of the infected person has a great influence on the disease, especially the effective contact rate of the mild infected person has a profound effect on the disease.
【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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