本文選題：血吸蟲病 + 平衡點��； 參考：《安徽大學》2017年碩士論文

【摘要】：本論文所要進行探討的是關(guān)于血吸蟲病在多個染病者群體中傳播的數(shù)學模型,通過對模型穩(wěn)定性分析及數(shù)值模擬,來推斷不同發(fā)生率,不同感染度以及時滯對血吸蟲病的影響.具體內(nèi)容如下:1、研究了兩種不同的發(fā)生率對這一類模型的影響,分別對采用雙線性發(fā)生率和標準發(fā)生率產(chǎn)生的模型進行穩(wěn)定性分析.求出模型的平衡點和疾病爆發(fā)的閾值,再分別討論無病平衡點和地方病平衡點的穩(wěn)定性情況,并通過數(shù)值模擬加以說明.2、在具有多個染病者群體的血吸蟲病模型的基礎(chǔ)上,考慮不同感染度對疾病的影響,著重考慮輕度感染者在一定條件下可以轉(zhuǎn)化為重度感染者這一事實,我們對這一類模型進行修正,就不同感染度對病人數(shù)量和基本再生數(shù)的影響進行了討論,發(fā)現(xiàn)輕度感染者轉(zhuǎn)化為重度感染者會對疾病產(chǎn)生更加復雜的影響.3、引入時滯來討論帶時滯的血吸蟲病模型,通過對此模型的穩(wěn)定性分析及數(shù)值模擬發(fā)現(xiàn)時滯對此模型并無太大影響,但染病者的有效接觸率對疾病有很大影響,尤其是輕度感染者的有效接觸率對疾病有著深刻的影響.
[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.
【學位授予單位】：安徽大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175

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