發(fā)布時(shí)間：2018-07-10 19:03

  本文選題：血吸蟲(chóng)病 + 平衡點(diǎn)��； 參考：《安徽大學(xué)》2017年碩士論文

【摘要】：本論文所要進(jìn)行探討的是關(guān)于血吸蟲(chóng)病在多個(gè)染病者群體中傳播的數(shù)學(xué)模型,通過(guò)對(duì)模型穩(wěn)定性分析及數(shù)值模擬,來(lái)推斷不同發(fā)生率,不同感染度以及時(shí)滯對(duì)血吸蟲(chóng)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(duì)這一類模型的影響,分別對(duì)采用雙線性發(fā)生率和標(biāo)準(zhǔn)發(fā)生率產(chǎn)生的模型進(jìn)行穩(wěn)定性分析.求出模型的平衡點(diǎn)和疾病爆發(fā)的閾值,再分別討論無(wú)病平衡點(diǎn)和地方病平衡點(diǎn)的穩(wěn)定性情況,并通過(guò)數(shù)值模擬加以說(shuō)明.2、在具有多個(gè)染病者群體的血吸蟲(chóng)病模型的基礎(chǔ)上,考慮不同感染度對(duì)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(shí),我們對(duì)這一類模型進(jìn)行修正,就不同感染度對(duì)病人數(shù)量和基本再生數(shù)的影響進(jìn)行了討論,發(fā)現(xiàn)輕度感染者轉(zhuǎn)化為重度感染者會(huì)對(duì)疾病產(chǎn)生更加復(fù)雜的影響.3、引入時(shí)滯來(lái)討論帶時(shí)滯的血吸蟲(chóng)病模型,通過(guò)對(duì)此模型的穩(wěn)定性分析及數(shù)值模擬發(fā)現(xiàn)時(shí)滯對(duì)此模型并無(wú)太大影響,但染病者的有效接觸率對(duì)疾病有很大影響,尤其是輕度感染者的有效接觸率對(duì)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(xué)位授予單位】：安徽大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175

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本文編號(hào)：2114378