本文關(guān)鍵詞： 生態(tài)流行病 全局穩(wěn)定性 平衡點(diǎn) 數(shù)值模擬　出處：《蘭州交通大學(xué)》2015年碩士論文　論文類(lèi)型：學(xué)位論文

【摘要】：流行病長(zhǎng)期威脅著人類(lèi)健康,在人類(lèi)發(fā)展的歷史長(zhǎng)河中扮演著不同的角色。它不僅威脅人類(lèi)生命財(cái)產(chǎn)安全,更是無(wú)數(shù)家禽牲畜的克星。近些年來(lái),不少專(zhuān)家學(xué)者研究了幾類(lèi)傳染病的流行規(guī)律。發(fā)現(xiàn)了傳染病既在人群中傳播,也在生物種群中傳播,而且很容易造成交叉感染。為此,研究生態(tài)流行病顯得尤為重要。(1)研究一類(lèi)具有治愈率且捕食者染病的生態(tài)流行病模型。通過(guò)雅可比矩陣判斷平衡點(diǎn)E0,E1的局部穩(wěn)定性,構(gòu)造Dulac函數(shù)判斷平衡點(diǎn)E0的全局穩(wěn)定性,得到當(dāng)此時(shí)患病的捕食者滅絕,食餌和易感捕食者共存。(2)分析食餌染病的生態(tài)流行病動(dòng)力學(xué)模型,討論了平衡點(diǎn)E0,E2的局部穩(wěn)定性。構(gòu)造V函數(shù)判斷平衡點(diǎn)E0的全局穩(wěn)定性,得到當(dāng)c(d2+u2)時(shí),V≤0。即食餌種群滅絕,捕食者種群持續(xù)生存。(3)探討一類(lèi)具有垂直傳染的生態(tài)流行病動(dòng)力學(xué)模型。根據(jù)當(dāng)R0≤1時(shí),平衡點(diǎn)E0的全局穩(wěn)定性以及當(dāng)R01時(shí),平衡點(diǎn)E*的全局穩(wěn)定性,進(jìn)行Matlab數(shù)值模擬,直觀地觀察食餌,捕食者種群數(shù)量隨時(shí)間t的變化情況。
[Abstract]:Epidemic disease is a long-term threat to human health and plays a different role in the history of human development. It not only threatens the safety of human life and property, but also the enemy of countless poultry and livestock in recent years. Many experts and scholars have studied the epidemic law of several infectious diseases, and found that infectious diseases not only spread among the population, but also in the biological population, and it is easy to cause cross-infection. A class of ecological epidemic models with cure rate and predator infection are studied. The local stability of equilibrium point E _ (0) E _ (1) is judged by Jacobian matrix. The Dulac function is constructed to determine the global stability of the equilibrium point E _ 0. When the diseased predator is extinct and the prey and susceptible predator coexist. In this paper, the local stability of equilibrium point E _ 0 E _ 2 is discussed. The global stability of equilibrium point E _ 0 is determined by constructing V function, and it is obtained that V 鈮，

本文編號(hào)：1471673