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標題: 捕食與被捕食族群皆帶有傳染病的數學模式研究
A predator-prey model with infection in both populations
作者: 蕭金魁
Hsiao, Chin-Kuei
關鍵字: predator-prey model;捕食模式;disease infection;global stability analysis;basic reproduction numbers;unique periodic solution;傳染病;穩定性分析;分歧現象;傳染基數;週期解
出版社: 應用數學系所
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In this work, we propose a predator-prey model with disease infection in both populations. Global analysis is given for the disease free model. For the full model with disease, we obtain five threshold parameters (or basic reproduction numbers). Coupled conditions given in the form of the threshold parameters are needed for the local stability of the equilibria under consideration. One of the conditions, in the form of a basic reproduction number for the predator-prey system, always determines the coexistence of the predators and prey; the other condition, in the form of a basic reproduction number for the infectious disease, dictates whether the disease will be eradicated. This phenomenon of dual conditions was also ob-served by Hethcote et al. [16, 17] in their studies of predator-prey model with infection in the prey population. In some cases, the existence of a unique periodic solution which is orbitally stable is obtained through numerical simulation. The mathematical proof of uniqueness and existence of periodic solution, as well as the stability of endemic positive equilibrium, are still the open problems.
其他識別: U0005-2305200609381700
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