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    题名: 某個確定性流行病學模型和其相關的隨機流行病學模型;On the study of a deterministic and its related stochastic epidemiological population model
    作者: 曲紹瑜;Chu,Shao-Yu
    贡献者: 數學系
    关键词: 流行病學模型;epidemiological population model
    日期: 2016-07-13
    上传时间: 2016-10-13 14:47:51 (UTC+8)
    出版者: 國立中央大學
    摘要: 在本篇論文中,我們立足於SIS模型、SIR模型及具有Allee效應的一般性SI模型,並假設人口的生存和易感個體的群聚效應有關,其中,受感染類(I)會因為生殖及資源獲得的影響而有負面的影響。經由Allee效應在SI模型中的影響,簡單的模型具有了豐富的動態行為。在[1]中,得到以下結論,(i)一個物種的最大出生率、(ii)感染者的相對繁殖能力、(iii)一個感染者在低密度的競爭力、(iv)人口平均死亡率,可以穩定系統;(i) Allee效應、(ii)疾病的傳播率、(iii)感染者在高密度的競爭力,可以使系統不穩定,可能導致易感染者及感染者的滅絕。由於擾動的現象在自然界中時常發生,因此我們把這個模型擴展到隨機流行病學的跌代模型,以測試一般性SI模型是否能夠承受擾動。;In this work, we base on the research of the SIS model, SIR model and the general SI model with an Allee effect then assume that a population′s survival is dependent on the existence of a critical mass of susceptible individuals. The implications of this Allee effect is considered within the context of a Susceptible-Infectious (SI) model where infection has a negative effect on an individual′s fitness: with respect to both reproduction and resource acquisition. These assumptions are built into as simple a model as possible which yields surprisingly rich dynamics. In [1], we conclude that increases in (i) the maximum birth rate of a species, (ii) the relative reproductive ability of infected individuals, or (iii) the competitive ability of a infected individuals at low density levels, or in (iv) the per-capita death rate (including disease-induced) of infected individuals, can stabilize the system (resulting in disease persistence). Conversely, increases in (a) the Allee effect threshold, (b) disease transmission rates, or (c) the competitive ability of infected individuals at high density levels, can destabilize the system, possibly leading to the eventual collapse of the population. This highlights the significant role that factors like an Allee effect may play on the survival and persistence of animal populations. Scientists involved in biological conservation and pest management or interested in finding sustainability solutions, may find these results of this study compelling enough to suggest additional focused research on the role of disease in the regulation and persistence of animal populations. Owing to the disturbances occur usually to the nature, we extend this model into the stochastic epidemiological iteration population model to test whether the disturbances can be combined with the general SI model or not.
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