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姓名 曲紹瑜(Shao-Yu Chu)  查詢紙本館藏   畢業系所 數學系
論文名稱 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)
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摘要(中) 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。
摘要(英) 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.
關鍵字(中) ★ 流行病學模型 關鍵字(英) ★ epidemiological population model
論文目次 中文摘要 ……………………………………………………………………… i

目錄 ……………………………………………………………………… ii

英文摘要 ……………………………………………………………………… iii

零 Notation …………………………………………………………… 1

一 Introduction …………………………………………………… 3

二 The SIS model and the SIR model …………………………… 6

三 The general SI model with an Allee effect ……………… 10

四 Stochastic epidemiological iteration population model … 15

五 conclusion remark ……………………………………………… 24

六 Future work ……………………………………………………… 26

參考文獻 ……………………………………………………………………… 27
參考文獻 [1] Kang. Y., and C. Calos Castillo,
A Simple Epidemiological Model for Populations in The Wild with Allee Effects and Disease-Modified Fitness,
{sl Discrete and Continuous Dynamical Systems Series B}, (2014), pp. 89-130.

[2] Ramasubramanian. B.,
Stochastic Differential Equations in Population Dynamics,
pp. 1-19.

[3] Hutson. V.,Sheffield,
A Theorem on Average Liapunov Functions,
{sl Monatsheftefur Mathematik}, 98 (1984), pp. 267-275.

[4] Hsu. S. B.,
Ordinary Differential Equations with Applications,
{sl World Scientific}, pp. 157.

[5] Kuo. H. H.,
Introduction to Stochastic Integration,
{sl Springer}, pp. 102-137.

[6] Shlomo. S.,
Dynamical Systems,
(2011), pp. 204-211.

[7] I. Bendixson.,
Sur les curbes d′e fini´es par des ′e quations diff′e rentielles,
{sl Acta Math}, 24 (1901), pp. 1-88.

[8] H. Dulac.,
Recherche des cycles limites,
{sl C. R. Acad. Sci. Paris}, 204 (1937), pp. 1703-1706.

[9] C. Castillo-Chavez, K. Cooke, W. Huang and S. A. Levin, Results on the dynamics for models for the sexual transmission of the human immunodeficiency virus, Applied Math. Letters, 2 (1989), 327-331.

[10] A. Cintron-Arias, C. Castillo-Chavez, L. M. Bettencourt, A. L. Lloyd and H. T. Banks, Estimation of the effective reproductive number from disease outbreak data, Math. Biosc. $&$ Eng., 6 (2009), 261-282.

[11] H. Hethcote and J. Yorke, Gonorrhea: Transmission Dynamics and Control, Lecture Notes in Biomathematics, 56, Springer-Verlag, Berlin, 1984.

[12] W. F. Fagan, M. A. Lewis, M. G. Neubert and P. Van Den Driessche, Invasion theory and biological control, Ecology Letters, 5 (2002), 148-157.

[13] Z. Feng, C. Castillo-Chavez and A. Capurro, A model for tb with exogenous reinfection, Journal of Theoretical Population Biology, 57 (2000), 235-247.

[14] G. Dwyer, S. A. Levin and L. Buttel, A simulation model of the population dynamics and evolution of myxomatosis, Ecological Monographs, 60 (1990), 423-447.

[15] F. Courchamp,T. Clutton-Brock and B. Grenfell, Multipack dynamics and the Allee effect in the African wild dog, Lycaon pictus, Animal Conservation, 3 (2000), 277-285.

[16] F. M. Hilker, M. Langlais and H. Malchow, The Allee Effect and Infectious Diseases: Extinction, Multistability, and the (Dis-)Appearance of Oscillations, The American Naturalist, 173 (2009), 72–88.

[17] H. R. Thieme, T. Dhirasakdanon, Z. Han and R. Trevino, Species decline and extinction: Synergy of infectious disease and Allee effect?, Journal of Biological Dynamics, 3 (2009), 305-323

[18] D. Pauly, V. Christensen, S. Guenette, T. J. Pitcher, U. R. Sumaila, C. J. Walters and D. Zeller, Towards sustainability in world fisheries, Nature, 418 (2002), 689-695.

[19] K. Sherman and A. M. Duda, Large marine ecosystems: An emerging paradigm for fishery sustainability, Fisheries, 24 (1999), 15-26.

[20] F. S. Berezovskaya, B. Song and C. Castillo-Chavez, Role of prey dispersal and refuges on predator-prey dynamics, SIAM J. APPL. MATH., 70 (2010), 1821-1839

[21] C. Castillo-Chavez and A. A. Yakubu, Dispersal,disease and life history evolution, Math. Biosc., 173 (2001), 35-53.

[22] F. Berezovskaya, G. Karev, B. Song and C. Castillo-Chavez, A simple epidemic model with surprising dynamics, Mathematical Biosciences and Engineering, 2 (2005), 133-152.

[23] R. M. Anderson and R. M. May, Regulation and stability of host-parasite population interactions I: Regulatory processes; II: Destabilizing processes, J. Anita. Ecol. 47 (1978), 219-247; 249-267.

[24] P. Daszak, L. Berger, A. A. Cunningham, A. D. Hyatt, D. E. Green and R. Speare, Emerging infectious diseases and amphibian population declines, Emerging Infectious Diseases, 5 (1999), 735-748.

[25] C. D. Harvell, C. E. Mitchell, J. R. Ward, S. Altizer, A. P. Dobson, R. S. Ostfeld and M. D. Samuel, Climate warming and disease risks for terrestrial and marine biota, Science, 296 (2002), 2158-2162.

[26] K. F. Smith, D. F. Sax and K. D. Lafferty, Evidence for the role of infectious disease in species extinction and endangerment, Conservation Biology, 20 (2006), 1349-1357.

[27] W. C. Allee, The Social Life of Animals, Norton, New York, 1938.

[28] F. Courchamp, L. Berec and J. Gascoigne, Allee Effects in Ecology and Conservation, Oxford University Press, 2008.

[29] Y. Kang and N. Lanchier, Expansion or extinction: deterministic and stochastic two-patch models with Allee effects, Journal of Mathematical Biology, 62 (2011), 925-973.

[30] P. A. Stephens and W. J. Sutherland, Consequences of the Allee effect for behaviour, ecology and conservation, Trends in Ecology $&$ Evolution, 14 (1999), 401-405.

[31] P. A. Stephens, W. J. Sutherland and R. P. Freckleton, What is the Allee effect?, Oikos, 87 (1999), 185-190.

[32] L. Berec, D. S. Boukal and M. Berec, Linking the Allee effect, sexual reproduction, and temperature-dependent sex determination via spatial dynamics, The American Naturalist, 157 (2001), 217-230.

[33] K. R. Hopper and R. T. Roush, Mate finding, dispersal, number released, and the success of biological control introductions, Ecological Entomology, 18 (1993), 321-331.

[34] R. Lande, Anthropogenic, ecological and genetic factors in extinction and conservation, Re- searches on Population Ecology, 40 (1998), 259-269.

[35] J. C. Gascoigne and R. N. Lipcius, Allee effects driven by predation, Journal of Applied Ecology, 41 (2004), 801-810.

[36] B. R. Clark and S. H. Faeth, The consequences of larval aggregation in the butterfly Chlosyne lacinia, Ecological Entomology, 22 (1997), 408-415.

[37] R. Burrows, H. Hofer and M. L. East, Population dynamics, intervention and survival in African wild dogs (Lycaon pictus), Proceedings of the Royal Society B: Biological Sciences, 262 (1995), 235-245.

[38] E. Angulo, G. W. Roemer, L. Berec, J. Gascoigne and F. Courchamp, Double Allee effects and extinction in the island fox, Conservation Biology, 21 (2007), 1082-1091.

[39] D. L. Clifford, J. A. K. Mazet, E. J. Dubovi, D. K. Garcelon, T. J. Coonan, P. A. Conrad and L. Munson, Pathogen exposure in endangered island fox (Urocyon littoralis) populations: implications for conservation management, Biological Conservation, 131 (2006), 230-243.

[40] L. J. Rachowicz, J.-M. Hero, R. A. Alford, J. W. Taylor, J. A. T. Morgan, V. T. Vredenburg, J. P. Collins and C. J. Briggs, The novel and endemic pathogen hypotheses: Competing explanations for the origin of emerging infectious diseases of wildlife, Conserv. Biol., 19 (2005), 1441-1448.

[41] L. F. Skerrat, L. Berger, R. Speare, S. Cashins, K. R. McDonald, A. D. Phillott, H. B. Hines and N. Kenyon, Spread of chytridiomycosis has caused the rapid global decline and extinction of frogs, EcoHealth, 4 (2007), 125-134.

[42] A. Deredec and F. Courchamp, Combined impacts of Allee effects and parasitism, OIKOS, 112 (2006), 667-679.

[43] F. M. Hilker, M. A. Lewis, H. Seno, M. Langlais and H. Malchow, Pathogens can slow down or reverse invasion fronts of their hosts, Biol. Invasions, 7 (2005), 817-832.

[44] A-A. Yakubu, Allee effects in a discrete-time SIS epidemic model with infected newborns, Journal of Difference Equations and Applications, 13 (2007), 341-356.

[45] F. M. Hilker, Population collapse to extinction: The catastrophic combination of parasitism and Allee effect, Journal of Biological Dynamics, 4 (2010), 86-101.

[46] A. Friedman and A-A. Yakubu, Fatal disease and demographic Allee effect: Population per- sistence and extinction, Journal of Biological Dynamics, 6 (2012), 495C-508.

[47] J. M. Cushing, Oscillations in age-structured population models with an Allee effect. Oscillations in nonlinear systems: Applications and numerical aspects, J. Comput. Appl. Math., 52 (1994), 71-80.

[48] A. Drew, E. J. Allen and L. J. S. Allen, Analysis of climate and geographic factors affecting the presence of chytridiomycosis in Australia, Dis. Aquat. Org., 68 (2006), 245-250.

[49] K. E. Emmert and L. J. S. Allen, Population persistence and extinction in a discrete-time stage-structured epidemic model, J. Differ. Eqn Appl., 10 (2004), 1177-1199.

[50] S. R.-J. Jang and S. L. Diamond, A host-parasitoid interaction with Allee effects on the host, Comp. Math. Appl., 53 (2007), 89-103.

[51] Y. Kang and D. Armbruster, Dispersal effects on a two-patch discrete model for plant- herbivore interactions, Journal of Theoretical Biology, 268 (2011), 84-97.

[52] O. Diekmann and M. Kretzshmar, Patterns in the effects of infectious diseases on population growth, Journal of Mathematical Biology, 29 (1991), 539-570.
指導教授 陳建隆(Jann-Long Chern) 審核日期 2016-7-13
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