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Resumenes 112 Travelling Waves in a Model describing “mal de las caderas” in capybaras (Hydrochaeris hydrochaeris) including the vector presence. The aim of this work is to describe the capybara (Hydrochaeris hydrochaeris) dynamic. The model, proposed by Silvio Pregnolatto in [5], considers the presence of the ‘‘Mutuca’’ (Diptera: Tabanidae), vector which transmit the disease called ‘‘mal de las caderas’’ in Estero del Ibera, Argentina. The study of this problem have ecological and economical importance: for example de meat and the hide of the capybara can be an exploitable resource. An analysis of a possible exploitation has been made in [2]. The model is a system of partial differential equation of reactiondiffusion and transport. Four classes are studied: susceptible capybaras, infected capybaras, infected insects and non-infected insects. The dynamic is as follows: a susceptible capybara moves into the infected class by contact with an infected insect. A non-infected insect moves into the infected class by contact with an infected capybara. This is how the disease spreads. The mortality of the susceptible and infected capybaras are considered, and include external factors, such as predation, exploitation, or disease-related mortality. The mortality considered in the infected and noninfected insects is assume to be the same. The growth dynamic of both species is given by a logistic function. The diffusion is considered in both species, and is greater for the insects than for capybaras. The diffusion in infected capybaras is not considered because the disease affects the capybara’s mobility. At first, a threshold value is determined as a function of the model parameters, obtaining a critical carrying capacity for the disease propagation or eradication [10]. As the carrying capacity condition for the disease existence is satisfied , the existence of travelling wave solution is studied [3], [8]. Independent velocities are considered for the susceptible capybaras, the non-infected insect and the disease. The minimum speed of the disease propagation for this model is obtained [1], [4], [9], because the travelling wave solution with minimum speed is stable and represent the dynamic of the system [6], [7]. Control strategies are discusses to decrease the minimum speed of propagation in function of the model parameters. References [1] Tiemi Takahashi, L. Maidana, N.A., Castro Ferreira Jr., W. Petronio, P. Yang, H.M. (2005). Mathematical models for the Aedes aegypti dispersal dynamic: travelling waves by wings and wind. Bulletin of mathematical biology 67. 509-528. [2] Federico, P. Canziani, G.A. (2005). Modeling the population dynamic of capybara Hydrochaeris hydrochaeris: a first step towards a management plan. Ecological Modelling 186. 111-121. [3] Maidana, N.A. (2004). Algumas aplicaçoes das ondas viajantes a fenômenos biológicos. Ph. D. Tesis. IMEC-UNICAMP, CAMPINAS, BRASIL . [4] Abramson, G. Kenkre, V.M. (2003) Traveling waves of infections in the Hantavirus Epidemic. Bulletin of mathematical biology 65. 519-534.
Resumenes 113 [5] Pregnolatto S. de A. (2002). O mal das cadeiras em capivaras: estudo, modelagem e simulcao deum caso. Ph. D. Tesis. BAE-UNICAMP, CAMPINAS, BRASIL. [6] Sandstede, B. (2002). Stability of travelling waves. In: Fiedler, B. (Ed), Handbook of Dynamical System II. Elsevier, Amsterdam, pp 983-1059. [7] Volpert, A.I., Volpert, V.A. (1994). Travelling Waves Solutions of Parabolic System. American Mathematical Society, Providence, RI. [8] Murray, J.D. (1989). Mathematical Biology. Springer-Verlag, Berlin. [9] Murray, J.D. Stanley , E.A. Brown, D.L. (1986). On the Spatial Spread of Rabies Foxes. Proc. R. Soc. Lond. B229. 111-150. [10] Anderson, R.M., Jackson, H.C., May, R.M., Smith, A. (1981). Population dynamic of fox rabies in Europe. Nature, Lond. vol. 289. 765-771.
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ORGANIZADO POR LA SOCIEDAD LATINOAM
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(en orden alfabético) COMITÉ CIEN
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CURSILLOS Cursillo Nº1: Dinámica
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CONFERENCIAS INVITADAS
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Conferencias 10 Estabilidad y persi
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Conferencias 12 (K, the ‘carrying
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Conferencias 14 Víctimas Inmigrant
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Conferencias 16 Influencia de la di
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Resumenes 19 Bifurcaciones de Hopf
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Resumenes 21 where y = y(t) represe
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Resumenes 23 Dinámica del modelo d
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Resumenes 25 In this work, we propo
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Resumenes 27 Simulação computacio
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Resumenes 29 of the minisymposium:
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Resumenes 31 Honeybee, Apis mellife
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Resumenes 33 The minimum ratio is t
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Resumenes 35 [1] On the role of end
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Resumenes 37 Modelo matemático de
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Resumenes 39 Figure 1: Plano de fas
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Resumenes 41 Dinámica de poblacion
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Resumenes 43 El método de las solu
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Resumenes 45 Dinámica de un tumor
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Resumenes 47 Several cancer models
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Resumenes 49 process is physically
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Resumenes 51 For the analysis of fr
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Resumenes 53 Sustainability in floo
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Resumenes 55 Sincronismo em redes d
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Resumenes 57 Um modelo de autômato
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Resumenes 59 Um modelo matemático
Page 63 and 64: Resumenes 61 Redes de mapas acoplad
Page 65 and 66: Resumenes 63 Sobre la dinámica de
Page 67 and 68: Resumenes 65 Un modelo de depredaci
Page 69 and 70: Resumenes 67 There exists wide evid
Page 71 and 72: Resumenes 69 Modelado del control n
Page 73 and 74: Resumenes 71 Modelo de red neuronal
Page 75 and 76: Resumenes 73 Efectos de la radiaci
Page 77 and 78: Resumenes 75 Un modelo matemático
Page 79 and 80: Resumenes 77 Estudio comparativo de
Page 81 and 82: Resumenes 79 Introduction The proje
Page 83 and 84: Resumenes 81 formulation to obtain
Page 85 and 86: Resumenes 83 tiene un único punto
Page 87 and 88: Resumenes 85 [4] Courchamp, F., Clu
Page 89 and 90: Resumenes 87 An important part of a
Page 91 and 92: Resumenes 89 A(H3N2). Starting in V
Page 93 and 94: Resumenes 91 i) Panmixia, donde se
Page 95 and 96: Resumenes 93 punto de equilibrio y
Page 97 and 98: Resumenes 95 Un modelo epidemiológ
Page 99 and 100: Resumenes 97 Aproximación saddlepo
Page 101 and 102: Resumenes 99 [3] Daniels, H. E. 196
Page 103 and 104: Resumenes 101 bloqueados. El nudo q
Page 105 and 106: Resumenes 103 Referencias • Stauf
Page 107 and 108: Resumenes 105 Un modelo dinámico d
Page 109 and 110: Resumenes 107 Un modelo en ecuacion
Page 111 and 112: Resumenes 109 The mite show a prefe
Page 113: Resumenes 111 Ondas viajantes en un
Page 117 and 118: Resumenes 115 All this will enable
Page 119 and 120: Resumenes 117 Extensión de un mode
Page 121 and 122: Resumenes 119 ∂C ∂C C = 0. = 0.
Page 123 and 124: Resumenes 121 Comparación de Enfoq
Page 125 and 126: Resumenes 123 Refúgios Espaciais e
Page 127 and 128: Resumenes 125 La dinámica del sest
Page 129 and 130: Resumenes 127 Dinámica poblacional
Page 131 and 132: Resumenes 129 Aproximación y simul
Page 133 and 134: Resumenes 131 An age-structured fin
Page 135 and 136: Resumenes 133 Respuestas demográfi
Page 137 and 138: Resumenes 135 Modelando el efecto A
Page 139 and 140: Resumenes 137 the Allee effect are
Page 141 and 142: Resumenes 139 Tratamientos de endom
Page 143 and 144: Resumenes 141 Implicaciones del efe
Page 145 and 146: Resumenes 143 phenomenon has been e
Page 147 and 148: Resumenes 145 Dinámica individual
Page 149 and 150: Resumenes 147 • f mixing ⇔ f mi
Page 151 and 152: Resumenes 149 Introduction The inve
Page 153 and 154: Resumenes 151 DNA microarrays are t
Page 155 and 156: Resumenes 153 V. Cholerae: Primeros
Page 157 and 158: Resumenes 155 Análisis cuantitativ
Page 159 and 160: Resumenes 157 Dinámica de un model
Page 161 and 162: Resumenes 159 Obtención de paráme
Page 163 and 164: Resumenes 161 [4] Nagy K. A (1987)
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Resumenes 163 diferencial automáti
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Resumenes 165 The localized peaks S
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Resumenes 167 obteniéndose que sie
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Resumenes 169 [CLARK 90] Clark, C.
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Resumenes 171 Numerical algorithms
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Resumenes 173 The second method of
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Resumenes 175 los parámetros son t
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Resumenes 177 Bifurcación hacia at
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Resumenes 179 Malaria is the tropic
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