本篇論文討論的是SIR模型的反應擴散方程
s_t = d_1 s_xx − βsi/(s + i),
i_t = d_2 i_xx + βsi/(s + i) − γi,
r_t = d_3 r_xx + γi,
之行進波的存在性，其中模型描述的是在一個封閉區域裡流行疾病爆發的狀態。這裡的 β 是傳播係數，γ 是治癒或移除(即死亡)速率，s 是未被傳染個體數，i 是傳染源個體數，d_1、d_2、d_3分別為其擴散之係數。
我們將使用Schauder不動點定理(Schauder fixed point theorem)、Arzela-Ascoli定理和最大值原理(maximum principle)來證明：該系統存在最小速度為c=c*:=2√(d2( β - γ ))之行進波解。我們的結果回答了[11]裡所提出的開放式問題。 / In this thesis, we study the existence of traveling waves of a reaction-diffusion equation for a diffusive epidemic SIR model
s_t = d_1 s_xx − βsi/(s + i),
i_t = d_2 i_xx + βsi/(s + i) − γi,
r_t = d_3 r_xx + γi,
which describes an infectious disease outbreak in a closed population. Here β is the transmission coefficient, γ is the recovery or remove rate, and s, i, and r rep-resent numbers of susceptible individuals, infected individuals, and removed individuals, respectively, and d_1, d_2, and d_3 are their diffusion rates. We use the Schauder fixed point theorem, the Arzela-Ascoli theorem, and the maximum principle to show that this system has a traveling wave solution with minimum speed c=c*:=2√(d2( β - γ )). Our result answers an open problem proposed in [11].
| Identifer | oai:union.ndltd.org:CHENGCHI/G1027510071 |
| Creators | 余陳宗, Yu, Chen Tzung |
| Publisher | 國立政治大學 |
| Source Sets | National Chengchi University Libraries |
| Language | 英文 |
| Detected Language | English |
| Type | text |
| Rights | Copyright © nccu library on behalf of the copyright holders |
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