Traveling wave solutions for a diffusive SIR model

• Main Authors: Yu, Chen Tzung, 余陳宗
• Other Authors: Fu, Sheng Chen
• Format: Others
• Language: en_US
• Online Access: http://ndltd.ncl.edu.tw/handle/29m432

碩士 === 國立政治大學 === 應用數學系 === 105 === 　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].