本計畫研究擴散時疫系統的行波解。考慮下列反應擴散系統 ut = d1uxx ? u + h(v); (1a) vt = d2vxx ? v + g(u); (1b) 其中t 0, x 2 R, di 0 for i = 1; 2. 此處u(x; t) 代表病菌的密度； v(x; t) 代表被感染人的密度； ? u 是病菌的自然死亡率； h(v) 代表被感染人對病菌密度成長的貢獻度； ? v 是被感染人密度的自然衰減率； g(u) 是人的被感染率； d1 與d2 分別是病菌與人的擴散係數。本計畫研究該系統的行波解的存在、單調、與唯一性。 This project concerns with the traveling wave solutions for the following reaction di?usion system arises from the spread of the epidemic with oral-fecal transmission, ut = d1uxx ? ?u + h(v); (1a) vt = d2vxx ? ?v + g(u); (1b) where t ? 0, x 2 R and di ? 0 for i = 1; 2. Here u(x; t) and v(x; t) stand for the spatial concentration of the bacteria and the spatial concentration of infective human population respectively in an urban community at time t and the point x in the one-dimensional habit region; ??u is the natural death rate of the bacterial population and h(v) is the contribution of the infective humans to the growth rate of the bacterial; ??v is the natural diminishing rate of the infective population due to the ?nite mean duration of the infectious population. The nonlinearity g(u) is the infection rate of the human population under the assumption that the total susceptible human population is constant during the evolution of the epidemic; d1 and d2 are di?usion coe?cients. We will investigate the existence, asymptotic behavior, monotonicity and uniqueness of traveling wave solutions.
