AI 中文总结
研究流行病向不稳定健康状态的空间传播，通过数值求解方程和理论分析确定牵引与推动前沿的参数相空间，发现两者间的连续和不连续转变、双稳区域，且理论与数值结果相符。
AI 中文摘要
我们考虑流行病向不稳定健康状态的空间传播。当传播率取决于感染比例时，感染传播脉冲可以是牵引前沿或推动前沿。我们通过数值求解空间SIR偏微分方程以及对前沿传播现象进行理论分析，确定了牵引和推动区域的参数相空间。我们发现牵引和推动前沿解之间存在连续和不连续转变；在后者转变中，当某个参数越过临界阈值时，前沿速度会跳跃。分析了转变附近传播脉冲的行为，理论与数值结果吻合良好。最后，发现了一个能实现推动和牵引传播脉冲的双稳区域。
英文摘要
We consider the spatial spread of epidemic into an unstable, healthy state. When the transmission rate depends on the fraction of infected, the propagating pulse of infection can be either a pulled front or a pushed front. We determined the phase space of parameters for the pulled and pushed regions both by numerically solving the spatial SIR partial differential equations and by a theoretical analysis of the front propagation phenomenon. We found both a continuous and a discontinuous transition between the pulled and pushed front solutions; in the latter transition, the front speed undergoes a jump as a certain parameter crosses the critical threshold. The behavior of the propagating pulses near the transitions has been analyzed and a good agreement between the theory and numerics has been observed. Finally, a bistable region where both pushed and pulled propagating pulses can be realized has been discovered.
Comments6 pages, 6 figures
