Department of Mathematical Sciences, KAIST, Daejeon, 34141, Republic of Korea.
Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano ku, Tokyo, 164-8525, Japan.
Bull Math Biol. 2023 Mar 27;85(5):35. doi: 10.1007/s11538-023-01138-3.
The bacterial traveling waves observed in experiments are of pulse type which is different from the monotone traveling waves of the Fisher-KPP equation. For this reason, the Keller-Segel equations are widely used for bacterial waves. Note that the Keller-Segel equations do not contain the population dynamics of bacteria, but the population of bacteria multiplies and plays a crucial role in wave propagation. In this paper, we consider the singular limits of a linear system with active and inactive cells together with bacterial population dynamics. Eventually, we see that if there are no chemotactic dynamics in the system, we only obtain a monotone traveling wave. This is evidence that chemotaxis dynamics are needed even if population growth is included in the system.
在实验中观察到的细菌传播波是脉冲类型的，与 Fisher-KPP 方程的单调传播波不同。出于这个原因，Keller-Segel 方程被广泛应用于细菌波的研究。需要注意的是，Keller-Segel 方程并不包含细菌的种群动态，但细菌的种群会繁殖，并且在波的传播中起着至关重要的作用。在本文中，我们考虑了一个带有活跃和不活跃细胞的线性系统的奇异极限，以及细菌的种群动态。最终，我们发现如果系统中没有趋化动力学，我们只能得到一个单调的传播波。这表明即使在系统中包含种群增长，也需要趋化动力学。
