Wei Wei, Krone Stephen M
Department of Mathematics, University of Idaho, Moscow ID 83844-1103, USA.
J Theor Biol. 2005 Oct 7;236(3):335-48. doi: 10.1016/j.jtbi.2005.03.016.
Imagine a pathogen that is spreading radially as a circular wave through a population of susceptible hosts. In the interior of this circular region, the infection dies out due to a subcritical density of susceptibles. If a mutant pathogen, having some advantage over wild-type pathogens, arises in this region it is likely to die out without leaving a noticeable trace. Mutants that arise closer to the infection wavefront have access to more susceptible hosts and thus are more likely to become established and perhaps (locally) out-compete the original pathogen. Among the factors (position, transmission rate, pathogen-induced death rate) that influence the fate of a mutant, which are most important? What does this tell us about the types of mutants that are likely to invade and become established? How do such tendencies serve to steer the evolution of pathogens in a spatial setting? Do different types of models of the same phenomena lead to similar conclusions? We address these issues from the point of view of an individual-based stochastic spatial model of host-pathogen interactions. We consider the probability of a successful invasion by a single mutant as a function of the transmissibility and virulence strengths and the mutant position in the wavefront. Next, for a version of the model in which mutations arise spontaneously, we obtain analytical and simulation results on the mean time to a successful invasion. We also use our model predictions to gain insight into experimental data on bacteriophage plaques. Finally, we compare our results to those based on ordinary and partial differential equations to better understand how different models might influence our predictions on the fate of a mutant pathogen.
设想一种病原体以圆形波的形式在一群易感宿主中呈放射状传播。在这个圆形区域内部，由于易感宿主的密度低于临界值，感染会逐渐消失。如果在这个区域出现了一种相对于野生型病原体具有某些优势的突变病原体，它很可能会消失得无影无踪。在更接近感染波前的区域出现的突变体能够接触到更多的易感宿主，因此更有可能站稳脚跟，甚至（在局部）胜过原始病原体。在影响突变体命运的因素（位置、传播率、病原体诱导的死亡率）中，哪些是最重要的？这能告诉我们哪些类型的突变体可能会入侵并站稳脚跟？在空间环境中，这些趋势是如何推动病原体进化的？同一现象的不同类型模型会得出相似的结论吗？我们从宿主 - 病原体相互作用的基于个体的随机空间模型的角度来探讨这些问题。我们将单个突变体成功入侵的概率视为传播能力和毒力强度以及突变体在波前位置的函数。接下来，对于一个突变自发产生的模型版本，我们得到了关于成功入侵的平均时间的分析和模拟结果。我们还利用模型预测来深入了解噬菌体噬菌斑的实验数据。最后，我们将我们的结果与基于常微分方程和偏微分方程的结果进行比较，以更好地理解不同模型可能如何影响我们对突变病原体命运的预测。
