Mosquera J, Adler F R
Group of Nonlinear Physics, Faculty of Physics, University of Santiago de Compostela, Santiago de Compostela, 15706, Spain.
J Theor Biol. 1998 Dec 7;195(3):293-313. doi: 10.1006/jtbi.1998.0793.
Models of the evolution of parasite virulence have focused on computing the evolutionarily stable level of virulence favored by tradeoffs within a host and by competition for hosts, and deriving conditions under which strains with different virulence levels can coexist. The results depend on the type of interaction between disease strains, such as single infection (immunity of infected individuals to other strains), coinfection (simultaneous infection by two strains), and superinfection (instantaneous takeover of host by the more virulent strain). We present a coinfection model with two strains and derive the superinfection model as the limit where individuals are rapidly removed from the doubly-infectious class. When derived in this way, the superinfection model includes not only the takeover of hosts infected by the less virulent strain, but new terms which take into account the possibility of increased mortality of doubly-infected individuals. Coinfection tends to favor higher virulence and support more coexistence than the single infection model, but the detailed results depend sensitively on two factors: (1) whether and how the model is near the superinfection limit, and (2) the shape of the coinfection function (the function describing the rate at which a more virulent strain can infect a host). If the superinfection limit arises due to rapid mortality of doubly-infected hosts, there is a region of uninvadable virulence levels rather than coexistence. When the coinfection function is discontinuous, as in many previous models, neither the coinfection model nor the superinfection limit can support an evolutionarily stable virulence level. Piecewise differentiable and differentiable coinfection functions produce qualitatively different results, and we propose that these more general cases should be used to study evolution of virulence when other mechanisms like space, population dynamics, and stochasticity interact.
寄生虫毒力进化模型主要关注计算宿主内部权衡以及宿主竞争所青睐的进化稳定毒力水平，并推导不同毒力水平菌株能够共存的条件。结果取决于疾病菌株之间的相互作用类型，例如单一感染（感染个体对其他菌株具有免疫力）、共感染（两种菌株同时感染）和重复感染（毒性更强的菌株瞬间取代宿主）。我们提出了一个包含两种菌株的共感染模型，并将重复感染模型推导为个体迅速从双重感染类别中移除的极限情况。以这种方式推导时，重复感染模型不仅包括毒性较弱菌株感染的宿主被取代的情况，还包括考虑双重感染个体死亡率增加可能性的新项。与单一感染模型相比，共感染倾向于更高的毒力并支持更多的共存情况，但具体结果敏感地取决于两个因素：（1）模型是否以及如何接近重复感染极限，以及（2）共感染函数的形状（描述毒性更强的菌株感染宿主速率的函数）。如果重复感染极限是由于双重感染宿主的快速死亡导致的，那么存在一个不可入侵的毒力水平区域而非共存情况。当共感染函数不连续时，如同许多先前模型那样，共感染模型和重复感染极限都无法支持进化稳定的毒力水平。分段可微和可微的共感染函数会产生质的不同的结果，并且我们提出当空间、种群动态和随机性等其他机制相互作用时，这些更一般的情况应该用于研究毒力的进化。
