The basic reproduction ratio, R0, is a fundamental concept in epidemiology. It is defined as the total number of secondary infections brought on by a single primary infection, in a totally susceptible population. The value of R0 indicates whether a starting epidemic reaches a considerable part of the population and causes a lot of damage, or whether it remains restricted to a relatively small number of individuals. To calculate R0 one has to evaluate an integral that ranges over the duration of the infection of the host. This duration is, of course, limited by remaining host longevity. So, R0 depends on remaining host longevity and in this paper we show that for long-lived hosts this aspect may not be ignored for long-lasting infections. We investigate in particular how this epidemiological measure of pathogen fitness depends on host longevity. For our analyses we adopt and combine a generic within- and between-host model from the literature. To find the optimal strategy for a pathogen from an evolutionary point of view, we focus on the indicator $$R_0^{{opt}}$$R0opt, i.e., the optimum of R0 as a function of its replication and mutation rates. These are the within-host parameters that the pathogen has at its disposal to optimize its strategy. We show that $$R_0^{{opt}}$$R0opt is highly influenced by remaining host longevity in combination with the contact rate between hosts in a susceptible population. In addition, these two parameters determine whether a killer-like or a milker-like strategy is optimal for a given pathogen. In the killer-like strategy the pathogen has a high rate of reproduction within the host in a short time span causing a relatively short disease, whereas in the milker-like strategy the pathogen multiplies relatively slowly, producing a continuous small amount of offspring over time with a small effect on host health. The present research allows for the determination of a bifurcation line in the plane of host longevity versus contact rate that forms the boundary between the milker-like and killer-like regions. This plot shows that for short remaining host longevities the killer-like strategy is optimal, whereas for very long remaining host longevities the milker-like strategy is advantageous. For in-between values of host longevity, the contact rate determines which of both strategies is optimal.

中文翻译：

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R0：主机寿命很重要

基本繁殖率 R0 是流行病学中的一个基本概念。它被定义为在完全易感人群中由单一原发感染引起的继发感染总数。R0 的值表明起始流行病是否影响了相当一部分人口并造成了大量破坏，或者它是否仍然仅限于相对较少的个体。要计算 R0，必须评估一个在宿主感染持续时间范围内的积分。当然，这个持续时间受到剩余宿主寿命的限制。因此，R0 取决于剩余的宿主寿命，在本文中，我们表明对于长寿宿主，对于长期感染可能不会忽略这一方面。我们特别调查了这种病原体适应性的流行病学测量如何取决于宿主寿命。对于我们的分析，我们采用并结合了文献中的通用宿主内和宿主间模型。为了从进化的角度寻找病原体的最佳策略，我们关注指标 $$R_0^{{opt}}$$R0opt，即 R0 作为其复制和突变率的函数的最佳值。这些是病原体可以用来优化其策略的宿主内参数。我们表明 $$R_0^{{opt}}$$R0opt 受剩余宿主寿命以及易感人群中宿主之间的接触率的高度影响。此外，这两个参数决定了对于给定的病原体，杀手式还是挤奶器式策略是最佳的。在类似杀手的策​​略中，病原体在短时间内在宿主内具有很高的繁殖率，导致相对较短的疾病，而在类似挤奶器的策略中，病原体繁殖相对缓慢，随着时间的推移产生连续的少量后代，对宿主健康的影响很小。本研究允许确定宿主寿命与接触率平面中的分叉线，该平面形成挤奶器状区域和杀手状区域之间的边界。该图表明，对于较短的剩余宿主寿命，类杀手策略是最佳的，而对于非常长的剩余宿主寿命，类挤奶器策略是有利的。对于宿主寿命的中间值，接触率决定了两种策略中的哪一种是最佳的。本研究允许确定宿主寿命与接触率平面中的分叉线，该平面形成挤奶器状区域和杀手状区域之间的边界。该图表明，对于较短的剩余宿主寿命，类杀手策略是最佳的，而对于非常长的剩余宿主寿命，类挤奶器策略是有利的。对于宿主寿命的中间值，接触率决定了两种策略中的哪一种是最佳的。本研究允许确定宿主寿命与接触率平面中的分叉线，该平面形成挤奶器状区域和杀手状区域之间的边界。该图表明，对于较短的剩余宿主寿命，类杀手策略是最佳的，而对于非常长的剩余宿主寿命，类挤奶器策略是有利的。对于宿主寿命的中间值，接触率决定了两种策略中的哪一种是最佳的。