Andreasen V, Christiansen F B
Department of Mathematics and Physics, Roskilde University, Denmark.
Theor Popul Biol. 1993 Dec;44(3):261-98. doi: 10.1006/tpbi.1993.1029.
Using for each genotype an SIR-type model of disease transmission dynamics, we describe natural selection in a continuously breeding diploid host whose disease susceptibility and resistance are carried at one locus with two alleles. The system is transformed into variables that for each disease class describe the number of individuals, the gene frequency, and the deviation from Hardy-Weinberg proportions as measured by Wright's fixation index. An assumption of small variation in disease response among genotypes (slow selection) separates the system to first-order into three blocks. One block describes the population-wide disease dynamics, the second considers the fixation index in each class, and the third block provides the change in gene frequencies. The first two blocks settle to equilibrium at a rate determined by the population turnover time while the last block after a while is dominated by a slowly changing variable, the average gene frequency. The dynamics of the gene frequency take the usual form for a continuous time slow selection model, and this provides explicit, epidemiologically justified expressions for the genotypic fitnesses. We apply the method to other disease transmission patterns (SEI and SIS) and discuss how suitable time averages extend our results to diseases with temporally varying incidence.
我们使用针对每种基因型的疾病传播动力学的SIR型模型，来描述在一个连续繁殖的二倍体宿主中的自然选择，该宿主的疾病易感性和抗性由一个具有两个等位基因的位点携带。该系统被转换为变量，这些变量针对每个疾病类别描述个体数量、基因频率以及由赖特固定指数衡量的与哈迪 - 温伯格比例的偏差。基因型间疾病反应的小变异假设（缓慢选择）将系统一阶分离为三个模块。一个模块描述全人群的疾病动态，第二个模块考虑每个类别中的固定指数，第三个模块给出基因频率的变化。前两个模块以由种群周转时间决定的速率达到平衡，而最后一个模块一段时间后由一个缓慢变化的变量，即平均基因频率主导。基因频率的动态呈现连续时间缓慢选择模型的常见形式，这为基因型适合度提供了明确的、基于流行病学的表达式。我们将该方法应用于其他疾病传播模式（SEI和SIS），并讨论合适的时间平均值如何将我们的结果扩展到发病率随时间变化的疾病。
