In the modeling of parasite transmission dynamics, understanding the reproductive characteristics of these parasites is crucial. This paper presents a mathematical model that explores the reproductive behavior of dioecious parasites and its impact on transmission dynamics. Specifically, the study focuses on the investigation of various reproductive variables such as the mating probability and the fertilized egg production in the case of helminth parasites. While previous studies have commonly assumed Poisson and negative binomial distributions to describe the distribution of parasites among hosts, this study adopts an arbitrary distribution model and examines its consequences on some reproductive variables. These variables include mean number of fertile females, mean egg production, mating probability and mean fertilized egg production. In addition, the study of these variables takes into account the sex distribution of the parasites and whether male and female parasites are considered to be distributed together or separately. We show that the models obtained for the case of male and female parasites distributed separately in the hosts are ecologically unrealistic. We present the results obtained for some specific models and we tested the models obtained in this work using Monte Carlo simulations.

翻译：在寄生虫传播动力学建模中，理解这些寄生虫的繁殖特性至关重要。本文提出了一个数学模型，探讨雌雄异体寄生虫的繁殖行为及其对传播动力学的影响。具体而言，本研究聚焦于多种繁殖变量的分析，例如寄生虫（蠕虫）的交配概率和受精卵产量。以往研究通常假设泊松分布和负二项分布来描述寄生虫在宿主中的分布，而本研究采用任意分布模型，并考察其对若干繁殖变量的影响。这些变量包括可育雌虫平均数量、平均产卵量、交配概率和平均受精卵产量。此外，对这些变量的研究还考虑了寄生虫的性别分布，以及雄性和雌性寄生虫是共同分布还是单独分布。我们表明，对于雄性和雌性寄生虫在宿主中分别分布的情况所获得的模型在生态学上不切实际。我们展示了针对某些特定模型获得的结果，并利用蒙特卡洛模拟对本研究得到的模型进行了验证。