Mathematical model of mating probability and fertilized egg production in helminth parasites

Abstract: 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.