Mathematical Modeling of Mating Probability and Fertile Egg Production in Helminth Parasites

Abstract

In this work, we obtained a general formulation for the mating probability and fertile egg production in helminth parasites, focusing on the reproductive behavior of polygamous parasites and its implications for transmission dynamics. By exploring various reproductive variables in parasites with density-dependent fecundity, such as helminth parasites, we departed from the traditional assumptions of Poisson and negative binomial distributions to adopt an arbitrary distribution model. Our analysis considered critical factors such as mating probability, fertile egg production, and the distribution of female and male parasites among hosts, whether they are distributed together or separately. We show that the distribution of parasites within hosts significantly influences transmission dynamics, with implications for parasite persistence and, therefore, with implications in parasite control. Using statistical models and empirical data from Monte Carlo simulations, we provide insights into the complex interplay of reproductive variables in helminth parasites, enhancing our understanding of parasite dynamics and the transmission of parasitic diseases.

Keywords: Helminth Infection; Mathematical model; Mating probability; Negative binomial distribution; Parasite distribution; Transmission dynamics.