Mathematical modelling of parasite dynamics: A stochastic simulation-based approach and parameter estimation via modified sequential-type approximate Bayesian computation

by Clement Twumasi, Joanne Cable and Andrey Pepelyshev. 

In an era marked by global health challenges and re-emerging infections, the need for sophisticated and robust mathematical models to better understand infectious diseases has never been more pressing. Our impactful study focused on a biological system known as the gyrodactylid-fish system. While existing modelling studies have fallen short in capturing vital information to reflect the biological realism of this system, our research introduced a novel individual-based stochastic simulation model to realistically simulate the spread of three different strains of Gyrodactylus across three different host populations, enhancing our knowledge of this system given observed experimental data. This study contributed mathematically and biologically to the gyrodactylid-fish system, offering insights that may apply to modelling other biological systems. Expanding on the existing studies, we have added to our understanding of this system and provided answers to open biological questions for the first time through model-based Bayesian analysis. The study also led to robust extensions of likelihood-free Bayesian estimation methods, commonly known as approximate Bayesian computation (ABC), to aid in calibrating complex models with mathematically intractable likelihood. After conducting additional posterior predictive checks, we found our proposed ABC methodologies' efficiency highly compelling and can readily be adapted to fit other highdimensional multi-parameter models.