Modelling Parasite-produced Marine Diseases: The case of the Mass Mortality Event of Pinna nobilis

The state of the art of epidemic modelling in terrestrial ecosystems is the compartmental SIR model
and its extensions from the now classical work of Kermack-Mackendrick. In contrast, epidemic
modelling of marine ecosystems is a bit behind, and compartmental models have been introduced
only recently. One of the reasons is that many epidemic processes in terrestrial ecosystems can be
described through a contact process, while modelling marine epidemics is more subtle in many cases.
Here we present a model describing disease outbreaks caused by parasites in bivalve populations.
The SIRP model is a multicompartmental model with four compartments, three of which describe
the different states of the host, susceptible (i.e. healthy), S, infected, I, and removed (dead), R, and
one compartment for the parasite in the marine medium, P, written as a 4-dimensional dynamical
system. Even if this is the simplest model one can write to describe this system, it is still too
complicated for both direct analytical manipulation and direct comparison with experimental
observations, as it depends on four parameters to be fitted. We show that it is possible to simplify
the model, including a reduction to the standard SIR model if the parameters fulfil certain conditions.
The model is validated with available data for the recent Mass Mortality Event of the noble pen
shell Pinna nobilis, a disease caused by the parasite Haplosporidium pinnae, showing that the
reduced SIR model is able to fit the data. So, we show that a model in which the species that suffers
the epidemics (host) cannot move, and contagion occurs through parasites, can be reduced to the
standard SIR model that represents epidemic transmission between mobile hosts. The fit indicates
that the assumptions made to simplify the model are reasonable in practice, although it leads to an
indeterminacy in three of the original parameters. This opens the possibility of performing direct
experiments to be able to solve this question.