A new explicit numerical method for solving size-structured PDEs with a linear growth rate and birth and death rates depending on the total population size is proposed. The global error of approximation is of third order. The method is based on the combined discretization of the implicit along the characteristics solution and of an equation satisfied by the total population size. Diplectanum aequans , an ectoparasite of the sea bass, can cause pathological problems especially in fish farms. A discrete deterministic model was built to describe the dynamic of this fish-macroparasite parasite system.
Numerical simulations mimic some of the observed dynamics and supply a tool to validate the model.
Aggregation has an important role to play in many host-parasite systems. For the specific bass- Diplectanum aequans system it has been observed that above some threshold the more parasites a host has, the more parasites it will recruit, leading to possibly highly parasitized hosts. Our model includes a non-uniform dynamics within the cohorts of parasites. Several biological processes are combined to reach a good level of realism, but numerical simulations brought about too large computations and some simulations have run-times of one month on a workstation. A high-performance simulator working on parallel machines and providing more accurate computations has been implemented.