Mathematical models of a host-parasite system in a marine environment

Curtis Alan Patton, Purdue University

Abstract

We consider a host-parasite system that arises in aquaculture. The host is the sea-bass, Dicentrarchus labrax, and the parasite is the macroparasite, Diplectanum aequans. The parasite attaches itself to the gills of the sea-bass and eventually may suffocate the host if enough parasites are present. We present three mathematical models of the dynamics of the system, two of which are new. The first one, due to Langlais and Silan, [11], is a discrete model where we use a time step of two days and divide the hosts into classes of hosts with no parasites, hosts with one parasite, hosts with two parasites, and so on. We also divide the parasite population into two classes: younger juvenile parasites and older adult parasites. We attempt to model the recruitment of new parasites by a host effectively. A second model is a continuous one where we take time and the number of parasites present on a host to be continuous variables. We attempt to incorporate some of the features of the discrete model into the continuous one. In particular, we model the recruitment process in the same fashion, and we maintain the juvenile and adult structure in the parasite population. We present a proof that a solution exists to these equations using a fixed point argument. The third model is again a continuous model. We argue that including a diffusion term in the equations describing host dynamics matches previously used models. Finally, we describe the numerical methods we used to perform numerical simulations of the two continuous models and show some results from the simulations.

Degree

Ph.D.

Advisors

Milner, Purdue University.

Subject Area

Mathematics|Aquaculture|Fish production

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