THEORETICAL AND MATHEMATICAL APPROACH OF SOME REGULATION MECHANISMS IN A MARINE HOST-PARASITE SYSTEM

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Abstract
Host-parasite systems offer such a complex behaviour that few quantitative analysis of their coupled dynamics have been performed. Many intertwinned factors play a role, such as intensity-dependent (intra or interspecific competition, pathogeny, immunological reactions) and/or intensity-independent (abiotic factors, host ethology). Most biomathematical approaches to host-parasite systems are concerned with infectious processes. Corresponding epidemiological models are not well-adapted to macroparasites whose demographical behaviour is quite specific: host mortality, parasite fertility and sometimes recruitment mechanisms depend on the amount of already fixed parasites on a given host and not on the mere existence of parasites. Overdispersion processes are fundamental and determine for a large part the regulation of both populations. A central issue is therefore a reliable description of these processes and their interactions with the global dynamics of the system. Our goal is to develop a mixed deterministic and stochastic model describing the dynamics of a host-parasite system (fish-helminth parasite) having a direct cycle within a marine environment. A dynamical analysis combining a deterministic approach and a stochastic one adapted to macroparasites allows the introduction of spatial and temporal heterogeneities. A particular effort is made towards the recruitment process.

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