Abstract

ARBELAEZ A., Daniel  and  RUIZ V., Jorge Mauricio. Mathematical model for toxin transport in a marine food chain. Rev. Mat [online]. 2014, vol.21, n.2, pp.227-247. ISSN 1409-2433.

Some cases of poisoning by consumption of contaminated fish, like the Ciguatera poisoning, occur unexpectedly and they are not easy to detect previously since the fish that carry the toxin do not have appearance and/or symptoms of illness. In this paper a mathematical model for transport and acumulation of a toxin through a food chain is proposed. The model is a stiff system of ordinary differential equations that describes the dynamic. We propose a numerical scheme that combines a third-order Runge-Kutta method and trapezoidal rule to avoid the stiffness of the system. Several scenarios of toxin outbreaks are simulated; the results show that the time it takes to the toxin disappear in the trophic chain, depends on the state of the dynamics population at the time of the outbreak. This information can be used to set a ban on fishing until the toxin be reduced to harmless levels for the human health.

Keywords : food chain; mathematical modeling; biotoxin transport; stiff differential equations.

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