The mathematical model of Eunice Siciliensis lifecycle: A study on Lombok Baunyale Festival Preserving Effort

Abstract

Baunyale Festival or sea worms (nyales) catching event is one of the traditions or heritage culture of the Lombok Sasak tribe community. The appearance of the colorful nyales on the sea surface in large quantities is actually a mass spawning of nyales. The most number of appearing nyales founded during the Baunyale festival is Eunice (palola) siciliensis. It was reported an excessive catching of nyales happened at the event in 2016 that endanger its existence. This paper is a scientific study of the dynamics of Eunice (palola) siciliensis growth represented in an ordinary differential equations system with a harvesting function. The system has an existing critical point that determined by the parameter that represents the number of population to be maintained (M). The stability of the system is evaluated locally at the critical point using the linearization method. The critical point is stable for a specific condition of M and s, where the second parameter represent the predation rate of phytoplankton as the prey of nyales. The simulation shows that the population of the solution converges to the some amount of nyales populations. It means that the proportional type of harvesting function prevents the number of existing nyales for the festival.