Stochastic differential equation with jumps for tilapia population

Abstract

Tilapia population with harvesting in the tilapia farm can be modeled by an ordinary differential equation (ODE). In real life, tilapia population can be affected by many factors. To make the model for tilapia population more realistic, we develop the ODE into the stochastic differential equation (SDE) together with jumps that represent the epidemic occuring for tilapia. Furthermore, we study the effect of some important parameters in the model to the number of tilapia in the tilapia farm via simulation. Both SDEs for tilapia population with and without jumps are simulated by using Euler-Maruyama and jump-adapted Euler methods.