Technical report: mathematical modelling of fish and predator based on logistic and Von Bertalanffy growth models / Wan Natasha Wan Hussin, Siti Noor Fatihah Mohd Yusoff and Nurul Anisa Ain Mustafa Kamal

A mathematical model is considered to study the relationship of fish and predator with the different values of birth and death parameter for predator population and different values of harvesting rate of fish. The logistic and Von Bertalanffy growth models are used to study this relationship. The relationship can be interpret by sketch a graph of prey and predator ver­sus time using MATLAB software. The difference values of birth and death parameters may be affect the predator population. The predator models corresponding to prey growth models have been solved analytically by using separation of variable and partial fraction techniques. The stability of non-coexistence equilibrium points for non-linear logistic and Von Bertalanffy growth models can be identify based on the graph of vector fields and trajectories. By using the formula of Maximum Sustainable Yield (MSY), the value of harvesting or fishing rate that can kept the population of prey above sustainable level can be obtain.