Dynamic Behaviors of a Stochastic Eco-Epidemiological Model for Viral Infection in the Toxin-Producing Phytoplankton and Zooplankton System

It is well known that the evolution of natural populations is almost inevitably disturbed by various environmental factors. Various experiments have shown that the growth of phytoplankton might be affected by nutrient availability, water temperature, and light, while the development of zooplankton is more disturbed by the pH value of the seawater, water temperature, and water movement. However, it is not clear how these environmental fluctuations affect the dynamical behavior of the phytoplankton and zooplankton system. In this paper, a stochastic eco-epidemiological model for viral infection in the toxin-producing phytoplankton and zooplankton system is proposed. Firstly, the existence and uniqueness of globally positive solutions for this model is shown. Secondly, the stochastic boundedness of solutions for the model is proved. Moreover, sufficient conditions for the extinction and persistence in the mean for the phytoplankton and zooplankton are obtained by constructing appropriate stochastic Lyapunov functions and using analytical techniques. Numerical simulations are carried out to demonstrate different dynamical behaviors including coexistence, extinction of the whole plankton system, partial persistence and extinction, and their corresponding probability density curves.

Dynamic analysis of a fractional order system

In this paper, we investigate the dynamical behavior of a fractional order phytoplankton–zooplankton system. In this paper, stability analysis of the phytoplankton–zooplankton model (PZM) is studied by using the fractional Routh–Hurwitz stability conditions. We have studied the local stability of the equilibrium points of PZM. We applied an efficient numerical method based on converting the fractional derivative to integer derivative to solve the PZM.

A fractional-order toxin producing phytoplankton and zooplankton system

In this work, we investigate the dynamical behavior of a fractional-order toxin producing on a phytoplankton–zooplankton (TPPZ) system with nutrient cycling. We propose a mathematical system to model this situation. All the feasible equilibria of the system are obtained and the conditions for the existence of the equilibriums are determined. Local stability analysis of the TPPZ is studied by using the fractional Routh–Hurwitz stability conditions. Numerical simulations are carried out for a hypothetical set of parameter values to substantiate our analytical findings.