Effects of toxicity and zooplankton selectivity on plankton dynamics under seasonal patterns of viruses with time delay

Abstract

Intricate functional diversities in marine ecosystems often lead to exhibit a variety of dynamical behaviors, including chaos. To bring order into such chaotic situations, the system develops different mechanisms of self‐adaptability. Our present investigation is based on the study of an eco‐epidemiological model for virally infected toxic phytoplankton and zooplankton system. Both healthy and infected phytoplankton are assumed to be exposed to grazer zooplankton with a varying degree of exposure. An extension is made by introducing the fact that viral replication process in a lysis event is mediated by some time lag. To achieve more realistic and explicit outcomes of the existing phenomena correlated with our model, we consider the force of infection and replication of free viruses as seasonally forced. We find that time delay accounts for recurrent stability switching event in the system. The chaotic behavior is observed in the seasonally forced delayed system, which indicates the emergence of harmful blooms. The main motive is to gain a clear insight into the field of synchronization and stabilization of the irregular behaviors of the system. Our investigations suggest that increased strength of toxic compounds exuded by phytoplankton species may suppress the prevalence of chaotic disorder and drives the system into a zooplankton‐free zone. The intensity of selective grazing of zooplankton changes the state of chaos to order and promotes the disease‐free system.

Impact of fear-effect on a delayed eco-epidemiological model with standard incidence rate, Holling type-II functional response and fading memory

“…Every biological process is time-consuming. 9,12,35,36 For example, a parasite's transfer from an infected individual to a susceptible one is not instantaneous. Therefore, the impact of this time delay (or, incidence delay) can't be ignored.…”

“…They have shown that the system executes a strange attractor via limit cycle for a higher value of incidence delay, but a lower infection rate can annihilate the impact of incidence delay. Biswas et al 36 investigated the effect of time delay in phytoplankton (susceptible and infected) and zooplankton ecosystems with seasonally dependent virus replication patterns. They observed that the system's dynamics (stable, periodic, and chaotic) switches several times due to the variation of delay parameter.…”

“…Previous authors 10,12,17,36 have considered a fixed 'gestation delay', a discrete-time delay in transferring biomass from prey to a predator due to predation. Here, the generalized concept is considered by assuming a continuous delay, i.e., a predator's growth rate is dependent not only on the immediate past, but also on the entire past.…”