Catastrophic and noncatastrophic population crashes in a bitrophic system with dynamic additional food provision to cooperative predators.

In this article we contemplate the dynamics of an additional food-provided prey-predator system. We assume that the behavior of cooperative predators induces fear in prey, which radically affects the prey's birth and death rates. We observe that the structural instability imposed by strong cooperative hunting among predators goes away with higher intensities of fear levels affecting the prey's reproductive output and mortality. High levels of prey refuge are not conducive to the survival of predators. In such a situation, adequate supply of high-quality additional food is favorable regarding the persistence and stability of the system. Interestingly, the system potentially exhibits two stable configurations under identical ecological conditions by allowing different bifurcation scenarios, including saddle-node and backward bifurcations, and associated hysteresis effects with prey refuge along with additional food quantity and quality. In the stochastic environment, the system experiences critical transitions through bifurcation-induced tipping events with time-varying additional food for predators. Enhanced disturbance events promote noise-induced switching and tipping events. Finally, our investigation explores whether impending population crashes resulting from the variability of additional food quantity and quality can reliably be predicted using early warning signals in the context of redshifted noise. Overall, our results may provide insights for finding control strategies in the context of community ecology.

Vaccination impact on impending HIV-COVID-19 dual epidemic with autogenous behavior modification: Hill-type functional response and premeditated optimization technique.

An HIV-COVID-19 co-infection dynamics is modeled mathematically assimilating the vaccination mechanism that incorporates endogenous modification of human practices generated by the COVID-19 prevalence, absorbing the relevance of the treatment mechanism in suppressing the co-infection burden. Envisaging a COVID-19 situation, the HIV-subsystem is analyzed by introducing COVID-19 vaccination for the HIV-infected population as a prevention, and the "vaccination influenced basic reproduction number" of HIV is derived. The mono-infection systems experience forward bifurcation that evidences the persistence of diseases above unit epidemic thresholds. Delicate simulation methodologies are employed to explore the impacts of baseline vaccination, prevalence-dependent spontaneous behavioral change that induces supplementary vaccination, and medication on the dual epidemic. Captivatingly, a paradox is revealed showing that people start to get vaccinated at an additional rate with the increased COVID-19 prevalence, which ultimately diminishes the dual epidemic load. It suggests increasing the baseline vaccination rate and the potency of propagated awareness. Co-infection treatment needs to be emphasized parallelly with single infection medication under dual epidemic situations. Further, an optimization technique is introduced to the co-infection model integrating vaccination and treatment control mechanisms, which approves the strategy combining vaccination with awareness and medication as the ideal one for epidemic and economic gain. Conclusively, it is manifested that waiting frivolously for any anticipated outbreak, depending on autogenous behavior modification generated by the increased COVID-19 prevalence, instead of elevating vaccination campaigns and the efficacy of awareness beforehand, may cause devastation to the population under future co-epidemic conditions.

Toxicity-mediated regime shifts in a contaminated nutrient-plankton system.

In this article, we contemplate the dynamics of a three-tier system of nutrient, phytoplankton, and zooplankton with a gestation delay of discrete type and a distributed delay in nutrient recycling. Phytoplankton secretion-mediated alteration in the grazing pattern of zooplankton is encapsulated by a Monod-Haldane functional response. We carry out global sensitivity analysis for identifying the crucial model parameters having a significant impact on zooplankton density. The system potentially exhibits bistable configurations under identical ecological conditions by allowing different bifurcation scenarios, including multiple saddle-node and transcritical bifurcations with varying input rates of nutrients and inhibitory effects of phytoplankton against zooplankton. We observe that the gestation delay in zooplankton is responsible for the emergence of noxious bloom events. Interestingly, when the delay parameter crosses a threshold, the system experiences chaotic disorder, which prognosticates the onset of irregular bloom. Furthermore, by adding Gaussian white noise, we have extended the deterministic model to its stochastic counterpart. We found that white noise appears to regulate the survival and extinction of interacting populations. Comprehensive numerical simulations are consistent with mathematical results prognosticated by linear analysis.

Schooling behavior driven complexities in a fear-induced prey-predator system with harvesting under deterministic and stochastic environments.

The well-being of humans is closely linked to the well-being of species in any ecosystem, but the relationship between humans and nature has changed over time as societies have become more industrialized. In order to ensure the future of our ecosystems, we need to protect our planet's biodiversity. In this work, a prey-predator model with fear dropping prey's birth as well as death rates and nonlinear harvesting, is investigated. In addition, we consider that the consumption rate of predators, i.e., the functional response, is dependent on schooling behavior of both species. We have investigated the local stability of the equilibrium points and different types of bifurcations, such as transcritical, saddle-node, Hopf and Bogdanov-Takens (BT). We find that consumption rate of predator, fear and harvesting effort give complex dynamics in the neighbourhood of BT-points. Harvesting effort has both stabilizing and destabilizing effects. There is bistability between coexistence and predator-free equilibrium points in the system. Further, we have studied the deterministic model in fluctuating environment. Simulation results of stochastic system includes time series solutions of one simulation run and corresponding phase portraits. Notably, several simulation runs are conducted to obtain time series solutions, histograms, and stationary distributions. Our findings exhibit that during stochastic processes, model species fluctuate around some average values of the deterministic steady-state for lower environmental disturbances. However, higher values of environmental disturbances lead the species to extinction.

Effect of seasonally forced noisy environment on aquatic prey-predator model with water level fluctuations.

In this paper, the impact of environmental noise on prey-predator interactions with seasonal fluctuations in water levels has been studied. Both intensity of noise and water level variations together play a significant role in the dynamics of an aquatic prey-predator system. Analytically, we have shown the existence of a positive solution and its uniqueness, the ultimate bound of the system's solutions, and the global attractivity of the solution. Moreover, parametric conditions for which model species either persist (strongly or weakly) in the system or go into extinction are derived and their biological significance is also discussed. The sufficient condition of stochastic permanence is also analyzed. To justify the analytical results, we have performed numerical simulations of both deterministic and stochastic systems and observed some significant dynamics in the considered system.

Impact of saturated treatments on HIV-TB dual epidemic as a consequence of COVID-19: optimal control with awareness and treatment.

In this study, we propose an HIV-TB co-infection model by considering the treatment provision limitation induced by recent COVID-19 pandemic that impacts this dual epidemic immensely, assimilating the significance of educational attempts. We analyze the model and its submodels with single infections individually. We obtain the awareness-induced basic reproduction numbers and discuss the global stability of disease-free equilibrium when provision limitation is zero. We observe that the submodels exhibit forward as well as backward bifurcations under provision restriction. Further, we derive thresholds for resource limitations regulating the dynamical behavior of the systems while analyzing the stability of endemic equilibrium of the models with single infections. Sophisticated simulation approaches are implemented to discover the influences of provision-restricted medication and awareness on dual epidemic. Our findings convey the persistence of co-infection though the basic reproduction number is below unity, if the provision restriction remains uncurbed. An observable insight is that, in spite of having epidemic threshold less than unity and no limitation in TB treatment, co-infection relapses and persists in the population, when there is no awareness attempt. Numerical findings emphasize the urgent need of increased treatment accessibility and importance of awareness in the current situation. Moreover, an optimization problem incorporating treatment and awareness controls is formulated and solved to find the ideal strategy to manage HIV-TB co-epidemic that recommends to diminish the medical resource limitation to get the enormous impact in dominating the adversity caused by COVID-19.

A delay non-autonomous model for the combined effects of fear, prey refuge and additional food for predator.

In this paper, we investigate the combined effects of fear, prey refuge and additional food for predator in a predator-prey system with Beddington type functional response. We observe oscillatory behaviour of the system in the absence of fear, refuge and additional food whereas the system shows stable dynamics if anyone of these three factors is introduced. After analysing the behaviour of system with fear, refuge and additional food, we find that the system destabilizes due to fear factor whereas refuge and additional food stabilize the system by killing persistent oscillations. We extend our model by considering the fact that after sensing the chemical/vocal cue, prey takes some time for assessing the predation risk. The delayed system shows chaotic dynamics through multiple stability switches for increasing values of time delay. Moreover, we see the impact of seasonal change in the level of fear on the delayed as well as non-delayed system.

Modeling the avoidance behavior of zooplankton on phytoplankton infected by free viruses.

In any ecosystem, chaotic situations may arise from equilibrium state for different reasons. To overcome these chaotic situations, sometimes the system itself exhibits some mechanisms of self-adaptability. In this paper, we explore an eco-epidemiological model consisting of three aquatic groups: phytoplankton, zooplankton, and marine free viruses. We assume that the phytoplankton population is infected by external free viruses and zooplankton get affected on consumption of infected phytoplankton; also, the infected phytoplankton do not compete for resources with the susceptible one. In addition, we model a mechanism by which zooplankton recognize and avoid infected phytoplankton, at least when susceptible phytoplankton are present. The zooplankton extinction chance increases on increasing the force of infection or decreasing the intensity of avoidance. Further, when the viral infection triggers chaotic dynamics, high zooplankton avoidance intensity can stabilize again the system. Interestingly, for high avoidance intensity, nutrient enrichment has a destabilizing effect on the system dynamics, which is in line with the paradox of enrichment. Global sensitivity analysis helps to identify the most significant parameters that reduce the infected phytoplankton in the system. Finally, we compare the dynamics of the system by allowing the infected phytoplankton also to share resources with the susceptible phytoplankton. A gradual increase of the virus replication factor turns the system dynamics from chaos to doubling state to limit cycle to stable state and the system finally settles down to the zooplankton-free equilibrium point. Moreover, on increasing the intensity of avoidance, the system shows a transcritical bifurcation from the zooplankton-free equilibrium to the coexistence steady state and remains stable thereafter.

Effects of zooplankton selectivity on phytoplankton in an ecosystem affected by free-viruses and environmental toxins.

In the present study, we investigate the selective feeding of zooplankton on phytoplankton infected by free-viruses in the presence of environmental toxins in the marine ecosystem. The environmental toxins assume to decrease the growth rate of susceptible phytoplankton, and increase the death rate of infected phytoplankton and zooplankton. Global sensitivity analysis identifies important parameters of the system having crucial impact on the aquatic health. The coexistence equilibrium of the system stabilizes on increasing the parameters related to inhibition of phytoplankton growth due to environmental toxins and the force of infection, and destabilizes on increasing the carrying capacity of susceptible phytoplankton and preference of zooplankton on infected phytoplankton. The chance of extinction of free-viruses increases on increasing the preference of zooplankton on infected phytoplankton or decreasing the force of infection. Moreover, if the input rate of environmental toxins is high, then the system becomes zooplankton-free for higher values of force of infection. On increasing the values of preference of zooplankton on infected phytoplankton, the system exhibits transition from stable coexistence to oscillations around coexistence equilibrium to oscillations around disease-free equilibrium. We observe that the presence of free-viruses and environmental toxins in the system drive zooplankton population to very low equilibrium values but the ecological balance of the aquatic food web can be maintained by modulating the decay (depletion) rate of free-viruses (environmental toxins).

Hysteresis in coral reefs under macroalgal toxicity and overfishing.

Macroalgae and corals compete for the available space in coral reef ecosystems.While herbivorous reef fish play a beneficial role in decreasing the growth of macroalgae, macroalgal toxicity and overfishing of herbivores leads to proliferation of macroalgae. The abundance of macroalgae changes the community structure towards a macroalgae-dominated reef ecosystem. We investigate coral-macroalgal phase shifts by means of a continuous time model in a food chain. Conditions for local asymptotic stability of steady states are derived. It is observed that in the presence of macroalgal toxicity and overfishing, the system exhibits hysteresis through saddle-node bifurcation and transcritical bifurcation. We examine the effects of time lags in the liberation of toxins by macroalgae and the recovery of algal turf in response to grazing of herbivores on macroalgae by performing equilibrium and stability analyses of delay-differential forms of the ODE model. Computer simulations have been carried out to illustrate the different analytical results.

Stage-structured cannibalism with delay in maturation and harvesting of an adult predator.

A three-dimensional stage-structured predator-prey model is proposed and analyzed to study the effect of predation and cannibalism of the organisms at the highest trophic level with non-constant harvesting. Time lag in maturation of the predator is introduced in the system and conditions for local asymptotic stability of steady states are derived. The length of the delay preserving the stability is also estimated. Moreover, it is shown that the system undergoes a supercritical Hopf bifurcation when the maturation time lag crosses a certain critical value. Computer simulations have been carried out to illustrate various analytical results.

Allelopathy of plasmid-bearing and plasmid-free organisms competing for two complementary resources in a chemostat.

We consider a model of competition between plasmid-bearing and plasmid-free organisms for two complementary nutrients in a chemostat. We assume that the plasmid-bearing organism produces an allelopathic agent at the cost of its reproductive abilities which is lethal to plasmid-free organism. Our analysis leads to different thresholds in terms of the model parameters acting as conditions under which the organisms associated with the system cannot thrive even in the absence of competition. Local stability of the system is obtained in the absence of one or both the organisms. Also, global stability of the system is obtained in the presence of both the organisms. Computer simulations have been carried out to illustrate various analytical results.