Forage fish play a crucial role in aquatic food webs by transferring energy from lower trophic levels to piscivorous fish and supporting economically important fisheries. In this study, we develop an eco-epidemiological forage–piscivorous fishery model incorporating disease transmission, harvesting, schooling behavior, and a forage fish-induced variable carrying capacity. Our results show that disease prevalence, harvesting pressure, and environmental feedback jointly regulate species persistence, ecosystem stability, and the risk of population collapse. More specifically, whereas favorable environmental conditions support the long-term maintenance of both forage and piscivorous fish populations, excessive harvesting and unfavorable ecological conditions may cause sudden regime shifts, hysteresis, bistability, and loss of coexistence. Mathematical analysis reveals critical ecological thresholds through Hopf, saddle-node, and backward bifurcations, while numerical investigations uncover Neimark–Sacker, period-doubling, zero-Hopf, Bogdanov–Takens, and homoclinic bifurcations, highlighting the rich dynamical structure of the system. Furthermore, environmental stochasticity can substantially alter persistence and extinction outcomes and may facilitate disease eradication under suitable conditions. These findings demonstrate how disease, harvesting, and environmental variability interact to shape the long-term dynamics of aquatic fisheries and provide valuable insights for preventing undesirable regime shifts and supporting ecosystem-based fishery management.

Submerged macrophytes are crucial in aquatic ecosystem as they enhance the apparent clarity of lakes and rivers by absorbing significant amount of nutrients and control eutrophication. Epiphytic species create shading effect that inhibits the growth of submerged macrophytes and they generally sensitive to allelopathically active substances produced by submerged plants. Both submerged macrophytes and epiphytes are impacted significantly by selective predation of snails. A mathematical model involving snails, epiphytes, and submerged macrophytes characterized by SI-type disease in submerged macrophytes is proposed and examined in this article. Hopf and transcritical bifurcations are explored comprehensively in order to demonstrate the one parametric bifurcations in the deterministic model. Additionally, the model undergoes quasiperiodic and chaotic dynamics through period doubling and Neimark-Sacker bifurcations. Under chaotic conditions, the detrimental allelopathic effect of the submerged macrophytes on epiphytes may prevent epiphyte growth, helping the system to recover from chaos and retain stability. The suggested model system also shows bi-parametric bifurcations including generalized Hopf, double Hopf, and Chenciner bifurcations. The deterministic model is extended by including environmental white noise. At low white noise strength, we found that the stochastic system oscillates around the solutions of the equivalent deterministic system, but at high intensity, the populations are driven to extinction. Crucially, the elimination of infection from aquatic ecosystems can be achieved with high white noise levels and low infection rate. This comprehensive investigation of the interactions involving snails, submerged macrophytes, and epiphytes offers significant new knowledge of the intricate dynamics of aquatic environments.

In many ecological circumstances, fear of predation and its carry-over effects are crucial elements of the predator–prey system. Since predators can identify infected animals, they try to avoid prey that have a parasite infection to reduce fitness costs. Here, we consider a predator–prey eco-epidemic model that takes into account fear caused by selective predation and its carry-over effect. Assume that the disease is of the SI − type. Using the carry-over effect as the potential bifurcation parameter, we address fundamental features such as boundedness, feasible equilibria and their stability, and Hopf bifurcation’s incidence in the analytical section. Validation of analytical results is done by numerical simulation. According to the results of our simulation, the intensity of fear and its carry-over effect might cause instability in the dynamics of a system. Increased predation fear due to disease leads to the elimination of persistent oscillations, restoring system stability. The feeding preference of predator can destabilize the system. We obtained a formula for the basic reproduction number (R0). The disease-free equilibrium is stable for R0<1, whereas the endemic equilibrium appears for R0>1. In order to better accurately describe the aforementioned scenarios, we take into account the non-autonomous system by varying the parameters that show the strength of fear, the carry-over impact, the prevalence of disease, and the predators’ selective preference over time. Conditions for which the system has at least one positive periodic solution are found for the seasonally forced system. In our seasonally forced model, complex bursting patterns, higher periodic solutions, and a distinct periodic solution occur.

In ecology, prey-predator interaction is a natural occurrence that greatly influences the composition of ecological variation. According to recent research, predators have the ability to significantly alter the physiological habits of prey species, making them more effective than direct predation at reducing prey biomass. Furthermore, these non-lethal impacts may persist throughout generations or seasons. We investigate in this paper the consequences of predator-induced fear and its carry-over impact in a predator-prey context whereby the prey might band together to defeat or perhaps kill the predators. The system's well-posedness and a few fundamental dynamical characteristics are covered in detail. Our results reveal how non-lethal influences alter the dynamics of a prey-predator scenario and provides useful bifurcation curves (i.e., saddle node, Hopf, homoclinic, limit point of cycles, etc). Moreover, our spatio-temporal model exhibits various special patterns.

In the realm of pollinator declination, understanding the dynamics of plant-pollinator interactions is a critical area of research to maintain healthy ecosystems. This study employs a mathematical modeling approach to investigate the dynamics of a saturated plant-pollinator mutualism, particularly aiming on the effect of predation on pollinator species. Using dynamical system theory, stability analysis of various ecological equilibria is investigated, and bifurcation phenomena such as transcritical and hopf are revealed. Furthermore, numerical results suggest that higher initial predator density can lead to pollinator extinction, although the predator population may not survive eventually. However, increased mutualistic strengths along with reduced predation rate can promote stability and support the sustainability of the plant-pollinator-predator ecosystem. These findings can be helpful for conservation strategies aimed at preserving pollinators and enhancing biodiversity.

In this work, we formulate and analyze a mathematical model capturing the trade-off dynamics arising from pollinator behavioral modifications in response to predation within a plant–pollinator–predator system. Using dynamical systems theory, we investigate the stability of various ecological equilibria and identify bifurcation phenomena. To explore the impact of key ecological parameters, we examine how changes in the behavior modification rate influence system outcomes. Furthermore, the system admits a stable coexistence equilibrium only when the mutualistic interaction strength exceeds a certain minimum. We investigate how changes in key parameters influence population dynamics and system resilience using sensitivity analysis. To further investigate the system’s dynamics, we introduce time delay into the model. We demonstrate that the delayed system exhibits stability switching for the increment of time delay. Also, chaotic behavior is observed as confirmed by a positive maximum Lyapunov exponent.

In this paper, a mathematical model for the dynamics of the interaction between zooplankton and fish is proposed with the effects of fear, refuge in zooplankton and fish populations. It is assumed that the disease has no chance of recovery, is exclusive to the fish species, and cannot be passed down via generations. Additionally, we suppose that the susceptible and infected fishes are consumed by their predator, but at two different rates. We provide detailed mathematical analysis for positivity, boundedness of the system. We also provide all feasible equilibria and their stability, Hopf bifurcation and global stability of the system. Numerical simulation is performed to validate our analytical findings. Our simulation results demonstrate the stabilizing effect of fear, however, the rate of zooplankton’s growth and infection in fish population are what lead to limit cycle oscillations. We take into account that the parameters that indicate the cost of fear, refuge, growth rate of zooplankton, and disease prevalence of fishes change over time in order to more accurately depict the situation. Conditions are derived for the seasonally forced system such that there exists at least one periodic solution that is positive; additionally, a periodic solution’s global attractivity is looked at. We demonstrate that in our seasonally forced model, a unique periodic solution, higher periodic solutions, and complicated bursting patterns appear.

Several experimental evidences and field data documented that zooplankton may alter its behavioral response in the presence of toxic phytoplankton, reducing its consumption to the point of starvation. This paper is devoted to the mathematical study of such interactions of toxic phytoplankton with grazer zooplankton. The non-toxic phytoplankton is assumed to adopt a density-dependent refuge strategy to avoid over-predation by zooplankton. Both groups of phytoplankton are assumed to suffer direct harm from anthropogenic toxicants, while zooplankton is affected indirectly by ingesting contaminated phytoplankton. We calibrate the proposed model with the field data from Talsari and Digha Mohana, India, and estimate some crucial model parameters consistent with the behavior of the observed data. Our results demonstrate that zooplankton grazing on toxic phytoplankton plays a key role in the emergence or mitigation of plankton blooms. We also highlight the system’s potential to exhibit multiple stable configurations under the same ecological conditions. The plankton system experiences significant regime shifts, which are explored through various bifurcation scenarios, such as transcritical and saddle-node bifurcations. These shifts are influenced by changes in refuge capacity, species growth rates, and environmental carrying capacity. Furthermore, we incorporate environmental variations due to seasonal periodic or almost periodic changes, allowing the refuge parameter to be time-dependent. We observe that the forced system exhibits double periodic solutions. Moreover, stronger seasonal variations in the refuge pattern lead to irregular chaotic blooms. In conclusion, the results offer valuable insights into the sustainability of biodiversity, potentially shedding light on the origin of diverse plankton bloom phenomena.

Coral reef ecosystems are most vulnerable to changes in sea surface temperature (SST), a key environmental factor critical to reef-building growth. Elevated SST reduces the ability of corals to produce their calcium carbonate skeletons. Prolonged high SST results in coral bleaching, owing to the uncoupling of symbiosis among corals and microalgae. Corals have narrow temperature tolerances. The skeletal growth rate of corals falls sharply to zero even at a slight increase of SST above its temperature tolerance level. Corals are also vulnerable to macroalgal toxicity. Several benthic macroalgae species are known to bring about allelopathic chemical compounds that are very harmful to corals. The toxic macroalgae produce allelochemicals for which the survivability and settlement of coral larvae are highly affected. Toxic macroalgae species damage coral tissues when in contact by transferring hydrophobic allelochemicals present on macroalgal surfaces, leading to a reduction of corals and even coral mortality. The abundance of toxic macroalgae changes the community structure toward a macroalgae-dominated reef ecosystem. We use a continuous-time model to investigate coral-macroalgal phase shifts in the presence of elevated SST and macroalgal toxicity. We have derived the conditions for locally asymptotic stability of steady states. Computer simulations have been carried out to illustrate different analytical results.

The sterile insect technique (SIT) is an environmentally friendly approach to insect management involving the release of sterile insects to reduce the population of their wild counterparts. In this study, we analyze a stage-structured entomological model depicting the dynamics of a wild-type mosquito population. Our observations reveal that mosquitoes exhibiting the Allee effect are prone to population collapse. Extending the model, we introduce sterile mosquitoes as a control measure against the wild-type mosquito species and explore the efficacy of SIT with three release strategies for sterile mosquitoes: constant release (CR), proportional release (PR), and saturated proportional release (SPR). Comparative analysis reveals that SIT with the PR strategy exhibits complex dynamics and superior effectiveness in eradicating mosquito populations over CR and SPR strategies. Additionally, the PR strategy demands a lower supply rate of sterile mosquitoes to eliminate the mosquito population and remains effective despite the low survival fitness of sterile mosquitoes. We also observe that SIT with the PR strategy is particularly effective in eliminating mosquito populations, especially in situations with a higher influx of wild mosquitoes from neighboring areas. Employing an optimal control approach further confirms the superiority of the PR strategy in suppressing wild mosquito populations compared to CR and SPR.

Eco-epidemiological models offer practical demonstrations of non-linear dynamics, enriching the realm of mathematical biology. The importance of viruses in oceanic plankton ecosystems is becoming more widely acknowledged. Infectious diseases have the potential to significantly alter the interaction within ecological systems. In this article we propose and analyze a three compartmental mathematical model of ODEs involving zooplankton and fish, with SI-type disease in the zooplankton population and two different non-linear infection rates. This study looks at how susceptible zooplankton species behave when in the presence of an infected zooplankton population. We further consider fish population as the sole predator of zooplankton population without considering the specific feeding habits of fish when they consume zooplankton. Additionally, it is thought that the zooplankton population that is infected is more likely to be preyed upon than their non-infected counterparts. The models describe when populations stay constant or show cyclical patterns in behavior. Our research shows that both the systems possess five different biologically feasible steady states. Our study also reveals that the susceptible zooplankton class is adversely impacted by the infection rate. The fish population disappears once the natural mortality rate of fish species surpasses a certain critical value. If the fish population is unable to exceed a certain threshold due to predation of infected zooplankton, they will not survive. For a healthy ecosystem, a lower infection rate and increased fish growth attributed to predation of susceptible zooplankton is preferred. However, an increased rate of infection may cause population collapse in the fish population.

In this investigation, we delve into the dynamics of an ecoepidemic model, considering the intertwined influences of fear, refuge-seeking behavior, and alternative food sources for predators with selective predation. We extend our model to incorporate the impact of fluctuating environmental noise on system dynamics. The deterministic model undergoes thorough scrutiny to ensure the positivity and boundedness of solutions, with equilibria derived and their stability properties meticulously examined. Furthermore, we explore the potential for Hopf bifurcation within the system dynamics. In the stochastic counterpart, we prioritize discussions on the existence of a globally positive solution. Through simulations, we unveil the stabilizing effect of the fear factor on susceptible prey reproduction, juxtaposed against the destabilizing roles of prey refuge behavior and disease prevalence intensity. Notably, when disease prevalence intensity is too low, the infection can be eradicated from the ecosystem. Our deterministic analysis reveals a complex interplay of factors: the system destabilizes initially but then stabilizes as the fear factor suppressing disease prevalence intensifies, or as predators exhibit a stronger preference for infected prey over susceptible ones, or as predators are provided with more alternative food sources. Moreover, for the stochastic system, the oscillations tend to cluster around the coexistence equilibrium of the corresponding deterministic model when white noise intensity is low. However, with increasing white noise intensity, oscillation amplitudes escalate. Critically, very high levels of white noise can lead to the eradication of infection from the ecosystem.

Sterile Insect Technique (SIT) is a biological insect (or pest) control tool aiming to reduce or eliminate wild insect (or pest) populations by releasing sterile insects (or pests). In this paper, we propose and study a stage- and sex-structured entomological model describing the dynamics of wild-type mosquito population and observed that the extinction equilibrium of the model is globally asymptotically stable when the basic offspring number is less than unity. However, when the basic offspring number is greater than unity, the extinction equilibrium becomes unstable, followed by the emergence of the stable interior equilibrium. We extend the model by introducing sterile male mosquitoes as a biological control agent against wild-type mosquito species. We have considered the Allee effect in the fertile female mosquito population due to the presence of non-egg-laying females in the mosquito population. While the wild mosquito-free equilibrium of the SIT model is always locally asymptotically stable, there exists either no interior equilibrium or a pair of interior equilibria, among which one is always unstable, and the other is always locally asymptotically stable. We observed that the wild mosquito population of the SIT system goes to extinction, followed by a saddle-node bifurcation when the supply rate of sterile males increases through some critical threshold value. As an alternative to the eradication policy, we formulated an optimal control problem to suppress the wild mosquito population, which suggests increasing the investment in awareness campaigns to suppress the mosquito population.

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.

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.

The aim of this paper is to investigate the role of plankton populations in the aquatic reservoir on the transmission dynamics of acute cholera within the human communities. To this, we develop a nonlinear six dimensional mathematical model that combines the plankton populations with the epidemiological SIR-type human subpopulations and the V. cholerae bacterial population in the aquatic reservoir. It is assumed that the susceptible humans become infected either by ingesting zooplankton, which serves as a reservoir for the cholera pathogen, by free-living V. cholerae in the water, or by cholera-infected individuals. We explore the existence and stability of all biologically plausible equilibria of the system. Also, we determine basic reproduction number (R0) and introduced an additional threshold, named planktonic factor (E0), that is found to significantly affect the cholera transmission. Furthermore, cholera-free equilibrium encounters transcritical bifurcation at R0=1 within the planktonic factor’s unitary range. We perform some sensitivity tests to determine how the epidemic thresholds R0 and E0 will respond to change in the parametric values. The existence of saddle–node bifurcation is shown numerically. Our findings reveal that there are strong connections between the planktonic blooms and the cholera epidemic. We observe that even while eliminating cholera from the human population is very difficult, we may nevertheless lessen the epidemic condition by enhancing immunization, treatment and other preventive measures.