Dynamics of a stage-structured predator-prey system with fear-induced group defense in autonomous and nonautonomous settings.

In this investigation, we construct a predator-prey model that distinguishes between immature and mature prey, highlighting group defense strategies within the mature prey. First, we embark on exploring the positivity and boundedness of the solution, unraveling sustainable equilibrium points, and deducing their stability conditions. Upon further investigation, we observe that the system exhibits diverse bifurcations, including Hopf, saddle-node, transcritical, generalized Hopf, cusp, and Bogdanov-Takens bifurcations. The results reveal that heightened fear decreases mature prey density, potentially causing prey extinction beyond a certain threshold. Increased maturation rates lead to the coexistence of immature and mature prey populations and higher predator density. Stronger group defense boosts mature prey density, while weaker defense results in weak persistence. Lower values of the maturation rate of prey and the decline rate of predators sustain only the predator population, reliant on resources other than focal prey. Furthermore, our model demonstrates intriguing and diverse dynamical phenomena, including various forms of bistability across distinct bi-parameter planes. We also explore the dynamics of a related nonautonomous system, where certain parameters are considered to vary with time. In the seasonally forced model, we set out to define criteria regarding the existence and stability of positive periodic solutions. Numerical investigations into the seasonally forced model uncover a spectrum of dynamics, ranging from simple periodic solutions to higher periodicities, bursting patterns, and chaotic behavior.

Chaos and extinction risks of sexually reproductive generalist top predator in a seasonally forced food chain system with Allee effect.

This paper investigates the dynamics of a tritrophic food chain model incorporating an Allee effect, sexually reproductive generalist top predators, and Holling type IV and Beddington-DeAngelis functional responses for interactions across different trophic levels. Analytically, we explore the feasible equilibria, their local stability, and various bifurcations, including Hopf, saddle-node, transcritical, and Bogdanov-Takens bifurcations. Numerical findings suggest that higher Allee intensity in prey growth leads to the inability of species coexistence, resulting in a decline in species density. Likewise, a lower reproduction rate and a higher strength of intraspecific competition among top predators also prevent the coexistence of species. Conversely, a rapid increase in the reproduction rate and a decrease in the strength of intraspecific competition among top predators enhance the densities of prey and top predators while decreasing intermediate predator density. We also reveal the presence of bistability and tristability phenomena within the system. Furthermore, we extend our autonomous model to its nonautonomous counterpart by introducing seasonally perturbed parameters. Numerical analysis of the nonautonomous model reveals that higher seasonal strength in the reproduction rate and intraspecific competition of top predators induce chaotic behavior, which is also confirmed by the maximum Lyapunov exponent. Additionally, we observe that seasonality may lead to the extinction of species from the ecosystem. Factors such as the Allee effect and growth rate of prey can cause periodicity in population densities. Understanding these trends is critical for controlling changes in population density within the ecosystem. Ecologists, environmentalists, and policymakers stand to benefit significantly from the invaluable insights garnered from this study. Specifically, our findings offer pivotal guidance for shaping future strategies aimed at safeguarding biodiversity and maintaining ecological stability amidst changing environmental conditions. By contributing to the existing body of knowledge, our study advances the field of ecological science, enhancing the comprehension of predator-prey dynamics across diverse ecological conditions.

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.

Fear effect in a three-species food chain model with generalist predator.

Within the framework of a food web, the foraging behavior of meso-carnivorous species is influenced by fear responses elicited by higher trophic level species, consequently diminishing the fecundity of these species. In this study, we investigate a three-species food chain model comprising of prey, an intermediate predator, and a top predator. We assume that both the birth rate and intraspecies competition of prey are impacted by fear induced by the intermediate predator. Additionally, the foraging behavior of the intermediate predator is constrained due to the presence of the top predator. It is essential to note that the top predators exhibit a generalist feeding behavior, encompassing food sources beyond the intermediate predators. The study systematically determines all feasible equilibria of the proposed model and conducts a comprehensive stability analysis of these equilibria. The investigation reveals that the system undergoes Hopf bifurcation concerning various model parameters. Notably, when other food sources significantly contribute to the growth of the top predators, the system exhibits stable behavior around the interior equilibrium. Our findings indicate that the dynamic influence of fear plays a robust role in stabilizing the system. Furthermore, a cascading effect within the system, stemming from the fear instigated by top predators, is observed and analyzed. Overall, this research sheds light on the intricate dynamics of fear-induced responses in shaping the stability and behavior of multi-species food web systems, highlighting the profound cascading effects triggered by fear mechanisms in the ecosystem.

Bifurcation analysis of autonomous and nonautonomous modified Leslie-Gower models.

In ecological systems, the predator-induced fear dampens the prey's birth rate; yet, it fails to extinguish their population, as they endure and survive even under significant fear-induced costs. In this study, we unveil a modified Leslie-Gower predator-prey model by incorporating the fear of predators, cooperative hunting, and predator-taxis sensitivity. We embark upon an exploration of the positivity and boundedness of solutions, unearthing ecologically viable equilibrium points and their stability conditions governed by the model parameters. Delving deeper, we unravel the scenario of transcritical, saddle-node, Hopf, Bogdanov-Takens, and generalized-Hopf bifurcations within the system's intricate dynamics. Additionally, we observe the bistable nature of the system under some parametric conditions. Further, the nonautonomous extension of our model introduces the intriguing interplay of seasonality in some crucial parameters. We establish a set of sufficient conditions that guarantee the permanence of the seasonally driven system. By conducting a numerical study on the seasonally forced model, we observe a myriad of phenomena manifesting the predator-prey dynamics. Notably, periodic solutions, higher periodic solutions, and bursting patterns emerge, alongside intriguing chaotic dynamics. Specifically, seasonal variations of the predator-taxis sensitivity and hunting cooperation can lead to the extinction of prey species and even the control of chaotic (higher periodic) solutions through the generation of a simple periodic solution. Remarkably, the seasonal forcing has the capacity to govern the chaotic behavior, leading to an exceptionally quasi-periodic arrangement in both prey and predator populations.

Stability switches and chaos induced by delay in a reaction-diffusion nutrient-plankton model.

In this paper, we investigate a reaction-diffusion model incorporating dynamic variables for nutrient, phytoplankton, and zooplankton. Moreover, we account for the impact of time delay in the growth of phytoplankton following nutrient uptake. Our theoretical analysis reveals that the time delay can trigger the emergence of persistent oscillations in the model via a Hopf bifurcation. We also analytically track the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions. Our simulation results demonstrate stability switches occurring for the positive equilibrium with an increasing time lag. Furthermore, the model exhibits homogeneous periodic-2 and 3 solutions, as well as chaotic behaviour. These findings highlight that the presence of time delay in the phytoplankton growth can bring forth dynamical complexity to the nutrient-plankton system of aquatic habitats.

Investigation of a nutrient-plankton model with stochastic fluctuation and impulsive control.

In this paper, we investigate a stochastic nutrient-plankton model with impulsive control of the nutrient concentration and zooplankton population. Analytically, we find that the population size is nonnegative for a sufficiently long time. We derive some sufficient conditions for the existence of stable periodic oscillations, which indicate that the plankton populations will behave periodically. The numerical results show that the plankton system experiences a transition from extinction to the coexistence of species due to the emergence of impulsive control. Additionally, we observe that the nutrient pulse has a stronger relationship with phytoplankton growth than the zooplankton pulse. Although the frequency of impulsive control and appropriate environmental fluctuations can promote the coexistence of plankton populations, an excessive intensity of noise can result in the collapse of the entire ecosystem. Our findings may provide some insights into the relationships among nutrients, phytoplankton and zooplankton in a stochastic environment.

A mathematical model for the impact of disinfectants on the control of bacterial diseases.

Here, we investigate a mathematical model to assess the impact of disinfectants in controlling diseases that spread in the population via direct contacts with the infected persons and also due to bacteria present in the environment. We find that the disease-free and endemic equilibria of the system are related via a transcritical bifurcation whose direction is forward. Our numerical results show that controlling the transmissions of disease through direct contacts and bacteria present in the environment can help in reducing the disease prevalence. Moreover, fostering the recovery rate and the death rate of bacteria play significant roles in disease eradication. Our numerical observations convey that reducing the bacterial density at the source discharged by the infected population through the use of chemicals has prominent effect in disease control. Overall, our findings manifest that the disinfectants of high quality can completely control the bacterial density and the disease outbreak.

Insight into the High Proton Conductivity of One-/Two-Dimensional Cadmium Phosphites.

The study describes the synthesis and structural attributes of two new cadmium phosphites, [Cd{OP(O)(OH)H}2(4,4'-bipy)] (1) and [H2pip][Cd(HPO3)2(H2O)]·H2O (2). The structure of 1 adopts a two-dimensional motif featuring alternate [Cd-µ2-O]2 and [Cd-O-P-O]2-cyclic rings, while the inorganic chains are held together by 4,4'-bipyridine. The presence of strong hydrogen bonding interactions between the appended H2PO3 groups (O---O = 2.55 Å) provides a facile proton conduction pathway and results in a proton conductivity of 3.2 × 10-3 S cm-1 at 75 °C under 77% relative humidity (RH). Compound 2 comprises an anionic framework formed by vertex-shared [Cd-O-P-O]2-cyclic rings, while the [H2pip] cations between the adjacent chains assist a well-directed O-H---O hydrogen-bonded network between coordinated water, lattice water, and phospite groups. The bulk proton conductivity value under conditions as in 1 reaches 4.3 × 10-1 S cm-1. For both 1 and 2, the proton conductivity remains practically unchanged under ambient temperatures (25-35 °C), suggesting their potential in low-temperature fuel cells.

A systematic study of autonomous and nonautonomous predator-prey models for the combined effects of fear, refuge, cooperation and harvesting.

In the present study, we investigate the roles of fear, refuge and hunting cooperation on the dynamics of a predator-prey system, where the predator population is subject to harvesting at a nonlinear rate. We also focus on the effects of seasonal forcing by letting some of the model parameters to vary with time. We rigorously analyze the autonomous and nonautonomous models mathematically as well as numerically. Our simulation results show that the birth rate of prey and the fear of predators causing decline in it, and harvesting of predators first destabilize and then stabilize the system around the coexistence of prey and predator; if the birth rate of prey is very low, both prey and predator populations extinct from the ecosystem, and for a range of this parameter, only the prey population survive. The fear of predators responsible for increase in the intraspecific competition among the prey species and the refuge behavior of prey have tendency to stabilize the system, whereas the cooperative behavior of predators during the hunting time destroys stability in the ecosystem. Numerical investigations of the seasonally forced model showcase the appearances of periodic solution, higher periodic solutions, bursting patterns and chaotic dynamics.

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.

Shifts in Bacterial Community Composition and Functional Traits at Different Time Periods Post-deglaciation of Gangotri Glacier, Himalaya.

Climate change causes an unprecedented increase in glacial retreats. The melting ice exposes land for colonization and diversification of bacterial communities leading to soil development, changes in plant community composition, and ecosystem functioning. Although a few studies have focused on macro-level deglaciation impacts, little is known about such effects on the bacterial community succession. Here, we provide meta-barcoding-based insight into the ecological attributes of bacterial community across different retreating periods of the Gangotri glacier, western Himalaya. We selected three sites along a terminal moraine representing recent (~ 20 yrs), intermediate (~ 100 yrs), and late (~ 300 yrs) deglaciation periods. Results showed that the genus Mycobacterium belonging to phylum Actinobacteria dominated recently deglaciated land. Relative abundance of these pioneer bacterial taxa decreased by 20-50% in the later stages with the emergence of new and rising of the less abundant members of the phyla Proteobacteria, Firmicutes, Planctomycetes, Acidobacteria, Verrucomicrobia, Candidatus TM6, and Chloroflexi. The community in the recent stage was less rich and harbored competitive interactions, while the later stages experienced a surge in bacterial diversity with cooperative interactions. The shift in α-diversity and composition was strongly influenced by soil organic carbon, carbon to nitrogen ratio, and soil moisture content. The functional analyses revealed a progression from a metabolism focused to a functionally progressive community required for bacterial co-existence and succession in plant communities. Overall, the findings indicate that the bacterial communities inhabit, diversify, and develop specialized functions post-deglaciation leading to nutrient inputs to soil and vegetation development, which may provide feedback to climate change.

Engineering a Hyperstable Yersinia pestis Outer Membrane Protein Ail Using Thermodynamic Design.

Development of viable therapeutics to effectively combat tier I pneumopathogens such as Yersinia pestis requires a thorough understanding of proteins vital for pathogenicity. The host invasion protein Ail, although indispensable for Yersinia pathogenesis, has evaded detailed characterization, as it is an outer membrane protein with intrinsically low stability and high aggregation propensity. Here, we identify molecular elements of the metastable Ail structure that considerably alter protein-lipid and intraprotein thermodynamics. In addition, we find that four residues Q50, L88, L92, and A94 contribute additively to the lowered stability of Ail, and their conserved substitution is sufficient to re-engineer Ail to Out14, a thermodynamically hyperstable low-aggregation variant with a functional scaffold. Interestingly, Ail also shows two (parallel) folding pathways, which has not yet been reported for ß-barrel membrane proteins. Additionally, we identify the molecular mechanism of enhanced thermodynamic stability of Out14. We show that this enhanced stability of Out14 is due to a favorable change in the nonpolar accessible surface, and the accumulation of a kinetically accelerated off-pathway folding intermediate, which is absent in wild-type Ail. Such engineered hyperstable Ail ß-barrels can be harnessed for targeted drug screening and developing medical countermeasures against Yersiniae. Application of similar strategies will help design effective translational therapeutics to combat biopathogens.

Impact of social media advertisements on the transmission dynamics of COVID-19 pandemic in India.

In this paper, we propose a mathematical model to assess the impact of social media advertisements in combating the coronavirus pandemic in India. We assume that dissemination of awareness among susceptible individuals modifies public attitudes and behaviours towards this contagious disease which results in reducing the chance of contact with the coronavirus and hence decreasing the disease transmission. Moreover, the individual's behavioral response in the presence of global information campaigns accelerate the rate of hospitalization of symptomatic individuals and also encourage the asymptomatic individuals for conducting health protocols, such as self-isolation, social distancing, etc. We calibrate the proposed model with the cumulative confirmed COVID-19 cases for the Republic of India. We estimate eight epidemiologically important parameters, and also the size of basic reproduction number for India. We find that the basic reproduction number for India is greater than unity, which represents the substantial outbreak of COVID-19 in the country. Sophisticated techniques of sensitivity analysis are employed to determine the impacts of model parameters on basic reproduction number and symptomatic infected population. Our results reveal that to reduce disease burden in India, non-pharmaceutical interventions strategies should be implemented effectively to decrease basic reproduction number below unity. Continuous propagation of awareness through the internet and social media platforms should be regularly circulated by the health authorities/government officials for hospitalization of symptomatic individuals and quarantine of asymptomatic individuals to control the prevalence of disease in India.

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.

Equilibrium in soil respiration across a climosequence indicates its resilience to climate change in a glaciated valley, western Himalaya.

Soil respiration (SR), a natural phenomenon, emits ten times more CO2 from land than anthropogenic sources. It is predicted that climate warming would increase SR in most ecosystems and give rise to positive feedback. However, there are uncertainties associated with this prediction primarily due to variability in the relationship of SR with its two significant drivers, soil temperature and moisture. Accounting for the variabilities, we use a climosequence in Himalaya with a temperature gradient of ~ 2.1 °C to understand the variations in the response of SR and its temperature sensitivity to climate change. Results indicate an equilibrium in SR ranging from 1.92 to 2.42 µmol m-2 s-1 across an elevation gradient (3300-3900 m) despite its increased sensitivity to temperature (Q10) from 0.47 to 4.97. Additionally, moisture reduction towards lower elevation weakens the temperature-SR relationship. Finally, soil organic carbon shows similarities at all the elevations, indicating a net-zero CO2 flux across the climosequence. The findings suggest that as the climate warms in this region, the temperature sensitivity of SR reduces drastically due to moisture reduction, limiting any change in SR and soil organic carbon to rising temperature. We introduce an equilibrium mechanism in this study which indicates the resilient nature of SR to climate change and will aid in enhancing the accuracy of climate change impact projections.

Dynamics of coronavirus pandemic: effects of community awareness and global information campaigns.

The effects of social media advertisements together with local awareness in controlling COVID-19 are explored in the present investigation by means of a mathematical model. The expression for the basic reproduction number is derived. Sufficient conditions for the global stability of endemic equilibrium are obtained. We perform sensitivity analysis to identify the key parameters of the model having great impacts on the prevalence and control of COVID-19. We calibrate the proposed model to fit the data set of COVID-19 cases for India. Our simulation results show that dissemination rate of awareness among susceptible individuals at community level and individual level plays pivotal role in curtailing the COVID-19 disease. Moreover, we observe that the global information distributing from social media and local awareness coming from mouth-to-mouth communication between unaware susceptible and aware people, together with hospitalization of symptomatic individuals and quarantine of asymptomatic individuals, are much beneficial in reducing COVID-19 cases in India. Our study suggests that both global and local awareness must be implemented effectively to manage the burden of COVID-19 pandemic.

Delay in budget allocation for vaccination and awareness induces chaos in an infectious disease model.

In this paper, we propose a model to assess the impacts of budget allocation for vaccination and awareness programs on the dynamics of infectious diseases. The budget allocation is assumed to follow logistic growth, and its per capita growth rate increases proportional to disease prevalence. An increment in per-capita growth rate of budget allocation due to increase in infected individuals after a threshold value leads to onset of limit cycle oscillations. Our results reveal that the epidemic potential can be reduced or even disease can be eradicated through vaccination of high quality and/or continuous propagation of awareness among the people in endemic zones. We extend the proposed model by incorporating a discrete time delay in the increment of budget allocation due to infected population in the region. We observe that multiple stability switches occur and the system becomes chaotic on gradual increase in the value of time delay.

Studies on the Genesis and Proton Conductivity of Imidazole-Based Linear and Open-Framework Zinc Phosphites.

Three new zinc phosphites, [HIm]2[Zn3(HPO3)4] (1), [Zn2(HPO3)2Im2] (2), and [Zn(HPO3)Im] (3) (Im = imidazole), have been synthesized from the hydro/solvothermal reaction of zinc acetate, dimethyl phosphite, and imidazole by varying the temperature and solvent of the reaction medium. The structure of 1 is built from vertex-sharing of four HPO3-capped Zn3P3 units and adopts an open framework with 12-ring channels stabilized by HIm cations via N-H···O hydrogen bonds. For 2, the inorganic skeleton is comprised of alternating ZnO4 and HPO3 tetrahedra, while the coordinatively associated ZnN2O2 fragments occupy the 12-ring hexagonal channels. Compound 3 adopts a ladder-type one-dimensional structure and exhibits N-H···O hydrogen-bonding interactions to afford a supramolecular assembly. A plausible rationale on the genesis of 1-3 has been put forth by reacting the preformed inorganic zinc phosphites Zn{OP(O)(OMe)H}2 or [Zn2(HPO3)2(H2O)4]·H2O with imidazole as the structure-directing ligand. Alternating-current impedance measurements reveal that 1 and 3 exhibit proton conductivities on the order of 10-3-10-4 S cm-1 between 25 and 100 °C under 35 and 77% relative humidity in repeated impedance cycles (Ea = 0.22-0.35 eV). On the contrary, the conduction property is completely impaired in 2 under similar conditions.

The Biomechanical Properties of Meshed versus Perforated Acellular Dermal Matrices (ADMs).

Acellular dermal matrices (ADMs) are used for soft tissue augmentation across surgical specialties. Since allograft incorporation depends on direct opposition between the ADM and a vascular bed, seroma formation can be detrimental to incorporation. Since most ADM products are available in many meshed and perforated forms, there is a lack of consistency between manufacture designs. We set out to determine the fluid egress properties and increase in surface area resulting from common cut patterns. METHODS: Three ADM cut patterns were studied: 1 meshed and 2 perforated. We calculated the surface area of these modified ADM samples. Fluid was passed through each ADM, and time required for fluid passage was recorded. An ANOVA (P < 0.05) was used to determine if there was a significant difference in egress properties across the 3 patterns. RESULTS: Meshing in a 1:1 pattern resulted in a 97.50% increase in surface area compared with the uncut product. In comparison, only a 0.30% increase resulted from Perforation Pattern #1 and a 0.59% increase resulted from Perforation Pattern #2. There was a significant difference in egress properties across the three cut patterns (P = 0.000). The average egress time of Mesh Pattern #1 was 1.974 seconds. The average egress time of Perforation Pattern #2 was 6.504 seconds, and of Perforation Pattern #1 was 10.369 seconds. CONCLUSIONS: Quantitative comparison revealed that meshing ADM significantly improves fluid egress and increases the surface area. Therefore, the use of meshed ADM tissue could improve the incorporation of ADM with the recipient, with improved patient outcomes.