Oscillations of algal cell quota: Considering two-stage phosphate uptake kinetics.

Elucidating the mechanism of effect of phosphate (PO43-) uptake on the growth of algal cells helps understand the frequent outbreaks of algal blooms caused by eutrophication. In this study, we develop a comprehensive mathematical model that incorporates two stages of PO43- uptake and accounts for transport time delay. The model parameter values are determined by fitting experimental data of Prorocentrum donghaiense and the model is validated using experimental data of Karenia mikimotoi. The numerical results demonstrate that the model successfully captures the general characteristics of algal growth and PO43- uptake under PO43- sufficient conditions. Significantly, the experimental and mathematical findings suggest that the time delay associated with the transfer of PO43- from the surface-adsorbed PO43- (Ps) pool to the intracellular PO43- (Pi) pool may serve as a physiologically plausible mechanism leading to oscillations of algal cell quota. These results have important implications for resource managers, enabling them to predict and deepen their understanding of harmful algal blooms.

The impact of water storage capacity on plant dynamics in arid environments: A stoichiometric modeling approach.

Plants in arid environments have evolved many strategies to resist drought. Among them, the developed water storage tissue is an essential characteristic of xerophytes. To clarify the role of water storage capacity in plant performance, we originally formulate a stoichiometric model to describe the interaction between plants and water with explicit water storage. Via an ecological reproductive index, we explore the effects of precipitation and water storage capacity on plant dynamics. The model possesses saddle-node bifurcation and forward or backward bifurcation, and the latter may lead to the emergence of alternative stable states between a stable survival state and a stable extinction state. Numerical simulations illustrate the persistence and resilience of plants regulated by soil conditions, precipitation and water storage capacity. Our findings contribute to the botanical theory in the perspectives of environmental change and plant water storage traits.

Threshold behavior and exponential ergodicity of an sir epidemic model: the impact of random jamming and hospital capacity.

This article uses hospital capacity to determine the treatment rate for an infectious disease. To examine the impact of random jamming and hospital capacity on the spread of the disease, we propose a stochastic SIR model with nonlinear treatment rate and degenerate diffusion. Our findings demonstrate that the disease's persistence or eradication depends on the basic reproduction number [Formula: see text]. If [Formula: see text], the disease is eradicated with a probability of 1, while [Formula: see text] results in the disease being almost surely strongly stochastically permanent. We also demonstrate that if [Formula: see text], the Markov process has a unique stationary distribution and is exponentially ergodic. Additionally, we identify a critical capacity which determines the minimum hospital capacity required.

Precipitation governing vegetation patterns in an arid or semi-arid environment.

In an arid or semi-arid environment, precipitation plays a vital role in vegetation growth. Recent researches reveal that the response of vegetation growth to precipitation has a lag effect. To explore the mechanism behind the lag phenomenon, we propose and investigate a water-vegetation model with spatiotemporal nonlocal effects. It is shown that the temporal kernel function does not affect Turing bifurcation. For better understanding the influences of lag effect and nonlocal competition on the vegetation pattern formation, we choose some special kernel functions and obtain some insightful results: (i) Time delay does not trigger the vegetation pattern formation, but can postpone the evolution of vegetation. In addition, in the absence of diffusion, time delay can induce the occurrence of stability switches, while in the presence of diffusion, spatially nonhomogeneous time-periodic solutions may emerge, but there are no stability switches; (ii) The spatial nonlocal interaction may trigger the pattern onset for small diffusion ratio of water and vegetation, and can change the number and size of isolated vegetation patches for large diffusion ratio. (iii) The interaction between time delay and spatial nonlocal competition may induce the emergence of traveling wave patterns, so that the vegetation remains periodic in space, but is oscillating in time. These results demonstrate that precipitation can significantly affect the growth and spatial distribution of vegetation.

Dynamics of a stochastic turbidostat model with sampled and delayed measurements.

In this paper, a stochastic turbidostat model with controllable output is established by using piecewise constant delayed measurements of the substrate concentration. We commence by proving the existence and uniqueness of the global positive solution of the stochastic delayed model. Then, sufficient conditions of extinction and stochastic strong permanence of the biomass are acquired. In quick succession, we investigate the stochastic asymptotical stability of the washout equilibrium as well as the asymptotic behavior of the random paths approaching the interior equilibrium of its corresponding deterministic model by employing the method of Lyapunov functionals. Numerical and theoretical findings show that the influence of environmental random fluctuations on the dynamics of the model may be more pronounced than that of time delay.

Stochastic sensitivity analysis and feedback control of noise-induced transitions in a predator-prey model with anti-predator behavior.

In this study, we investigate a stochastic predator-prey model with anti-predator behavior. We first analyze the noise-induced transition from a coexistence state to the prey-only equilibrium by using the stochastic sensitive function technique. The critical noise intensity for the occurrence of state switching is estimated by constructing confidence ellipses and confidence bands, respectively, for the coexistence the equilibrium and limit cycle. We then study how to suppress the noise-induced transition by using two different feedback control methods to stabilize the biomass at the attraction region of the coexistence equilibrium and the coexistence limit cycle, respectively. Our research indicates that compared with the prey population, the predators appear more vulnerable and prone to extinction in the presence of environmental noise, but it can be prevented by taking some appropriate feedback control strategies.

Controlling Biological Invasions: A Stochastic Host-Generalist Parasitoid Model.

On a global scale, biological invasions are seriously destroying the stability of ecosystem, sharply decreasing biodiversity and even endangering human health and causing huge economic losses. However, there exist few effective measures controlling biological invasions. To more accurately examine the prevention and control effects of biological control on biological invasions in real environments of random fluctuations, we construct a stochastic host-generalist parasitoid model. We first establish, respectively, the sufficient conditions for the persistence and extinction of invasive hosts and generalist parasitoids, including (1) only the intrusive hosts go extinct; (2) only the generalist parasitoids are extinct, and (3) the intrusive hosts and generalist parasitoids are both extinct or persistent. Then, we perform a series of numerical simulations to verify the validity of the theoretical results obtained, based on which we further discuss the impacts of stochastic environmental fluctuations on the control of intrusive hosts, especially the possible changes of qualitative behavior caused by environmental noises in the bistable scenario. Our theoretical and numerical results indicate that compared with the invasive hosts, the generalist parasitoids are more vulnerable to environmental noises, and the prevention and control effects of biological control on invasive hosts are closely dependent to the initial population sizes. Thus, improving the ability of early detection of ecosystems, including the initial densities of biological populations and their dynamic characteristics, will provide effective predictive guidance for the prevention and control of alien host invasions.

Stochastic switches of eutrophication and oligotrophication: Modeling extreme weather via non-Gaussian Lévy noise.

Disturbances related to extreme weather events, such as hurricanes, heavy precipitation events, and droughts, are important drivers of evolution processes of a shallow lake ecosystem. A non-Gaussian α-stable Lévy process is esteemed to be the most suitable model to describe such extreme events. This paper incorporates extreme weather via α-stable Lévy noise into a parameterized lake model for phosphorus dynamics. We obtain the stationary probability density function of phosphorus concentration and examine the pivotal roles of α-stable Lévy noise on phosphorus dynamics. The switches between the oligotrophic state and the eutrophic state can be induced by the noise intensity σ, skewness parameter ß, or stability index α. We calculate the mean first passage time, also referred to as the mean switching time, from the oligotrophic state to the eutrophic state. We observe that the increased noise intensity, skewness parameter, or stability index makes the mean switching time shorter and thus accelerates the switching process and facilitates lake eutrophication. When the frequency of extreme weather events exceeds a critical value, the intensity of extreme events becomes the most key factor for promoting lake eutrophication. As an application, we analyze the available data of Lake Taihu (2014-2018) for monthly precipitation, phosphorus, and chlorophyll-a concentrations and quantify the linkage among them using the Lévy-stable distribution. This study provides a fundamental framework to uncover the impact of any extreme climate event on aquatic nutrient status.

A coral reef benthic system with grazing intensity and immigrated macroalgae in deterministic and stochastic environments.

As the most diverse, productive but vulnerable marine habitats in the world, coral reefs are easily affected by the ubiquitous environmental fluctuations, which could change the population dynamics and induce phase shifts of the ecosystem. In this paper, we consider a coral reef benthic system, where macroalgae, corals and algal turfs compete for the available space on a given region of the seabed with grazing intensity and immigrated macroalgae in both deterministic and stochastic environments. For the deterministic system, we analyze the existence and stability of equilibria, as well as the existence of bifurcations. For the stochastic system, sufficient conditions for the existence of the unique ergodic stationary distribution as well as the extinction of corals are obtained, by choosing suitable Lyapunov functions. Moreover, for the scenario that the system exhibits bistability between a macroalgal-coral coexistence equilibrium and a coral-free equilibrium in the absence of environmental fluctuation, we further investigate the irreversible noise-induced transition from macroalgal-coral coexistence to coral extirpation, and numerically estimate the critical values of noise intensity for the occurrence of such transition with the aids of the technique of stochastic sensitivity functions.

Threshold dynamics of a stochastic SIHR epidemic model of COVID-19 with general population-size dependent contact rate.

In this paper, we propose a stochastic SIHR epidemic model of COVID-19. A basic reproduction number $ R_{0}^{s} $ is defined to determine the extinction or persistence of the disease. If $ R_{0}^{s} < 1 $, the disease will be extinct. If $ R_{0}^{s} > 1 $, the disease will be strongly stochastically permanent. Based on realistic parameters of COVID-19, we numerically analyze the effect of key parameters such as transmission rate, confirmation rate and noise intensity on the dynamics of disease transmission and obtain sensitivity indices of some parameters on $ R_{0}^{s} $ by sensitivity analysis. It is found that: 1) The threshold level of deterministic model is overestimated in case of neglecting the effect of environmental noise; 2) The decrease of transmission rate and the increase of confirmed rate are beneficial to control the spread of COVID-19. Moreover, our sensitivity analysis indicates that the parameters $ \beta $, $ \sigma $ and $ \delta $ have significantly effects on $ R_0/ $.

Spatiotemporal patterns of a diffusive prey-predator model with spatial memory and pregnancy period in an intimidatory environment.

Spatial memory and predator-induced fear have recently been considered in modeling population dynamics of animals independently. This paper is the first to integrate both aspects in a prey-predator model with pregnancy cycle to investigate the direct and indirect effects of predation on the spatial distribution of prey. We extensively study Turing instability and Hopf bifurcation. When the prey population has slow memory-based diffusion, the model is easier to generate Turing patterns. While when the prey population has fast memory-based diffusion, the model can exhibit rich dynamics. Specifically, (1) for the model with spatial memory delay only, the prey population with long term memory shows a spatially nonhomogeneous periodic distribution; (2) for the model with pregnancy delay only, the prey population with long pregnancy cycles shows a spatially homogeneous (or nonhomogeneous) periodic distribution, and (3) for the model with both the two time delays, more interesting spatiotemporal dynamics can be observed for long memory delay and (or) long pregnancy cycles. Our findings indicate that both spatial memory and pregnancy cycle play significant roles in the pattern formation of prey-predator interactions.

Using an age-structured COVID-19 epidemic model and data to model virulence evolution in Wuhan, China.

COVID-19 is a disease caused by infection with the virus 2019-nCoV, a single-stranded RNA virus. During the infection and transmission processes, the virus evolves and mutates rapidly, though the disease has been quickly controlled in Wuhan by 'Fangcang' hospitals. To model the virulence evolution, in this paper, we formulate a new age structured epidemic model. Under the tradeoff hypothesis, two special scenarios are used to study the virulence evolution by theoretical analysis and numerical simulations. Results show that, before 'Fangcang' hospitals, two scenarios are both consistent with the data. After 'Fangcang' hospitals, Scenario I rather than Scenario II is consistent with the data. It is concluded that the transmission pattern of COVID-19 in Wuhan obey Scenario I rather than Scenario II. Theoretical analysis show that, in Scenario I, shortening the value of L (diagnosis period) can result in an enormous selective pressure on the evolution of 2019-nCoV.

Microrisk Lab: An Online Freeware for Predictive Microbiology.

Microrisk Lab is an R-based online modeling freeware designed to realize parameter estimation and model simulation in predictive microbiology. A total of 36 peer-reviewed models were integrated for parameter estimation (including primary models of bacterial growth/inactivation under static and nonisothermal conditions, secondary models of specific growth rate, and competition models of two-flora growth) and model simulation (including integrated models of deterministic or stochastic bacterial growth/inactivation under static and nonisothermal conditions) in Microrisk Lab. Each modeling section was designed to provide numerical and graphical results with comprehensive statistical indicators depending on the appropriate data set and/or parameter setting. In this study, six case studies were reproduced in Microrisk Lab and compared in parallel with DMFit, GInaFiT, IPMP 2013/GraphPad Prism, Bioinactivation FE, and @Risk, respectively. The estimated and simulated results demonstrated that the performance of Microrisk Lab was statistically equivalent to that of other existing modeling systems. Microrisk Lab allows for a friendly user experience when modeling microbial behaviors owing to its interactive interfaces, high integration, and interconnectivity. Users can freely access this application at https://microrisklab.shinyapps.io/english/ or https://microrisklab.shinyapps.io/chinese/.

Dynamics of a ratio-dependent population model for Green Sea Turtle with age structure.

The reproduction of the green sea turtles is characterized by the temperature dependent sex determination (TSD). Green sea turtle eggs are laid asexually. Temperature during hatching determines the sex of baby green sea turtles. In order to study the population dynamics of the green sea turtles and understand the dynamics of the sex ratio, in this paper we establish a stage-structured model by incorporating TSD and the ratio dependent Holling III functional response in the reproduction process of the green sea turtle population. The effects of incubation temperature and sex ratio deviation on persistence of the population are captured by the sole basic reproduction number. The persistent mode can be either a stable equilibrium or periodic oscillations. Numerical simulations and sensitive analysis help us to identify vital parameters in our model. Our research in the paper is in favor of elevating sexual encounter rates, reducing the searching time for males and increasing survival odds from baby state into adult in order to maintain sustainability of the green sea turtles.

Competitive Exclusion in a General Multi-species Chemostat Model with Stochastic Perturbations.

Based on the fact that the continuous culture of microorganisms in a chemostat is subject to environmental noises, we present and analyze a stochastic competition chemostat model with general monotonic response functions and differential removal rates. The existence and boundedness of the unique positive solution are first obtained. By defining a stochastic break-even concentration for every species, we prove that at most one competitor survives in the chemostat and the winner has the smallest stochastic break-even concentration, provided its response function satisfies a technical assumption. That is to say, the competitive exclusion principle holds for the stochastic competition chemostat model. Furthermore, we find that the noise experienced by one species is adverse to its growth while may be favorable for the growth of other one species. Namely, the destinies can be exchanged between two microorganism species in the chemostat due to the environmental noise.

Stability and Hopf bifurcation for a delayed diffusive competition model with saturation effect.

This paper presents an investigation on the dynamics of a delayed diffusive competition model with saturation effect. We first perform the stability analysis of the positive equilibrium and the existence of Hopf bifurcations. It is shown that the positive equilibrium is asymptotically stable under some conditions, and that there exists a critical value of delay, when the delay increases across it, the positive equilibrium loses its stability and a spatially homogeneous or inhomogeneous periodic solution emerges from the positive equilibrium. Then, we derive the formulas for the determination of the direction of Hopf bifurcation and the properties of the bifurcating periodic solutions. Finally, some numerical simulations are performed to illustrate the obtained results.

Survival analysis of a stochastic predator-prey model with prey refuge and fear effect.

In this paper, we propose and investigate a stochastic Holling type-II predator-prey model with prey refuge and fear effect. We first prove the existence and uniqueness of the global positive solution. Then we perform the survival analysis of the model, including the existence of a unique ergodic stationary distribution and the extinction of the model. Numerical simulations are carried out to validate our analytical results. Our findings indicate that the white noise is adverse to the growth of predator and prey populations, and the increase of fear effect will lead to the decrease of predator density, but with no obvious effect on prey density.

Noise-Induced Transitions in a Nonsmooth Producer-Grazer Model with Stoichiometric Constraints.

Stoichiometric producer-grazer models are nonsmooth due to the Liebig's Law of Minimum and can generate new dynamics such as bistability for producer-grazer interactions. Environmental noises can be extremely important and change dynamical behaviors of a stoichiometric producer-grazer model. In this paper, we consider a stochastically forced producer-grazer model and study the phenomena of noise-induced state switching between two stochastic attractors in the bistable zone. Namely, there is a frequent random hopping of phase trajectories between attracting basins of the attractors. In addition, by applying the stochastic sensitivity function technique, we construct the confidence ellipse and confidence band to find the configurational arrangement of equilibria and a limit cycle, respectively.

Noise-induced transitions in a non-smooth SIS epidemic model with media alert.

We investigate a non-smooth stochastic epidemic model with consideration of the alerts from media and social network. Environmental uncertainty and political bias are the stochastic drivers in our mathematical model. We aim at the interfere measures assuming that a disease has already invaded into a population. Fundamental findings include that the media alert and social network alert are able to mitigate an infection. It is also shown that interfere measures and environmental noise can drive the stochastic trajectories frequently to switch between lower and higher level of infections. By constructing the confidence ellipse for each endemic equilibrium, we can estimate the tipping value of the noise intensity that causes the state switching.

Regulation of phosphate uptake kinetics in the bloom-forming dinoflagellates prorocentrum donghaiense with emphasis on two-stage dynamic process.

Phosphorus is an essential element for the growth and reproduction of algae. In recent years, the frequent outbreaks of algal blooms caused by eutrophication have drawn much attention to the influence of phosphate (P) uptake on the growth of algal cells. The previous study only considered the effect of total P pools on the P uptake process of algal cells and considered the process as one stage, which is insufficient. P uptake by algae is actually a two-stage kinetic process because in many algae species, surface-adsorbed P pools account for a large proportion of total P pools. In this paper, we fit one-stage and two-stage models of P uptake by algae to our experimental data on short-term uptake kinetics of algae Prorocentrum donghaiense under P-deplete and P-replete conditions at 24°C. According to the experimental results, P. donghaiense possesses different P uptake characteristics under different P concentrations. P. donghaiense grows faster and exponentially for longer periods of time under P-replete condition. Ranges of change of Qc (cell quota of intracellular P) and Sp (cell quota of surface-adsorbed P) during the culture time are obviously larger under P-replete condition than those under P-deplete condition. The value of Kp (represents the impact of P-starvation on P uptake rate) in one-stage model under P-deplete condition is smaller than that under P-replete condition, which is opposite to results of two-stage model and does not meet the actual biological significance of Kp. The two-stage model gives more reasonable and realistic explanations to the process of P uptake by algae no matter from the perspective of intuitive fitting effect, biological significance of parameters, statistical test results or essential dynamic process. These results, combined with long-term lab and field data in ocean, could be used to effectively predict algal blooms.