Threshold dynamics of a switching diffusion SIR model with logistic growth and healthcare resources.

In this article, we have constructed a stochastic SIR model with healthcare resources and logistic growth, aiming to explore the effect of random environment and healthcare resources on disease transmission dynamics. We have showed that under mild extra conditions, there exists a critical parameter, i.e.

Stability and Hopf bifurcation of an intraguild prey-predator fishery model with two delays and Michaelis-Menten type predator harvest.

In this paper, we have proposed and investigated an intraguild predator-prey system incorporating two delays and a harvesting mechanism based on the Michaelis-Menten principle, and it was assumed that the two species compete for a shared resource. Firstly, we examined the properties of the relevant characteristic equations to derive sufficient conditions for the asymptotical stability of equilibria in the delayed model and the existence of Hopf bifurcation. Using the normal form method and the central manifold theorem, we analyzed the stability and direction of periodic solutions arising from Hopf bifurcations.

Bifurcation analysis in a modified Leslie-Gower predator-prey model with fear effect and multiple delays.

In this paper, we explored a modified Leslie-Gower predator-prey model incorporating a fear effect and multiple delays. We analyzed the existence and local stability of each potential equilibrium. Furthermore, we investigated the presence of periodic solutions via Hopf bifurcation bifurcated from the positive equilibrium with respect to both delays.

Theory of Stoichiometric Intraguild Predation: Algae, Ciliate, and Daphnia.

Consumers respond differently to external nutrient changes than producers, resulting in a mismatch in elemental composition between them and potentially having a significant impact on their interactions. To explore the responses of herbivores and omnivores to changes in elemental composition in producers, we develop a novel stoichiometric model with an intraguild predation structure. The model is validated using experimental data, and the results show that our model can well capture the growth dynamics of these three species.

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

Elucidating the mechanism of effect of phosphate (PO) 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 PO 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 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.

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].

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Stochastic modeling of algal bloom dynamics with delayed nutrient recycling.

Using the discrete Markov chain, in this paper we develop a stochastic model for algal bloom, in which white noise terms are introduced to describe the effects of environmental random fluctuations and time delay to account for the time needed in the conversion of detritus into nutrient. For the proposed model, we firstly discuss the well-posedness, namely the existence and uniqueness of the global positive solution. Then, it is followed by seeking the sufficient conditions for the stochastic stability of its washout equilibrium.

The effect of media coverage on threshold dynamics for a stochastic SIS epidemic model.

Media coverage is one of the important measures for controlling infectious diseases, but the effect of media coverage on diseases spreading in a stochastic environment still needs to be further investigated. Here, we present a stochastic susceptible-infected-susceptible (SIS) epidemic model incorporating media coverage and environmental fluctuations. By using Feller's test and stochastic comparison principle, we establish the stochastic basic reproduction number , which completely determines whether the disease is persistent or not in the population.