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.

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.

Dynamics of prion proliferation under combined treatment of pharmacological chaperones and interferons.

Prions are proteins that cause fatal neurodegenerative diseases. The misfolded conformation adopted by prions can be transmitted to other normally folded proteins. Therapeutics to stop prion proliferation have been studied experimentally; however, it is not clear how the combination of different types of treatments can decrease the growth rate of prions in the brain. In this article, we combine the implementation of pharmacological chaperones and interferons to develop a novel model using a non-linear system of ordinary differential equations and study the quantitative effects of these two treatments on the growth rate of prions. This study aims to identify how the two treatments affect prion proliferation, both individually and in tandem. We analyze the model, and qualitative global results on the disease-free and disease equilibria are proved analytically. Numerical simulations, using parameter values from in vivo experiments that provide a pharmaceutically important demonstration of the effects of these two treatments, are presented here. This mathematical model can be used to identify and optimize the best combination of the treatments within their safe ranges.

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.

[The discovery, application and enlightenment of Lanwei (EX-LE 7)].

The discovery and application of Lanwei (EX-LE 7) was reviewed to elaborate its enlightenment on the inheritance and innovation of acupuncture. Literature published before April of 2017 was searched in CNKI and VIP database with"Lanwei (EX-LE 7)"and"acupuncture"as key words. Related references and publications were retrieved. According to the purpose, literature was screened and key information was extracted to perform systematic review and analysis. The results indicated Lanwei (EX-LE 7), reflection of relationship between organ and body surface under the guidance of acupuncture and meridians theory, was not a point, but an area. The discovery and application of Lanwei (EX- LE 7) was the product of western and Chinese combination. The best indication was simple appendicitis, but operation should be applied once adhesion, purulent and perforation occurred. It is indicated to improve clinical efficacy and avoid accident, the reasoned core of theory system should be insisted and the communication with modern medicine should be reinforced.