Qun Liu

Bio: Qun Liu is an academic researcher from Northeast Normal University. The author has contributed to research in topics: Stationary distribution & Epidemic model. The author has an hindex of 16, co-authored 68 publications receiving 845 citations. Previous affiliations of Qun Liu include Yulin Normal University.

Dynamics of a Stochastic Predator–Prey Model with Stage Structure for Predator and Holling Type II Functional Response

Abstract: In this paper, we develop and study a stochastic predator–prey model with stage structure for predator and Holling type II functional response First of all, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model Then, we obtain sufficient conditions for extinction of the predator populations in two cases, that is, the first case is that the prey population survival and the predator populations extinction; the second case is that all the prey and predator populations extinction The existence of a stationary distribution implies stochastic weak stability Numerical simulations are carried out to demonstrate the analytical results

Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence

Abstract: In this paper, we consider a stochastic SEIR epidemic model with standard incidence. By constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution to the model. Our result does not depend on the positive endemic equilibrium E ∗ of the deterministic system, which improves the previous result to a greater extent. Moreover, we also establish sufficient conditions for extinction of the disease.

Stochastic Differential Equations And Applications

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Elements Of Mathematical Ecology

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Chaos in a Three Species Food Chain

Abstract: Chaos is an important research direction in ecology and the number of species in a chaotic state has complex movements in strange attractor.The three species ratio dependent food chain model with Holling Ⅱ functional response was established.The boundedness of species was obtained by differential inequality.The quantitative analysis of the three species food chain model was investigated by numerical simulations and the existence of chaotic dynamic was studied by the bifurcation diagrams.The strange attractor was obtained for suitable choice of parametric values and is existence via double periods.The appearance of chaos in this model suggests that chaotic dynamics may be common in natural food webs.

Analysis of rabies in China: Transmission dynamics and control

Abstract: Human rabies is one of the major public-health problems in China. The number of human rabies cases has increased dramatically in the last 15 years, partially due to the poor understanding of the transmission dynamics of rabies and the lack of effective control measures of the disease. In this article, in order to explore effective control and prevention measures we propose a deterministic model to study the transmission dynamics of rabies in China. The model consists of susceptible, exposed, infectious, and recovered subpopulations of both dogs and humans and describes the spread of rabies among dogs and from infectious dogs to humans. The model simulations agree with the human rabies data reported by the Chinese Ministry of Health. We estimate that the basic reproduction number for the rabies transmission in China and predict that the number of the human rabies is decreasing but may reach another peak around 2030. We also perform some sensitivity analysis of in terms of the model parameters and compare the effects of culling and immunization of dogs. Our study demonstrates that (i) reducing dog birth rate and increasing dog immunization coverage rate are the most effective methods for controlling rabies in China; and (ii) large scale culling of susceptible dogs can be replaced by immunization of them.

Simulation of nanoparticles application for expediting melting of PCM inside a finned enclosure

Abstract: We presented a comprehensive method for modeling acceleration of melting by using extended surface and nanoparticles. On the base of the paraffin, copper oxide nanoparticles was distributed. Geometric configurations were categorized in three cases. Liquid fraction and isotherms as well as streamline were analyzed for all cases. We concluded that energy storage changes during this transient phenomenon. It has maximum point in its profile. Minimum time for melting is reported for case 3 in which longer fins have been used.