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- Shigui Ruan, Junjie Wei
- 2003

In this paper, we first establish a basic theorem on the zeros of general transcendental functions. Based on the basic theorem, we develop a decomposition technique to investigate the stability of some exponential polynomials, that is, to find conditions under which all zeros of the exponential polynomials have negative real parts. The technique combines… (More)

- R V Culshaw, S Ruan
- Mathematical biosciences
- 2000

A.S. Perelson, D.E. Kirschner and R. De Boer (Math. Biosci. 114 (1993) 81) proposed an ODE model of cell-free viral spread of human immunodeficiency virus (HIV) in a well-mixed compartment such as the bloodstream. Their model consists of four components: uninfected healthy CD4(+) T-cells, latently infected CD4(+) T-cells, actively infected CD4(+) T-cells,… (More)

In this paper, we first study the distribution of the zeros of a third degree exponential polynomial. Then we apply the obtained results to a delay model for the control of testosterone secretion. It is shown that under certain assumptions on the coefficients the steady state of the delay model is asymptotically stable for all delay values. Under another… (More)

- Dongmei Xiao, Shigui Ruan
- Mathematical biosciences
- 2007

In this paper we study an epidemic model with nonmonotonic incidence rate, which describes the psychological effect of certain serious diseases on the community when the number of infectives is getting larger. By carrying out a global analysis of the model and studying the stability of the disease-free equilibrium and the endemic equilibrium, we show that… (More)

Recently, ratio-dependent predator-prey systems have been regarded by some researchers to be more appropriate for predator-prey interactions where predation involves serious searching processes. However, such models have set up a challenging issue regarding their dynamics near the origin since these models are not well-defined there. In this paper, the… (More)

- Dongmei Xiao, Shigui Ruan
- SIAM Journal of Applied Mathematics
- 2001

A predator-prey system with nonmonotonic functional response is considered. Global qualitative and bifurcation analyses are combined to determine the global dynamics of the model. The bifurcation analysis of the model depending on all parameters indicates that it exhibits numerous kinds of bifurcation phenomena, including the saddle-node bifurcation, the… (More)

With the recent resurgence of vector-borne diseases due to urbanization and development there is an urgent need to understand the dynamics of vector-borne diseases in rapidly changing urban environments. For example, many empirical studies have produced the disturbing finding that diseases continue to persist in modern city centers with zero or low rates of… (More)

- H. L Freedman, Shigui Ruan
- 1994

In this paper, the behavior of a continuous flow in the vicinity of a closed positively .invariant subset in a metric space is investigated. The main theorem in this part in some sense generalizes previous results concerning classification of the flow near a compact invariant set in a locally compact metric space which was described by Ura-Kimura (1960) and… (More)

- Lan Zou, Weinian Zhang, Shigui Ruan
- Journal of theoretical biology
- 2010

Hepatitis B is a potentially life-threatening liver infection caused by the hepatitis B virus (HBV) and is a major global health problem. HBV is the most common serious viral infection and a leading cause of death in mainland China. Around 130 million people in China are carriers of HBV, almost a third of the people infected with HBV worldwide and about 10%… (More)

- Abba B Gumel, Shigui Ruan, +9 authors Beni M Sahai
- Proceedings. Biological sciences
- 2004

Severe acute respiratory syndrome (SARS), a new, highly contagious, viral disease, emerged in China late in 2002 and quickly spread to 32 countries and regions causing in excess of 774 deaths and 8098 infections worldwide. In the absence of a rapid diagnostic test, therapy or vaccine, isolation of individuals diagnosed with SARS and quarantine of… (More)