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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)
We propose a mathematical model to simulate the SARS outbreak in Beijing. The model consists of six subpopulations, namely susceptible, exposed, quarantined, suspect, probable and removed, as China started to report SARS cases as suspect and probable separately from April 27 and cases transferred from suspect class to probable class from May 2. By(More)
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)
This paper is devoted to the analysis of a mathematical model of blood cells production in the bone marrow (hematopoiesis). The model is a system of two age-structured partial differential equations. Integrating these equations over the age, we obtain a system of two nonlinear differential equations with distributed time delay corresponding to the cell(More)
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)
We consider a two-dimensional model of cell-to-cell spread of HIV-1 in tissue cultures, assuming that infection is spread directly from infected cells to healthy cells and neglecting the effects of free virus. The intracellular incubation period is modeled by a gamma distribution and the model is a system of two differential equations with distributed(More)
We establish the existence of traveling front solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-II functional response. The traveling front solutions are equivalent to heteroclinic orbits in R(4) and the small amplitude traveling wave train solutions are equivalent(More)
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)
BACKGROUND Methicillin-resistant Staphylococcus aureus (MRSA) has traditionally been associated with infections in hospitals. Recently, a new strain of MRSA has emerged and rapidly spread in the community, causing serious infections among young, healthy individuals. Preliminary reports imply that a particular clone (USA300) of a community-acquired MRSA(More)
Infections caused by antibiotic-resistant pathogens are a global public health problem. Numerous individual- and population-level factors contribute to the emergence and spread of these pathogens. An individual-based model (IBM), formulated as a system of stochastically determined events, was developed to describe the complexities of the transmission(More)