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The dynamics generated by the delay differential equation _ xðtÞZKmxðtÞC f ðxðtKtÞÞ with unimodal feedback is studied. The existence of the global attractor is shown and bounds of the attractor are given. We find attractive invariant intervals and give sufficient conditions that guarantee that all solutions enter the domain where f 0 is negative with(More)
Given the danger of an unprecedented spread of the highly pathogenic avian influenza strain H5N1 in humans, and great challenges to the development of an effective influenza vaccine, antiviral drugs will probably play a pivotal role in combating a novel pandemic strain. A critical limitation to the use of these drugs is the evolution of highly transmissible(More)
BACKGROUND The emergence of neuraminidase inhibitor resistance has raised concerns about the prudent use of antiviral drugs in response to the next influenza pandemic. While resistant strains may initially emerge with compromised viral fitness, mutations that largely compensate for this impaired fitness can arise. Understanding the extent to which these(More)
The use of antiviral drugs has been recognized as the primary public health strategy for mitigating the severity of a new influenza pandemic strain. However, the success of this strategy requires the prompt onset of therapy within 48 hours of the appearance of clinical symptoms. This requirement may be captured by a compartmental model that monitors the(More)
We give bounds for the global attractor of the delay differential equation ˙ x(t) = −µx(t) + f (x(t−τ)), where f is unimodal and has negative Schwarzian derivative. If f and µ satisfy certain condition, then, regardless of the delay, all solutions enter the domain where f is monotone decreasing and the powerful results for delayed monotone feedback can be(More)
A new SEIR model with distributed infinite delay is derived when the infectivity depends on the age of infection. The basic reproduction number R0, which is a threshold quantity for the stability of equilibria, is calculated. If R0 < 1, then the disease-free equilibrium is globally asymptotically stable and this is the only equilibrium. On the contrary, if(More)
BACKGROUND With the rise of the second pandemic wave of the novel influenza A (H1N1) virus in the current season in the Northern Hemisphere, pandemic plans are being carefully re-evaluated, particularly for the strategic use of antiviral drugs. The recent emergence of oseltamivir-resistant in treated H1N1 patients has raised concerns about the prudent use(More)
Keywords: Delay differential equation Global attractor Wright's equation Mackey–Glass equation One-dimensional map Schwarzian derivative a b s t r a c t We gain further insight into the use of the Schwarzian derivative to obtain new results for a family of functional differential equations including the famous Wright's equation and the Mackey-Glass type(More)
Recently, particular counterexamples were constructed to some theorems of a previous paper, concerning the global attractivity of the positive equilibrium for the delay equation _ pðtÞ ¼ bp m ðt À sÞ 1 þ p n ðt À sÞ À cpðtÞ: The purpose of this note is to explore the underlying phenomenon from a more general point of view, and to give an explanation of the(More)