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We consider a continuous age-structured two-sex population model which is given by a semilinear system of partial differential equations with nonlocal boundary conditions and is a simpler case of Fredrickson-Hoppensteadt model. The non-linearity is introduced by a source term, called from its physical meaning, the marriage function. The explicit form of the(More)
The evolution of influenza A virus is linked to a non-fixed evolutionary landscape driven by tight co-evolutionary interactions between hosts and influenza strains. Herd-immunity, cross-immunity and age-structure are among the factors shown to support the coexistence of multiple strain oscillations. In this study, we incorporate two influenza strains and(More)
We consider a model for a disease with a progressing and a quiescent exposed class and variable susceptibility to super-infection. The model exhibits backward bifurcations under certain conditions, which allow for both stable and unstable endemic states when the basic reproduction number is smaller than one.
Host immune systems impose natural selection on pathogen populations, which respond by evolving different antigenic signatures. Like many evolutionary processes, pathogen evolution reflects an interaction between different levels of selection; pathogens can win in between-strain competition by taking over individual hosts (within-host level) or by infecting(More)
A classical epidemiological framework is used to provide a preliminary cost analysis of the effects of quarantine and isolation on the dynamics of infectious diseases for which no treatment or immediate diagnosis tools are available. Within this framework we consider the cost incurred from the implementation of three types of dynamic control strategies.(More)
"In this paper we consider a two-sex population model proposed by Hoppenstead. We do not assume any special form of the mating function. We address the problem of existence and uniqueness of continuous and classical solutions. We give sufficient conditions for continuous solutions to exist globally and we show that they have in fact a directional(More)
At present H5N1 avian influenza is a zoonotic disease where the transmission to humans occurs from infected domestic birds. Since 2003 more than 500 people have been infected and nearly 60% of them have died. If the H5N1 virus becomes efficiently human-to-human transmittable, a pandemic will occur with potentially high mortality. A mathematical model of(More)
In this paper, we consider global stability for a heroin model with two distributed delays. The basic reproduction number of the heroin spread is obtained, which completely determine the stability of equilibria. Using the direct Lyapunov method with Volterra type Lyapunov function, we show that the drug use-free equilibrium is globally asymp-totically(More)