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Documents  92D30 | enregistrements trouvés : 6

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The aim is to describe the distribution of immune status in an age-structured population on the basis of a within-host sub-model [1] for continuous waning and occasional boosting. Inspired by both Feller's fundamental work [2] and the more recent delay equation formulation of physiologically structured populations [3,4], we derive, for a given force of infection, a linear renewal equation that can be solved by successive approximation, i.e., by generation expansion (with the generation number corresponding to the number of times an individual became infected).
In joint work in progress with Wilfred de Graaf, Peter Teunis and Mirjam Kretzschmar we want to use either the generation expansion or an invariant/stable distribution as the starting point for the efficient computation of coarse statistics.
The aim is to describe the distribution of immune status in an age-structured population on the basis of a within-host sub-model [1] for continuous waning and occasional boosting. Inspired by both Feller's fundamental work [2] and the more recent delay equation formulation of physiologically structured populations [3,4], we derive, for a given force of infection, a linear renewal equation that can be solved by successive approximation, i.e., by ...

92D30 ; 60J75 ; 45D05

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We consider a simple stochastic model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size N. In our model, the spread of each strain is described by the stochastic logistic SIS epidemic process in the absence of the other strain, and we assume that there is perfect cross-immunity between the two virus strains, that is, individuals infected by one strain are temporarily immune to re-infections and infections by the other strain. For the case where one strain has a strictly larger basic reproductive ratio than the other, and the stronger strain on its own is supercritical (that is, its basic reproductive ratio is larger than 1), we derive precise asymptotic results for the distribution of the time when the weaker strain disappears from the population, that is, its extinction time. We further consider what happens when the difference between the two reproductive ratios may tend to 0.
This is joint work with Fabio Lopes.
We consider a simple stochastic model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size N. In our model, the spread of each strain is described by the stochastic logistic SIS epidemic process in the absence of the other strain, and we assume that there is perfect cross-immunity between the two virus strains, that is, individuals infected by one strain are temporarily immune to re...

60J27 ; 92D30

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Multi angle  Modèles mathématiques des épidémies
Pardoux, Etienne (Auteur de la Conférence) | CIRM (Editeur )

Il y a cent ans, Sir Ronald Ross tentait de convaincre ses collègues médecins que l'épidémiologie doit être étudiée avec l'aide des mathématiques. Le but de cet exposé est d'expliquer pourquoi les mathématiques sont essentielles pour combattre les épidémies, et de donner quelques indications sur les avancées récentes de la modélisation mathématique en épidémiologie.

00A06 ; 00A08 ; 92C60 ; 92D30

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Antibiotic resistance is a serious public health concern. Responding to this problem effectively requires characterising the factors (i.e. evolutionary and ecological processes) that determine resistance frequencies. At present, we do not have ecologically plausible models of resistance that are able to replicate observed trends - we are therefore unable to make credible predictions about resistance dynamics. In this talk, I will present work motivated by three tends observed in Streptococcus pneumoniae resistance data: the stable coexistence of antibiotic sensitivity and resistance, variation between resistance frequencies between pneumococcal lineages and correlation in resistance to different antibiotics. I will propose that variation in the fitness benefit gained from resistance arising from variation in the duration of carriage of pneumococcal lineages is a parsimonious explanation for all three trends. This eco-evolutionary framework could allow more accurate prediction of future resistance levels and play a role in informing strategies to prevent the spread of resistance.
Antibiotic resistance is a serious public health concern. Responding to this problem effectively requires characterising the factors (i.e. evolutionary and ecological processes) that determine resistance frequencies. At present, we do not have ecologically plausible models of resistance that are able to replicate observed trends - we are therefore unable to make credible predictions about resistance dynamics. In this talk, I will present work ...

92D30 ; 92D40

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In an epidemic model, the basic reproduction number $ R_{0}$ is a function of the parameters (such as infection rate) measuring disease infectivity. In a large population, if $ R_{0}> 1$, then the disease can spread and infect much of the population (supercritical epidemic); if $ R_{0}< 1$, then the disease will die out quickly (subcritical epidemic), with only few individuals infected.
For many epidemics, the dynamics are such that $ R_{0}$ can cross the threshold from supercritical to subcritical (for instance, due to control measures such as vaccination) or from subcritical to supercritical (for instance, due to a virus mutation making it easier for it to infect hosts). Therefore, near-criticality can be thought of as a paradigm for disease emergence and eradication, and understanding near-critical phenomena is a key epidemiological challenge.
In this talk, we explore near-criticality in the context of some simple models of SIS (susceptible-infective-susceptible) epidemics in large homogeneous populations.
In an epidemic model, the basic reproduction number $ R_{0}$ is a function of the parameters (such as infection rate) measuring disease infectivity. In a large population, if $ R_{0}> 1$, then the disease can spread and infect much of the population (supercritical epidemic); if $ R_{0}< 1$, then the disease will die out quickly (subcritical epidemic), with only few individuals infected.
For many epidemics, the dynamics are such that $ R_{0}$ can ...

92D30 ; 05C80 ; 92D25 ; 60J28

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