SrasV1, Main, Merge, bibRecord, 002B10

On the final size of epidemics with seasonality.

Identifieur interne : 002B10 ( Main/Merge ); précédent : 002B09; suivant : 002B11

On the final size of epidemics with seasonality.

Auteurs : Nicolas Bacaër [France] ; M Gabriela M. Gomes

Source :

Bulletin of mathematical biology [ 1522-9602 ] ; 2009.

RBID : pubmed:19475453

Descripteurs français

KwdFr :
- Concepts mathématiques, Flambées de maladies (), Grippe humaine (épidémiologie), Humains, Infections à alphavirus (épidémiologie), Modèles biologiques, Modèles statistiques, Saisons, Virus du chikungunya.
MESH :
- épidémiologie : Grippe humaine, Infections à alphavirus.
- Concepts mathématiques, Flambées de maladies, Humains, Modèles biologiques, Modèles statistiques, Saisons, Virus du chikungunya.

English descriptors

KwdEn :
- Alphavirus Infections (epidemiology), Chikungunya virus, Disease Outbreaks (statistics & numerical data), Humans, Influenza, Human (epidemiology), Mathematical Concepts, Models, Biological, Models, Statistical, Seasons.
MESH :
- epidemiology : Alphavirus Infections, Influenza, Human.
- statistics & numerical data : Disease Outbreaks.
- Chikungunya virus, Humans, Mathematical Concepts, Models, Biological, Models, Statistical, Seasons.

Abstract

We first study an SIR system of differential equations with periodic coefficients describing an epidemic in a seasonal environment. Unlike in a constant environment, the final epidemic size may not be an increasing function of the basic reproduction number R(0) or of the initial fraction of infected people. Moreover, large epidemics can happen even if R(0) < 1. But like in a constant environment, the final epidemic size tends to 0 when R(0) < 1 and the initial fraction of infected people tends to 0. When R(0) > 1, the final epidemic size is bigger than the fraction 1 - 1/R(0) of the initially nonimmune population. In summary, the basic reproduction number R(0) keeps its classical threshold property but many other properties are no longer true in a seasonal environment. These theoretical results should be kept in mind when analyzing data for emerging vector-borne diseases (West-Nile, dengue, chikungunya) or air-borne diseases (SARS, pandemic influenza); all these diseases being influenced by seasonality.

Url:

https://hal.archives-ouvertes.fr/hal-01299608

DOI: 10.1007/s11538-009-9433-7
PubMed: 19475453

Links to Exploration step

pubmed:19475453

Le document en format XML

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<front><div type="abstract" xml:lang="de">              <p>Man studiert das SIR-System von Differentialgleichungen mit periodischen Koeffizienten, das eine Epidemie in einer jahreszeitlichen Umgebung beschreibt. Im Gegensatz zu den konstanten Umgebungen kann die Endgrösse einer Epidemie  eine steigende Funktion der Nettoreproduktionsrate oder des anfänglichen Anteils der infizierten Personen nicht sein. Grosse Epidemien können auch wenn $R_0<1$ stattfinden. Aber wie in den konstanten Umgebungen konvergiert die Endgrösse der Epidemie nach 0 wenn R0<1 und der anfängliche Anteil der infizierten Personen nach 0 konvergiert. Wenn R0>1 ist die Endgrösse der Epidemie grösser als der Anteil 1-1/R0 der anfänglichen nicht immunisierten Bevölkerung. Die Nettoreproduktionsrate R0 behält also die Rolle einer Schwelle, aber viele klassische Merkmale sind in einer jahreszeitlichen Umgebung nicht mehr wahr. Man sollte diese theoretischen Bemerkungen nicht vergessen wenn man Daten für Vektorkrankheiten wie das Chikungunyafieber, das Denguefieber oder das West-Nil-Virus untersucht, weil diese Krankheiten jahreszeitlich sind. Das gilt auch für Krankheiten, die direkt mit dem Luft übertragen sind, wie die Grippe oder das SARS.</p>
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<term>Seasons</term>
</keywords>
<keywords scheme="MESH" xml:lang="fr"><term>Concepts mathématiques</term>
<term>Flambées de maladies</term>
<term>Humains</term>
<term>Modèles biologiques</term>
<term>Modèles statistiques</term>
<term>Saisons</term>
<term>Virus du chikungunya</term>
</keywords>
</textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">We first study an SIR system of differential equations with periodic coefficients describing an epidemic in a seasonal environment. Unlike in a constant environment, the final epidemic size may not be an increasing function of the basic reproduction number R(0) or of the initial fraction of infected people. Moreover, large epidemics can happen even if R(0) < 1. But like in a constant environment, the final epidemic size tends to 0 when R(0) < 1 and the initial fraction of infected people tends to 0. When R(0) > 1, the final epidemic size is bigger than the fraction 1 - 1/R(0) of the initially nonimmune population. In summary, the basic reproduction number R(0) keeps its classical threshold property but many other properties are no longer true in a seasonal environment. These theoretical results should be kept in mind when analyzing data for emerging vector-borne diseases (West-Nile, dengue, chikungunya) or air-borne diseases (SARS, pandemic influenza); all these diseases being influenced by seasonality.</div>
</front>
</TEI>
</PubMed>
</double>
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On the final size of epidemics with seasonality.

On the final size of epidemics with seasonality.

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