{"docId":1966,"paperId":1966,"url":"https:\/\/arima.episciences.org\/1966","doi":"10.46298\/arima.1966","journalName":"Revue Africaine de Recherche en Informatique et Math\u00e9matiques Appliqu\u00e9es","issn":"","eissn":"1638-5713","volume":[{"vid":179,"name":"Volume 17 - 2014 - Special issue CARI'12"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01300058","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01300058v1","dateSubmitted":"2014-04-28 00:00:00","dateAccepted":null,"datePublished":"2014-11-26 00:00:00","titles":{"en":"Analysis of an Age-structured SIL model with demographics process and vertical transmission"},"authors":["Demasse, Ramses Djidjou","Tewa, Jean Jules","Bowong, Samuel"],"abstracts":{"fr":"We consider a mathematical SIL model for the spread of a directly transmitted infectious disease in an age-structured population; taking into account the demographic process and the vertical transmission of the disease. First we establish the mathematical well-posedness of the time evolution problem by using the semigroup approach. Next we prove that the basic reproduction ratio R0 is given as the spectral radius of a positive operator, and an endemic state exist if and only if the basic reproduction ratio R0 is greater than unity, while the disease-free equilibrium is locally asymptotically stable if R0<1. We also show that the endemic steady states are forwardly bifurcated from the disease-free steady state when R0 cross the unity. Finally we examine the conditions for the local stability of the endemic steady states."},"keywords":[["Age-structured model"],["Semigroup"],["Basic reproduction ratio"],["Stability."],"[INFO] Computer Science [cs]","[MATH] Mathematics [math]"]}