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Analysis of an Age-structured SIL model with demographics process and vertical transmission
Résumé : 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.
Cited literature [49 references]
https://hal.inria.fr/hal-01300058
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Submitted on : Friday, April 8, 2016 - 4:09:45 PM
Last modification on : Monday, January 10, 2022 - 9:36:03 AM
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Friday, April 8, 2016 - 4:09:45 PM
Last modification on : Monday, January 10, 2022 - 9:36:03 AM
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Vol.17.pp.23-52.pdf
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