10.46298/arima.1966
https://arima.episciences.org/1966
Demasse, Ramses Djidjou
Ramses Djidjou
Demasse
Tewa, Jean Jules
Jean Jules
Tewa
Bowong, Samuel
Samuel
Bowong
Analysis of an Age-structured SIL model with demographics process and vertical transmission
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.
episciences.org
Age-structured model
Semigroup
Basic reproduction ratio
Stability.
[INFO] Computer Science [cs]
[MATH] Mathematics [math]
2022-05-24
2014-11-26
2014-11-26
en
journal article
https://hal.archives-ouvertes.fr/hal-01300058v1
1638-5713
https://arima.episciences.org/1966/pdf
VoR
application/pdf
Revue Africaine de la Recherche en Informatique et MathÃ©matiques AppliquÃ©es
Volume 17 - 2014 - Special issue CARI'12
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