episciences.org_1966_1669644665
1669644665
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Revue Africaine de Recherche en Informatique et MathÃ©matiques AppliquÃ©es
16385713
11
26
2014
Volume 17  2014  Special...
Analysis of an Agestructured SIL model with demographics process and vertical transmission
Ramses Djidjou
Demasse
https://orcid.org/0000000316845190
Jean Jules
Tewa
Samuel
Bowong
We consider a mathematical SIL model for the spread of a directly transmitted infectious disease in an agestructured population; taking into account the demographic process and the vertical transmission of the disease. First we establish the mathematical wellposedness 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 diseasefree equilibrium is locally asymptotically stable if R0<1. We also show that the endemic steady states are forwardly bifurcated from the diseasefree steady state when R0 cross the unity. Finally we examine the conditions for the local stability of the endemic steady states.
11
26
2014
1966
https://hal.archivesouvertes.fr/hal01300058v1
10.46298/arima.1966
https://arima.episciences.org/1966

https://arima.episciences.org/1966/pdf