Ramses Djidjou Demasse ; Jean Jules Tewa ; Samuel Bowong
-
Analysis of an Age-structured SIL model with demographics process and vertical transmission
arima:1966 -
Revue Africaine de Recherche en Informatique et Mathématiques Appliquées,
November 26, 2014,
Volume 17 - 2014 - Special issue CARI'12
-
https://doi.org/10.46298/arima.1966
Analysis of an Age-structured SIL model with demographics process and vertical transmissionArticle
Authors: Ramses Djidjou Demasse 1,2; Jean Jules Tewa 3; Samuel Bowong 4,5
0000-0003-1684-5190##0000-0002-4700-3650##NULL
Ramses Djidjou Demasse;Jean Jules Tewa;Samuel Bowong
1 Département de Mathématiques Université de Yaoundé 1 = Department of Mathematics [Yaoundé, Cameroon]
2 Département de Mathématiques [Yaoundé I] = Department of Mathematics [Yaoundé, Cameroon]
3 Ecole Nationale Supérieure Polytechnique de Yaoundé
4 Laboratoire International de Recherche en Informatique et Mathématiques Appliquées
5 Faculté des Sciences [Douala]
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.