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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
1,2; Jean Jules Tewa 3; Samuel Bowong 4,5
- 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.