A model for hepatitis B disease with age-dependent susceptibility and vertical transmission

Abstract

In this paper, we construct a SEI model for hepatitis B where the susceptibility and transmission probabilities depend on the chronological age. We extend results of (Houpa et al, 2014) who studied it without vertical transmission. Moreover, we derive the basic reproductive rate R0. Under given assumptions, we prove that the disease free equilibrium is globally asymptotically stable if R0 <1; the endemic equilibrium is globally asymptotically stable if R0 >1 and that the system is uniformly persistent. Numerical simulations are carried out to illustrate our results.

https://doi.org/10.28919/cmbn/3126