A Model for Hepatitis B with Chronological and Infection Ages

T Y Kouakep

doi:10.4172/2168-9679.1000148

Abstract

We construct and study a differential infectivity model with chronological and infection age. The application is done on hepatitis B in Cameroon. We prove the global stability of the disease free equilibrium when the basic reproduction ratio R0 is less than one and the existence and uniqueness of an endemic equilibrium when R0>1 .

Highlights

We construct and study a differential infectivity model with chronological and infection age
We denote by i (t,τ) the density of infective that will develop acute disease at time t contaminated since a time and e (t,τ) the density of infective that will not develop acute disease at time t contaminated since a time τ
The model described by equations (1.1-1.2) exhibit a rich dynamic

Summary

Introduction

We construct and study a differential infectivity model with chronological and infection age. We introduce a model with differential infectivity and chronological or infection ages. The model we shall consider reads as follows: (∂t + ∂a )s(t, a) = −μs(t, a) − λ(t)s(t, a), t > 0, a > 0, s(t, 0) = Λ, (∂t + ∂τ )i(t,τ ) = −(μ + γ i ) i (t,τ ),t > 0,τ > 0, (1.1)

Results

Conclusion