Abstract
In this paper, we investigate an age-structured HIV infection model with logistic growth for target cell. We rewrite the model as an abstract non-densely defined Cauchy problem and obtain the condition which guarantees the existence of the unique positive steady state. By linearizing the model at steady state and analysing the associated characteristic transcendental equations, we study the local asymptotic stability of the steady state. Furthermore, by using Hopf bifurcation theorem in Liu et al., we show that Hopf bifurcation occurs at the positive steady state when bifurcating parameter crosses some critical values. Finally, we perform some numerical simulations to illustrate our results.
Highlights
The HIV (Human Immunodeficiency Virus) that causes AIDS (Acquired Immune Deficiency Syndrome) has attracted the attention of numerous researchers
By using centre manifold theory and Hopf bifurcation theorem of non-densely defined Cauchy problems in [17] and [14], Liu et al [15] showed that age-structured model of consumer-resource mutualism undergoes a Hopf bifurcation at the positive equilibrium under some conditions
We study an age-structured HIV infection model with logistic target-cell growth and employ Hopf bifurcation theorem in Liu et al to study that Hopf bifurcation occurs at the positive steady state when bifurcating parameter crosses some critical values in this paper
Summary
The HIV (Human Immunodeficiency Virus) that causes AIDS (Acquired Immune Deficiency Syndrome) has attracted the attention of numerous researchers. Wang and Liu [31] considered an age-structured compartmental pest–pathogen model Their results showed that Hopf bifurcation occurred at a positive steady state as bifurcating parameter passed some values. We study an age-structured HIV infection model with logistic target-cell growth and employ Hopf bifurcation theorem in Liu et al to study that Hopf bifurcation occurs at the positive steady state when bifurcating parameter crosses some critical values in this paper. (v) α(a) is new free virus particle production rate of an infected cell with infected age a and defined by α(a) = α∗, a ≥ τ ,. Based on the above discussion and assumptions, we obtain the following HIV infection model with logistic target-cell growth and virus-to-cell infection.
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