Modelling the spread of HIV/AIDS amongst injecting drug users taking into account variable infectivity and loss of infectivity

David Greenhalgh, Wafa Al-Fwzan

Research output: Contribution to conferenceAbstract

Abstract

We start off this paper with a brief introduction to modeling Human
Immunodeficiency Virus (HIV) and Acquired Immune Deficiency Syndrome
(AIDS) amongst sharing, injecting drug users (IDUs). Then we describe the
mathematical model which we shall use which extends an existing
model of the spread of HIV and AIDS amongst IDUs by
incorporating loss of HIV infectivity over time. This is followed by
the derivation of a key epidemiological parameter, the basic
reproduction number $R_0$. Next we give some analytical equilibrium,
local and global stability results. We show that if $R_0 \le 1$ then
the disease will always die out. For $R_0 > 1$ there is the
disease-free equilibrium (DFE) and a unique endemic equilibrium. The
DFE is unstable. An approximation argument
shows that we expect the endemic equilibrium to be locally stable. We next discuss a more
realistic version of the model, relaxing the assumption that the number
of addicts remains constant and obtain some results for this model.
The subsequent section gives simulations for both models confirming that if $R_0 \le 1$ then
the disease will die out and if $R_0 > 1$ then if it is initially present the disease will tend
to the unique endemic equilibrium. The simulation results are compared with the original model with no
loss of HIV infectivity. Next the implications of these results for control strategies are considered. A
brief summary concludes the paper.

Other

OtherFirst Workshop on Dynamical Systems Applied to Biology and Natural Sciences
Period31/03/11 → …

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Virus
Drugs
Endemic Equilibrium
Modeling
Die
Model
Local Stability
Global Stability
Control Strategy
Sharing
Simulation
Unstable
Approximation

Keywords

  • HIV/AIDS
  • basic reproduction number
  • loss of infectivity
  • equilibrium and stability analysis
  • global stability
  • modelling
  • spread
  • injecting drug users

Cite this

Greenhalgh, D., & Al-Fwzan, W. (2010). Modelling the spread of HIV/AIDS amongst injecting drug users taking into account variable infectivity and loss of infectivity. Abstract from First Workshop on Dynamical Systems Applied to Biology and Natural Sciences, .
Greenhalgh, David ; Al-Fwzan, Wafa. / Modelling the spread of HIV/AIDS amongst injecting drug users taking into account variable infectivity and loss of infectivity. Abstract from First Workshop on Dynamical Systems Applied to Biology and Natural Sciences, .
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abstract = "We start off this paper with a brief introduction to modeling HumanImmunodeficiency Virus (HIV) and Acquired Immune Deficiency Syndrome(AIDS) amongst sharing, injecting drug users (IDUs). Then we describe themathematical model which we shall use which extends an existingmodel of the spread of HIV and AIDS amongst IDUs byincorporating loss of HIV infectivity over time. This is followed bythe derivation of a key epidemiological parameter, the basicreproduction number $R_0$. Next we give some analytical equilibrium,local and global stability results. We show that if $R_0 \le 1$ thenthe disease will always die out. For $R_0 > 1$ there is thedisease-free equilibrium (DFE) and a unique endemic equilibrium. TheDFE is unstable. An approximation argumentshows that we expect the endemic equilibrium to be locally stable. We next discuss a morerealistic version of the model, relaxing the assumption that the numberof addicts remains constant and obtain some results for this model.The subsequent section gives simulations for both models confirming that if $R_0 \le 1$ thenthe disease will die out and if $R_0 > 1$ then if it is initially present the disease will tendto the unique endemic equilibrium. The simulation results are compared with the original model with noloss of HIV infectivity. Next the implications of these results for control strategies are considered. Abrief summary concludes the paper.",
keywords = "HIV/AIDS, basic reproduction number, loss of infectivity, equilibrium and stability analysis, global stability, modelling, spread, injecting drug users",
author = "David Greenhalgh and Wafa Al-Fwzan",
year = "2010",
month = "2",
language = "English",
note = "First Workshop on Dynamical Systems Applied to Biology and Natural Sciences ; Conference date: 31-03-2011",

}

Greenhalgh, D & Al-Fwzan, W 2010, 'Modelling the spread of HIV/AIDS amongst injecting drug users taking into account variable infectivity and loss of infectivity' First Workshop on Dynamical Systems Applied to Biology and Natural Sciences, 31/03/11, .

Modelling the spread of HIV/AIDS amongst injecting drug users taking into account variable infectivity and loss of infectivity. / Greenhalgh, David; Al-Fwzan, Wafa.

2010. Abstract from First Workshop on Dynamical Systems Applied to Biology and Natural Sciences, .

Research output: Contribution to conferenceAbstract

TY - CONF

T1 - Modelling the spread of HIV/AIDS amongst injecting drug users taking into account variable infectivity and loss of infectivity

AU - Greenhalgh, David

AU - Al-Fwzan, Wafa

PY - 2010/2

Y1 - 2010/2

N2 - We start off this paper with a brief introduction to modeling HumanImmunodeficiency Virus (HIV) and Acquired Immune Deficiency Syndrome(AIDS) amongst sharing, injecting drug users (IDUs). Then we describe themathematical model which we shall use which extends an existingmodel of the spread of HIV and AIDS amongst IDUs byincorporating loss of HIV infectivity over time. This is followed bythe derivation of a key epidemiological parameter, the basicreproduction number $R_0$. Next we give some analytical equilibrium,local and global stability results. We show that if $R_0 \le 1$ thenthe disease will always die out. For $R_0 > 1$ there is thedisease-free equilibrium (DFE) and a unique endemic equilibrium. TheDFE is unstable. An approximation argumentshows that we expect the endemic equilibrium to be locally stable. We next discuss a morerealistic version of the model, relaxing the assumption that the numberof addicts remains constant and obtain some results for this model.The subsequent section gives simulations for both models confirming that if $R_0 \le 1$ thenthe disease will die out and if $R_0 > 1$ then if it is initially present the disease will tendto the unique endemic equilibrium. The simulation results are compared with the original model with noloss of HIV infectivity. Next the implications of these results for control strategies are considered. Abrief summary concludes the paper.

AB - We start off this paper with a brief introduction to modeling HumanImmunodeficiency Virus (HIV) and Acquired Immune Deficiency Syndrome(AIDS) amongst sharing, injecting drug users (IDUs). Then we describe themathematical model which we shall use which extends an existingmodel of the spread of HIV and AIDS amongst IDUs byincorporating loss of HIV infectivity over time. This is followed bythe derivation of a key epidemiological parameter, the basicreproduction number $R_0$. Next we give some analytical equilibrium,local and global stability results. We show that if $R_0 \le 1$ thenthe disease will always die out. For $R_0 > 1$ there is thedisease-free equilibrium (DFE) and a unique endemic equilibrium. TheDFE is unstable. An approximation argumentshows that we expect the endemic equilibrium to be locally stable. We next discuss a morerealistic version of the model, relaxing the assumption that the numberof addicts remains constant and obtain some results for this model.The subsequent section gives simulations for both models confirming that if $R_0 \le 1$ thenthe disease will die out and if $R_0 > 1$ then if it is initially present the disease will tendto the unique endemic equilibrium. The simulation results are compared with the original model with noloss of HIV infectivity. Next the implications of these results for control strategies are considered. Abrief summary concludes the paper.

KW - HIV/AIDS

KW - basic reproduction number

KW - loss of infectivity

KW - equilibrium and stability analysis

KW - global stability

KW - modelling

KW - spread

KW - injecting drug users

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M3 - Abstract

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Greenhalgh D, Al-Fwzan W. Modelling the spread of HIV/AIDS amongst injecting drug users taking into account variable infectivity and loss of infectivity. 2010. Abstract from First Workshop on Dynamical Systems Applied to Biology and Natural Sciences, .