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bachar1

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bachar1

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Manuscript information

HIV treatment models with time delay.

  • Mostafa Bachar
C. R. Biol. 2004; 327 (11): 983-994
Abstract
The present paper shows possible effects of antiretroviral treatment on the dynamics of the spread of the disease of human immunodeficiency virus infection in a population of varying size. By introducing time delays, we model the latency period and the delayed onset of positive treatment effects in the patients. The Hopf bifurcation and stability behaviour of the delay differential-equation model are analysed and simulations for different scenarios depending on the size of the treatment-induced delay are presented, and the results are discussed in detail.

Unit definitions 0

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition

Compartments 1

Id Name Spatial dimensions Size
default — — 1.0

Species 4

Id Name Initial quantity Compartment Fixed
EXT EXT 1.0 default ✔
I1 Infectious stage 1 50.0 default ✘
I2 Infectious stage 2 0.0 default ✘
S Susceptible 4950.0 default ✘

Initial assignments 0

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Reactions 8
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
v_1 — EXT = S

b*(S+I1+I2)
v_2 — S = I1

c*Beta*(I1+a*I2)*S/(S+I1+I2)
v_3 — S = EXT

d*S
v_4 — I1 = EXT

d*I1
v_5 — I1 = I2

k1*I1
v_6 — I2 = I1

Alpha*I2
v_7 — I2 = EXT

d*I2
v_8 — I2 = EXT

k2*I2

Parameters 0   9

Global parameters

Id Value
Alpha 0.2
Beta 0.5
N —
a 0.6
b 0.001
c 0.3
d 0.0006
k1 0.019
k2 0.0159

Local parameters

Id Value Reaction

Rules 0   0   1

Assignment rules

Definition
N = S + I1 +I2

Rate rules

Definition

Algebraic rules

Definition

Events 0

Trigger Assignments