- #1
J6204
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- 2
Homework Statement
Given the following figure and the following variables and parameters, I have been able to come up with the set of differential equation below the image. My question is how does the system of equations 1 which I produced myself differ from the set of equations 2. Below I have a further explanation of this question. The image below was used to create my system of equations 1.
Homework Equations
Variables
R(t): number of susceptible T-cells
L(t): number of latently infected T-cells
E(t): number of actively infected T-cells
V(t): amount of virus
Parameters
$$\Gamma$$: rate of production of susceptible T-cells
$$\tau$$: fraction of T-cells susceptible to attack by HIV
$$\mu$$: removal rate of T-cells
$$\beta$$: rate of T-cell infection
p: fraction of infected T-cells that are latently infected
$$\alpha$$: rate that latent T-cells become activated
$$\delta$$: death rate/removal of actively infected T-cells
$$\pi$$: rate that virus is produced by actively infected T-cells
$$\sigma$$: rate of virus removal System of Equations 1
$$\frac{dR}{dt} = \Gamma \tau - \mu R - \beta VR $$
$$\frac{dL}{dt} = p \beta VR-\mu L - \alpha L$$
$$\frac{dE}{dt} = (1-p)\beta V R+ \alpha L - \delta E - \pi E$$
$$\frac{dV}{dt} = \pi E - \sigma V - \beta V R$$
System of Equations 2
$$\frac{dR}{dt} = \Gamma \tau - \mu R - \beta VR $$
$$\frac{dL}{dt} = p \beta VR-\mu L - \alpha L$$
$$\frac{dE}{dt} = (1-p)\beta V R+ \alpha L - \delta E $$
$$\frac{dV}{dt} = \pi E - \sigma V $$
The Attempt at a Solution
So clearly there is a difference between the number of infected T cells in system of equations 1 and
There is a difference between the amount of virus in system of equations 1 and 2. System 1 includes the loss of term $$\beta VR$$ while the system of equations of 2 in equation 4. Why is this?
