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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
##\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 2. System of equations 1 includes the term ##\pi E## while system of equations 2 does not in equation 3. Why is this?
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?
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?
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