Problem Set 4 (construct a flow diagram and the accompanying dynamical equations) (25 points)
The HIV & CD_(4). We have four classes we want to model: 3 cell stages (uninfected, infected-latent, infected-active) and 1 virus class.
Susceptible cells regenerate from some background process; transition to an infective stage based on encounters with viruses, some probability of successful transmission; susceptible cells can also just die
Infected-latent cells increase through the described process of transmission described above with a certain probability ( 1-p that the cell becomes infected but enters a latent stage; latent cells can turn in to active cells; latent cells can also just die
Infected-active cells increase through the described process of transmission described above with a certain probability, p, that the cell becomes infected and enters an active stage; latent cells decrease by either just dying or producing new virus particles
Virus particles increase by infected-active cells generating new virus particles; virus particles can also just die
Generate a flow diagram of the described processes and give all the flows/interactions some parameter names.
Then, write out the rate of change equations that mathematically describe the process of generating new HIV particles
Finally, solve for the equilibrium state for the infected-latent, infected-active, and virus particle stages.
HE+: Based on your equilibrium values, what are four ways one could design interventions to reduce virus levels in an infected host (i.e., human - not cells)? Please explain your answer mathematically (how is what you're doing changing the equilibrium value) and biologically (why will that change be beneficial to the patient)?
Problem Set 4 (construct a flow diagram and the accompanving dynamical equations) (25 points) The HIV & CD.. We have four classes we want to model: 3 cell stages (uninfected, infected-latent, infected-activeand1 virus class
Susceptible cells regenerate from some background process; transition to an infective stage based on encounters with viruses, some probability of successful transmission; susceptible cells can also just die Infected-latent cells increase through the described process of transmission described above with a certain probability (1-p) that the cell becomes infected but enters a latent stage; latent cells can turn in to active cells;latent cells can also just die Infected-active cells increase through the described process of transmission described above with a certain probability, p, that the cell becomes infected and enters an active stage; latent cells decrease by either just dying or producing new virus particles Virus particles increase by infected-active cells generating new virus particles; virus particles can also just die
1 Generate a flow diagram of the described processes and give all the flows/interactions some parameter names.
2 Then,write out the rate of change equations that mathematically describe the process of generating new HIV particles 3) Finally, solve for the equilibrium state for the infected-latent, infected-active, and virus particle stages.
HE+: Based on your equilibrium values,what are four ways one could design interventions to reduce virus levels in an infected host (i.e., human -- not cells)? Please explain your answer mathematically (how is what you're doing changing the equilibrium value) and biologically (why will that change be beneficial to the patient)?
