Modelling within-host immune
response
21/10 PROF. OGUNJIMI
Question 1:
Imagine a population of uninfected cells U, a population of infected cells I and a population of
circulating viruses v
U = uninfected cells
I = infected cells
V = virus (the infected cells produce viruses)
Try and write down with help from the SIR model how you would describe the kinetics / dynamics &
apply it on this system.
Answer:
Static model γ = bursting rate
β γ
dU
dt
=¿ - β * U * V U ---> I ---> V
dI
=¿ β * U * V – γ * I
dt
dV
=¿ γ * I
dt
Dynamic model B = new cell influx μ = death rate
dU
=¿ - β * U * V + B – μ * U
dt
dI dI
=¿ β * U * V – γ * I – μ * I or =¿ β * U * V – μI * I
dt dt
dV
=¿ γ * I – μV * V
dt
β∗B∗γ
R0 = ∗R 0
μI ∗μU ∗μV
R0 thus resembles the number of newly infected cells that arise from one initially infected cell given
an entirely susceptible cell population. Note that when no viruses are present the equilibrium
condition for the uninfected cells becomes U = B / µ U
response
21/10 PROF. OGUNJIMI
Question 1:
Imagine a population of uninfected cells U, a population of infected cells I and a population of
circulating viruses v
U = uninfected cells
I = infected cells
V = virus (the infected cells produce viruses)
Try and write down with help from the SIR model how you would describe the kinetics / dynamics &
apply it on this system.
Answer:
Static model γ = bursting rate
β γ
dU
dt
=¿ - β * U * V U ---> I ---> V
dI
=¿ β * U * V – γ * I
dt
dV
=¿ γ * I
dt
Dynamic model B = new cell influx μ = death rate
dU
=¿ - β * U * V + B – μ * U
dt
dI dI
=¿ β * U * V – γ * I – μ * I or =¿ β * U * V – μI * I
dt dt
dV
=¿ γ * I – μV * V
dt
β∗B∗γ
R0 = ∗R 0
μI ∗μU ∗μV
R0 thus resembles the number of newly infected cells that arise from one initially infected cell given
an entirely susceptible cell population. Note that when no viruses are present the equilibrium
condition for the uninfected cells becomes U = B / µ U
