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Modelling Within-Host Immune Response: Health economics and mathematical models of infectious diseases $3.76   Add to cart
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Modelling Within-Host Immune Response: Health economics and mathematical models of infectious diseases
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  • Course
  • Health economics and mathematical models (2108FBDBMW)
  • Institution
  • Universiteit Antwerpen (UA)

Part of the course Health economics and mathematical models of infectious diseases given by professor Ogunjimi on 21/10.

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Document information

  • November 26, 2022
  • 4
  • 2022/2023
  • Class notes
  • Professor ogunjimi
  • 21/10

Subjects

  • ogunjimi
  • modelling
  • health economics
  • health economics and mathematical models of infectious diseases

Written for

  • Universiteit Antwerpen (UA)
  • Biomedische Wetenschappen
  • Health economics and mathematical models (2108FBDBMW)
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Content preview

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

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