HIVAIDS: How Mathematics Has Saved Lives

1
HIV/AIDS How Mathematics HasSaved Lives

• Alan S. Perelson, PhD
• Theoretical Biology BiophysicsLos Alamos
  National LaboratoryLos Alamos, NM
• asp_at_lanl.gov

2
People living with HIV (2005)
TOTAL 40.3 (36.745.3) million
3
Deaths resulting from HIV (2005)
TOTAL 3.1 (2.83.6) million
4
New infections with HIV (2005)
TOTAL 4.9 (4.36.6) million
5
Mathematics entered the field
6
No treatment
7
Drug Therapy

• Medical a means of interfering with viral
  replication treat or cure disease
• Mathematical a means of perturbing a system and
  uncovering its dynamics

8
(No Transcript)
9
(No Transcript)
10
Model of HIV Infection
k Infection Rate
pVirions/d
T
T
Productively Infected Cell
Target Cell
c
d
Clearance
Death
11
(No Transcript)
12
Model of HIV Infection
Parameters
Variables
13
Model Used for Drug Perturbation Studies
Drug efficacy eRT ePI
Subscripts I infectious NI
non-infectious
From HIV-Dynamics in Vivo , Perelson, et al,
Science, 1996
14
Solution of Model Equations Assuming 100
Efficacy of Protease Inhibitor Therapy
Solution has two parameters c clearance rate
of virus d death rate of infected cells
15
HIV-1 First Phase Kinetics
Perelson et al. Science 271, 1582 1996
16
(No Transcript)
17
(No Transcript)
18
- 1 hr
1010 to 1012 virions/d from 107 to 109 T cells
19
Implications

• HIV infection is not a slow process
• Virus replicates rapidly and is cleared rapidly
  can compute to maintain set point level gt 1010
  virions produced/day
• Cells infected by HIV are killed rapidly
• Rapid replication implies HIV can mutate and
  become drug resistant

20
(No Transcript)
21
Combination therapy
22
HIV-1 Two Phase KineticsCombination Therapy
Perelson et al. Nature 387, 186 (1997)
23
Perelson Ho, Nature 1997
24
HIV-1 Two Phase Kinetics
Perelson et al. Nature 387, 186 (1997)
25
(No Transcript)
26
(No Transcript)
27
Basic Biology of HIV-1 In Vivo Revealed by
Modeling
Contribution to viral load gt1010/day 93-99 1-7

t1/2 lt 1 hr 0.7 d 14 d
Virions Infected T cells Infected long-lived
cells
lt 1
Latently infected T cells months
- years
28
Implications

• Due to long-lived infected cell populations,
  would need to treat HIV infected individuals for
  many years with 100 effective drugs to eradicate
  the virus. Initial estimates were 3-4 years of
  treatment, new estimates at least 10 years.
• But, do not have 100 effective therapy

29
Is eradication possible?

• Not known. Current therapy may not stop all
  ongoing replication, so viral reservoirs such as
  long-lived cells and latently infected cells may
  constantly be regenerated.
• Recent reports show massive early infection in
  gut associated lymphoid tissue 50-80 of CD4
  cells killed in these tissues in the first weeks
  of infection. Both resting and activated cells
  are infected.
• Spatial models and meta-population models needed.
  Replication may only be occurring in some locals,
  e.g., drug sanctuaries.

30
Summary

• Modeling has been used to analyze the many
  possible sources of HIV
• What was once thought to be a a simple slow
  infection has now been shown to involve at least
  4 time scales
• Clearance of free virus 1 hr
• Lifespan of virus producing CD4 T cells 1 day
• Lifespan of long-lived infected cells a few
  weeks
• Lifespan of latently infected cells between 6 -
  44 months
• Modeling also helped reveal the in vivo relative
  efficacy of drug regimes and the need for
  combination therapy.

31
Vaccines for HIV
32
Cytotoxic T Lymphocytes

CTLs can kill virus-infected cells. Here, a CTL
(arrow) is attacking and killing a much larger
influenza virus-infected target cell.
http//www.cellsalive.com/
33
CTL inducing vaccine
Barouch et al. Science 290, 486-492 (2000)
34
Viral Kinetics
Controls (die)
Viral load
Vaccinees (live)
Barouch et al Science 290, 486-492 (2000)
day
35
What about Cytotoxic T Lymphocyte (CTL) kinetics?
CTL are a type of CD8 T cell In these
experiments the number of HIV specific CD8 cells
was measured.
36
CD8 response to HIV
About 10x higher at peak
Vaccinees controls
37
We expect a vaccine to prevent infection

• A vaccine should create memory T cells
• The memory cells should respond earlier and
  faster than naïve T cells
• THIS IS NOT OCCURRING HERE

38
Vaccinees controls
No increase in CTL numbers in vaccinees prior to
day 10
39
Viral Kinetics
Controls
Viral load
Vaccinees
day
No difference in viral kinetics up to day 10
40
Vaccinees controls
0.73 0.22 day-1
0.94 0.22 day-1
No significant difference in CTL growth rates
between controls and vaccinees.
41
Abdel-Motal et al. Virol. 333 226 (2005)
V
V
V
CTL
42
Why is there a delay in CTL expansion?

• May be due to intrinsic delay in getting enough
  infection and antigen presentation to stimulate a
  response
• Is this delay the reason that this vaccine does
  not protect against infection?

43
Non-sterilizing vaccines
Viral load
time
Viral load reducing
Progression slowing
Barouch et al, Science, 290, pp486-492 (2000)
(figure 3c)
44
Whats the impact of such vaccines?

• Benefits
• Vaccinated individuals, if infected live longer
• Lower viral loads, thus less likely to transmit
  infection

• Risks
• Continued infections
• Increased sexual risk behavior
• Viral escape and transmission
• Loss of vaccine effect

45
No treatment
46
Unresolved Problems

• What causes T cell depletion?
• What determines the 10 year timescale?
• What determines the setpoint?
• Are immune responses important in protection
  against HIV?
• Can we develop a vaccine or a cure for HIV
  infection?

47
Collaborators

• David Ho Aaron Diamond AIDS Research Center,
  Rockefeller
• Miles Davenport, UNSW
• Ruy Ribeiro, LANL
• Many students, postdocs at LANL
• A. Neumann, D. Callaway, L. Jones, L. Rong,
  T. Reluga,