Disease emergence in
immunocompromised
populations
Jamie Lloyd-Smith
Penn State University
Africa: a changing immune landscape
HIV prevalence
in adult
populations
How might this influence disease emergence?
Heterogeneous immunity and disease emergence
In addition to HIV, many other factors affect the host immune
response to a given pathogen:
Host genetics
Co-infections
Immunosuppressive drugs
Nutrition
Age
Vaccination and previous exposure
Individual-level effects of compromised immunity can include:
greater susceptibility to infection
higher pathogen loads
disseminated infection and death
longer duration of infection
What are the population-level effects of immunocompromised
groups on pathogen emergence?
Modelling pathogen emergence
Building on work by Antia et al (2003), Andre & Day (2005), and
Yates et al (2006).
Emergence = introduction + adaptation + invasion
A simple model for pathogen invasion
Linearized birth-and-death process in continuous time.
Stochastic model for disease invasion
into a large population.
Population is structured into groups according to immunocompetence.
•
Each group has characteristic susceptibility and infectiousness,
which can vary independently or co-vary.
Pathogen is structured into strains representing stages of adaptation
to a novel host species.
Emergence = introduction + adaptation + invasion
A simple model for pathogen adaptation
Between-host
transmission bottleneck
causes founder effect
Model assumes:
Occurs with fixed probability
per transmission event.
Within-host
mutation arises during infection and
goes to fixation within host
Occurs at a constant rate
within each infected host.
 a probability over an average
duration of infection.
Pathogen fitness landscapes
adaptation
One-step adaptation
1.5
R0 in healthy
population
1
0.5
0
Initial
strain
Two-step adaptation
Adapted
strain
adaptation
R0 in healthy
population
1.5
1
0.5
0
Initial
strain
Intermediate Adapted
strain
strain
Model assumptions
Invasion model (epidemiology)
Susceptible pool is large compared to outbreak size.
Per capita rates of recovery and transmission are constant.
Type of index case is determined by group size weighted by
susceptibility:
Pr(index case in group i) =
(Size of group i) × (Susc. of group i) .
Sj (Size of group j) × (Susc. of group j)
Adaptation model (evolution)
Parameters describing relative susceptibility and infectiousness
don’t depend on pathogen strain.
Evolutionary and epidemiological parameters are independent of
one another.
Model equations: 1 group, 1 strain
q  Probabilit y that outbreak carried by
a single case will go extinct.
  Transmission rate
  Recovery rate
q   q 2    1     q
where, because of the large-population assumption:
Pr 2 chains go extinct   Pr 2 chains go extinct 
2
 q2
Model equations: 1 group, 2 strains
q ( i )  Probabilit y that outbreak of strain i carried by
a single case will go extinct.
 ( i )  Transmission rate for strain i
 ( i )  Recovery rate for strain i
  Rate of within - host evolution
u  Probabilit y of between - host transmission
q
(1)
 1  u
(1)
q   u q q    q
 1       q
(1) 2
(1)
(1)
q
( 2)

( 2)
q 
( 2) 2

(1) ( 2 )
(1)
(1)

  ( 2)  1   ( 2)   ( 2) q ( 2)
( 2)
  (1)
Model equations: 2 groups, 2 strains
q (j i )  Probabilit y that outbreak of strain i carried by
a single case in group j will go extinct.
 (jki )  Transmission rate from group j to group k for strain i
 (j i )  Recovery rate for case of strain i in group j
  within - host evolution rate;
q1(1)

 1  u 
(1)
11
 
(1) 2
q1

u  prob. of between - host evolution
  
 
q
  q
q
  q
  q
 12(1) q1(1) q2(1)  u 11(1) q1(1) q1( 2 )  12(1) q1(1) q2( 2 )

 1  u q q    q   u q q
  q    1        
  q    q q     1    
  q q    q     1    
  q1( 2 )   1(1)  1  11(1)  12(1)     1(1)
q2(1)
(1)
21
(1) (1)
1
2
(1)
22
( 2)
2
q1( 2 )
q2( 2 )
( 2)
11
( 2) 2
1
( 2)
21
( 2) ( 2)
1
2
( 2)
12
(1)
2
( 2) ( 2)
1
2
( 2)
22
( 2) 2
2
(1) 2
2
(1)
21
(1)
21
( 2 ) (1)
1
2
(1)
22
(1)
2
(1)
1
(1)
22
(1) ( 2 )
2 q2
(1)
2
( 2)
1
( 2)
11
( 2)
12
( 2)
1
( 2)
1
( 2)
2
( 2)
21
( 2)
22
( 2)
2
( 2)
2


20%
immunocompromised
80% healthy
Divide population into two groups, healthy and immunocompromised,
which mix at random.
Consider different epidemiological effects of immune compromise:
NO EFFECT (0), S, I , I, SI, SI
(assume 10-fold changes)
Infectiousness can vary via either the rate or duration of transmission.
Normal

I rate

t
I duration

t
t
Covariation of epidemiological parameters
When susceptibility and infectiousness co-vary,
R0 for the heterogeneous population  R0 in a healthy population.
R0 = 1
in healthy population
1000
R0 in
100
heterogeneous
population 10
1
100
10
1
Relative susceptibility
of group 2
0.1
0.01
0.01
0.1
1
10
100
Relative infectiousness
of group 2
Pathogen invasion, without evolution
Heterogeneous susceptibility only
Probability of invasion
0.8
0.6
0.4
0.2
0
0
2
4
R0 in healthy population
6
1
Probability of invasion
S
0
S
1
S
0
S
0.8
0.6
0.4
0.2
0
0
2
4
6
R0 in heterogeneous population
See Becker & Marschner, 1990.
Pathogen invasion, without evolution
Heterogeneous infectiousness only
1
I
0
I
0.8
0.6
Probability of invasion
Probability of invasion
1
0.4
0.2
0
0
2
4
R0 in healthy population
6
0
I
0.8
0.6
I
0.4
0.2
0
0
2
4
6
R0 in heterogeneous population
See Lloyd-Smith et al, 2005.
Pathogen invasion: co-varying parameters
Probability of invasion
0.8
0.6
SI
0.4
0.2
0
0
2
4
R0 in healthy population
6
1
Probability of invasion
SI
S
I
0
1
S, 0
SI
I SI
0.8
0.6
0.4
0.2
0
0
2
4
6
R0 in heterogeneous population
Solid lines: infectiousness varies in transmission rate
Pathogen invasion: co-varying parameters
Probability of invasion
0.8
0.6
SI
0.4
0.2
0
0
2
4
R0 in healthy population
6
1
Probability of invasion
SI
S
I
0
1
S, 0
SI
I SI
0.8
0.6
0.4
0.2
0
0
2
4
6
R0 in heterogeneous population
Dashed lines: infectiousness varies in duration
Pathogen invasion: co-varying parameters
Prob. of invasion
Population with heterogeneous infectiousness, I
R0 when
cov(inf, susc) = 0
Pathogen evolution: probability of adaptation
One-step adaptation
Pr(between) Pr(within)
R0
1
0
Adapted
1×10-3
1×10-3
w >> b
1×10-6
2×10-3
w << b
2×10-3
1×10-6
10 0
Probability of adaptation
Initial
w=b
0
-1
10
10
10
10
-2
-3
-4
within = between
within >> between
within << between
-5
10
-6
10
0
0.5
1
R in healthy population
1.5
Pathogen evolution: probability of adaptation
Assuming P(within) = P(between) = 1×10-3
-1
10
10
10
10
-2
-3
-4
-5
10
10
Probability of adaptation
Probability of adaptation
10
SI
S
I
0
SI
0
-1
SI
10
10
10
10
10
-6
10
S 0
SI
0
-2
I
-3
-4
-5
-6
0
0.5
1
R0 in healthy population
1.5
10
0
0.5
1
1.5
R0 in heterogeneous population
Solid lines: infectiousness varies in transmission rate
Dashed lines: infectiousness varies in duration
Pathogen evolution: probability of adaptation
Assuming P(within) = P(between) = 1×10-3
0
Probability of adaptation
10
10
10
-1
-2
-3
10
10
10
-4
-5
10
10
10
-1
SI
-2
I
-3
10
10
10
-6
10
S 0
SI
0
Probability of adaptation
SI
S
I
0
SI
-4
-5
-6
0
0.5
1
R0 in healthy population
1.5
10
0
0.5
1
1.5
R0 in heterogeneous population
Solid lines: infectiousness varies in transmission rate
Pathogen evolution: probability of adaptation
Assuming P(within) = P(between) = 1×10-3
Probability of emergence
10
10
10
-1
-2
-3
10
10
10
10
-4
-5
-6
0
0.5
1
R0 in healthy population
1.5
S 0
SI
0
10
Probability of emergence
SI
S
I
0
SI
0
10
10
-1
SI
-2
I
-3
10
10
10
10
-4
-5
-6
0
0.5
1
1.5
R0 in heterogeneous population
Dashed lines: infectiousness varies in duration
Where does adaptation occur?
Proportion of evolution within host
Assuming P(within) = P(between) = 1×10-3
1
SI
0.8
I
0.6
S, 0
0.4
SI
0.2
0
0
0.2
0.4
0.6
0.8
1
R0 in heterogeneous population
Solid lines: infectiousness varies in transmission rate
Dashed lines: infectiousness varies in duration
Where does adaptation occur?
Proportion of evolution within host
Assuming P(within) = P(between) = 1×10-3
1
SI
0.8
I
0.6
S, 0
0.4
SI
0.2
0
0
0.2
0.4
0.6
0.8
1
R0 in heterogeneous population
Solid lines: infectiousness varies in transmission rate
Dashed lines: infectiousness varies in duration
Two-step adaptation
adaptation
Jackpot model
R0 in healthy
population
1
0
Initial
strain
10
10
10
Solid lines: 2-step adaptation
0
Probability of adaptation
Probability of adaptation
Dashed lines: 1-step adaptation
-2
-4
-6
10
Intermediate Adapted
strain
strain
0
0.5
1
1.5
R0 in healthy population
10
10
10
0
-2
-4
-6
10
0
0.5
1
1.5
R0 in heterogeneous population
Two-step adaptation
adaptation
Jackpot model
R0 in healthy
population
1
0
Initial
strain
Intermediate Adapted
strain
strain
Initial
strain
Intermediate Adapted
strain
strain
Fitness valley model
R0 in healthy
population
1
0
Two-step adaptation: crossing valleys
Pr(between) Pr(within)
w=b
1×10-3
1×10-3
w >> b
1×10-6
2×10-3
w << b
2×10-3
1×10-6
-2
Probability of adaptation
10
1
0
Initial Intermediate Adapted
strain
strain
strain
within = between
within << between
within >> between
10
10
R0
I
0
-4
-6
-8
10
10
-10
10
-6
-4
10
10
-2
R0 of intermediate strain
10
0
HIV and acute respiratory infections
Studies from Chris Hari-Baragwanath Hospital in Soweto.
Bacterial respiratory tract infections (Madhi et al, 2000, Clin Inf Dis):
Viral respiratory tract infections (Madhi et al, 2000, J. Ped.):
HIV and acute respiratory infections
Alagiriswami & Cheeseman, 2001
Evans et al, 1995
Couch et al, 1997
Illustration: HIV prevalence and influenza emergence
Assuming:
Susceptibility is 8 higher in HIV+ group, and infections last 3 longer.
P(within) = 1×10-3
Two-step jackpot adaptation
P(between) = 1×10-6
R0 = 2 for adapted strain
Probability of emergence
1
20%
10%
10-3
5%
1%
0%
10-6
HIV prevalence
10-9
0
0.5
1
R0 in healthy population
1.5
Summary and future directions
Invasion
• An immunocompromised group can provide a toe-hold for
emergence of an unadapted pathogen.
• Positive covariance between susceptibility and infectiousness
can greatly amplify this effect.
Adaptation
• Within-host evolution is crucial at low R0, and when pathogen
must cross fitness valleys to adapt.
• Prolonged duration of infection has greater influence on
emergence than faster rate of transmission.
Next steps
• Link epi and evolution: incorporate effect of pathogen load?
• Data!! On susceptibility and infectiousness as a function of
immune status, and on pathogen fitness landscapes.
• HIV: more data needed at individual and population levels
Acknowledgements
Ideas and insights
Bryan Grenfell, Mary Poss, Peter Hudson,
and many other colleagues at CIDD (Penn State)
Wayne Getz (UC Berkeley)
Brian Williams (WHO)
Sebastian Schreiber
(UC Davis)
Funding
CIDD Fellowship for research
DIMACS and NSF for travel
Additional material
Pathogen evolution – approximate calculations
Can distinguish between mechanisms of evolution by considering
the total ‘opportunity’ for each to work.
 Total infectious duration = L
 Total number of transmission events = B
Andre & Day (2005) showed, for a homogeneous population, that
P(one-step adaptation) ~  L + u B
This argument can be generalized to the multi-group setting, using
the theory of absorbing Markov processes.
 In addition to the approximate P(adaptation), can derive the
approximate proportion of emergence events due to within-host
vs between-host adaptation
Influence of covariation when overall R0 is fixed
I
Prob. of emergence
1
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
5
4
R0 in
0
3
heterogeneous
population
100
2
10
1
1
0
0.01
0.1
Relative susceptibility
of group 2
Influence of covariation when overall R0 is fixed
I
Overall R0 = 3
P(emergence)
P(em if index in group 1)
P(em if index in group 2)
P(index in group 1)
1
0.9
0.8
Probability
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-2
10
-1
10
10
0
10
1
Relative susceptibility of group 2
2
10
Influence of covariation when overall R0 is fixed
Overall R0 = 3
S
P(emergence)
P(em if index in group 1)
P(em if index in group 2)
P(index in group 1)
0.8
0.7
Probability
0.6
0.5
0.4
0.3
0.2
0.1
0
-2
10
-1
10
10
0
10
1
Relative infectiousness of group 2
2
10
Previous work on modelling emergence
Antia et al, 2003 (between-host evolution, homogeneous population)
 If introduced strain has R0 < 1, ultimate emergence is more likely
as R0 approaches 1.
Andre & Day, 2005 (within- and between-host, homogeneous pop.)
 Duration of infection can be as important as R0.
Yates et al, 2006 (between-host only, heterogeneous population
without covariation between parameters)
 Host heterogeneity in susceptibility or infectiousness alone has little
effect on emergence.
Present goal: analyze disease emergence in a population with
heterogeneous immunocompetence so that parameters may
co-vary, with both within- and between-host evolution.
• But CD4 count isn’t the whole story… HIV’s impact on invasive
bacterial infection is thought to be mediated by mononuclear innate
immune cells (macrophages, dendritic cells, etc)
• Results are indicating that HAART (and resulting elevated CD4
counts) do not reduce risk of bacterial infections. (Noursadeghi et al,
Lancet Inf Dis 2006)