Immunity and pathogen competition
Dominik Wodarz
Department of Ecology and Evolution
321 Steinhaus Hall
University of California, Irvine CA 92697
Immune system /
evolutionary aspects
pathogen competition and
evolution on epidemiological level
Immunity and pathogen competition
Immune system /
evolutionary aspects
pathogen competition and
evolution on epidemiological level
1
Immunity and pathogen competition
Immune system /
evolutionary aspects
pathogen competition and
evolution on epidemiological level
1
2
Outline
1
Effect of immunity on competition between wild-type and
drug resistant rhinoviruses in a population of hosts
2
Effect of pathogen competition for hosts on the evolution
of immune protection and immunological memory
Effect of immunity on pathogen
competition
1
Context: Drug resistance in rhinovirus infections
Rhinoviruses basics:
•in 75% of cases: leads to common cold symptoms
•incubation period: 1-2 days
•virus shedding increases with onset of symptoms, and falls
sharply as patient recovers
•infection lasts on average 7 days
Rhinoviruses – immunological aspects
•rhinoviruses consist of about 100 serotypes (i.e. recognized
by different immune specificities)
•no geographic or temporal pattern observed in strain distribution
•strains may have different transmissibility
•infection leads to immunity (memory -> protection)
•protection is largely strain-specific -> people get colds
many times
•number of colds per year decreases with age, since people
become immune to more strains (kids vs adults)
Rhinovirus treatment: pleconaril
•originally developed by ViroPharma
•in 2002, rejected by FDA because
company did not demonstrate
adequate safety
•Now, further developed and in phase II
clinical trials with Schering-Plough
Will treatment result in a significant increase in
the prevalence of drug resistant virus strains?
Two types of drug resistance in rhinoviruses:
1. “Acquired resistance”: mutations during viral replication can give
rise to virus strains that are resistant to the drug
Will treatment result in a significant increase in
the prevalence of drug resistant virus strains?
Two types of drug resistance in rhinoviruses:
1. “Acquired resistance”: mutations during viral replication can give
rise to virus strains that are resistant to the drug
2. “Natural resistance”:
Rhinovirus population exists
as about 100 serotypes.
Some serotypes are more
susceptible to the drug
than others
Natural resistance: different serotypes
have different susceptibility
Will treatment result in a significant increase in the proportion of
less susceptible or resistant virus strains? What is the effect of immunity?
Because they are different serotypes, it is not likely that there is
much immunological cross-reactivity between “susceptible” and
“resistant” virus strains.
-> Analyze mathematical model that describes spread of two virus
strains in a population of hosts , assuming a varying degree of
immunoligical cross-reactivity.
Mathematical model
treatment: reduce the transmission parameter, bt< b1,
and speed up the rate of recovery, gt > g1.
cross-immunity parameter s:
if s=0: recovered individuals completely protected against 2nd strain.
if s=1: recovered individuals receive no protection against 2nd strain.
e = fraction of infected people treated
Outcomes of
the model
complete cross-immunity (s=0)
partial cross-immunity
no cross-immunity (s=1)
strain 1 = sensitive
strain 2 = resistant
Impact of treatment on equilibrium
prevalences
treatment reduces basic
reproductive ratio of
sensitive strain (strain 1)
extent to which differences in
competitiveness affect equilibrium
behavior depends on the strength
of cross-immunity between strains
no cross-immunity or partial cross-immunity
s=0.1
s=1
Impact of treatment on equilibrium
prevalences
treatment reduces basic
reproductive ratio of
sensitive strain (strain 1)
no cross-immunity or partial cross-immunity
s=0.1
s=1
extent to which differences in
competitiveness affect equilibrium
behavior depends on the strength
of cross-immunity between strains
strong cross-immunity
s=0.001
s=0.0001
Impact of treatment on equilibrium
prevalences
treatment reduces basic
reproductive ratio of
sensitive strain (strain 1)
no cross-immunity or partial cross-immunity
s=0.1
s=1
extent to which differences in
competitiveness affect equilibrium
behavior depends on the strength
of cross-immunity between strains
strong cross-immunity
-> Prediction: drug use is not likely
to lead to a major change in the
relative frequency of drug-sensitive
and drug-resistant strains
s=0.001
s=0.0001
Treatment dynamics and time scales
for different levels of cross-immunity
and fraction treated
Oscillatory behavior: time taken to reach equilibrium can be long
Implication: levels of resistance seen in short term may exceed the equilibrium value.
Thus, care must be taken in analyzing any short-term data on the prevalence of resistant virus,
as it may take some time for the underlying trend to be revealed.
What about “acquired resistance”?
With “natural resistance”, the prevalence of resistant strains is
unlikely to increase significantly because there is not much cross-immunity
With acquired resistance: data indicate that there is high degree of
cross-immunity -> model predicts that prevalence of resistant strains will
increase significantly in population of hosts.
But: Look at in vivo dynamics.
Acquired resistance and in vivo dynamics
•Similar in principle to HIV: mutation gives rise to a resistant strain, and
data indicate that resistant strain is likely to have a fitness cost.
•Rise of drug resistance in HIV is big problem.
Difference with rhinovirus infection: intact immune responses fight
rhinoviruses, and this might significantly reduce the risk of resistance
emerging in vivo.
In vivo dynamics, immune responses, and
the rise of resistance
susceptible host cells
wild-type virus
resistant virus
specific immune response
F(yw,yr,z)
In vivo dynamics, immune responses, and
the rise of resistance
susceptible host cells
wild-type virus
resistant virus
specific immune response
F(yw,yr,z)
The two virus strains share an enemy: the immune response
-> concept of apparent competition in ecology
I
W
R
(fitness cost)
if wild-type virus induces higher levels of
immune responses (because it grows faster in
in absence of treatment), then it can drive the
resistant virus extinct via the shared immune
response
In vivo dynamics, immune responses, and
the rise of resistance
early start of treatment:
wild-type has not grown enough
to induce sufficient levels of immunity.
-> resistant strain not suppressed
later start of treatment: wild-type
virus has grown more and induced
a sufficient level of immune resposnes.
-> resistant strain is suppressed
Start of treatment and suppression of
resistance
•In general: the resistant strain is
not likely to rise to significant levels
that can be transmitted if treatment
is started after a time threshold, once
immune responses have expanded
sufficiently.
•This is likely to be the case with
rhinovirus infection because symptoms
occur only after significant virus spread
and may even by caused in part by the
immune responses themselves
Start of treatment and suppression of
resistance
•In general: the resistant strain is
not likely to rise to significant levels
that can be transmitted if treatment
is started after a time threshold, once
immune responses have expanded
sufficiently.
•This is likely to be the case with
rhinovirus infection because symptoms
occur only after significant virus spread
and may even by caused in part by the
immune responses themselves
Even though “acquired resistance” would spread quickly on an epidemiological level, it is not
likely that a newly generated resistant mutant in the host would replicate sufficiently for it to be
transmitted.
Note: if treatment is started very early after infection, and little immunity exists, the prediction
is that a resistant mutant will not be suppressed. However, the probability that a resistant mutant
will have been generated during this time is extremely small!
Rhinovirus conclusion
Treatment of rhinovirus infection is might not
lead to an increase in the prevalence of resistant
relative to wild-type strains, because of the patterns of
immunity.
Effect of pathogen competition
on evolution of immune system
Immunological memory = protection of host against a
second infection by the same pathogen. Lasts for a very long
time, in some cases for life.
Is it advantageous to have long lasting protection against
re-infection?
At first, the answer seems obvious…
Simple mathematical model
one host – one virus
susceptible hosts
infected hosts
recovered hosts
pathogen

S
r S  I  R 
 dS  bSP  gR
e S  I  R   1

I  b SP  aI  I

R  I  dR  gR

P  kI  uP
Simple mathematical model
one host – one virus
susceptible hosts
infected hosts
recovered hosts
pathogen

S
r S  I  R 
 dS  bSP  gR
e S  I  R   1

I  b SP  aI  I

R  I  dR  gR

P  kI  uP
Parameter g: rate at which immunity is lost and host returns to being susceptible
G = 1/g = average duration of memory-mediated protection
Simple mathematical model
one host – one virus
susceptible hosts
infected hosts
recovered hosts
pathogen

S
r S  I  R 
 dS  bSP  gR
e S  I  R   1

I  b SP  aI  I

R  I  dR  gR

P  kI  uP
Parameter g: rate at which immunity is lost and host returns to being susceptible
G = 1/g = average duration of memory-mediated protection
To which g does the system evolve to?
G = ∞, i.e. maximum memory duration (discounting things like
metabolic
tradeoffs that could limit memory)
One host – 2 virus strains
Infected with
Pathogen 1
Immune to
Pathogen 1
Immune to 1
Infected with 2
Immune to
both
Susceptible
Infected with
Pathogen 2
Immune to
Pathogen 2
Immune to 2
Infected with 1
As before, the immune or recovered individuals become susceptible again with
a rate g.
In which direction does the duration of memory protection evolve now?
Equations

S
rH
 dS  b1SP1  b 2 SP2  g R1  R2  R12 
eH  1

I1  b1SP1  a1I1  1I1

R1  1 I1  dR1  gR1  b 2 R1P2

I 2  b 2 SP2  a2 I 2   2 I 2

R2   2 I 2  dR2  gR2  b1R2 P1

I12  b 2 R1P2  a2 I12   2 I12

I 21  b1R2 P1  a1 I 21  1 I 21

R12   2 I12  1 I 21  dR12  gR12

P1  k1 I1  I 21   uP1

P 2  k2 I 2  I12   uP2
where the sum of the host population is given by H = S + I1 + R1 + I2 + R2 + I12 + I21 +
R12.
Assumptions
Two virus strains:
strain 2 is competitively inferior
and
more virulent
interesting behavior:
remember rhinovirus model:
absence of immunological cross-reactivity between strains allows coexistence
if there is no such separation, we observe competitive exclusion
Duration of memory and outcome of
competition
superior pathogen
inferior pathogen
(a)
Short memory
Long memory
100
10
10
1
1
0.1
0
20
40
60
80
0.1
100
0
20
40
60
80
100
(b)
Abundance of inferior pathogen
Time (arbitrary units)
0.7
0.6
The longer the duration
of memory, the better
the inferior and more
virulent pathogen can
persist.
0.5
0.4
0.3
0.2
0.1
0
1
10
Duration of memory (arbitrary units)
100
Tradeoffs:
Longer duration of memory: longer protection against re-infection
but
higher prevalence of virulent pathogen
Shorter duration of memory: shorter protection against re-infection
but
lower prevalence or of virulent pathogen
(or absence)
Evolutionary dynamics: two stable states
Longer memory wins
Shorter memory wins
Longer memory wins
0
suboptimal
memory outcome
Gthr
Duration of memory (G)
maximum
memory outcome
Properties of Gthr – the threshold memory
duration that separates the 2 outcomes
Gthr
Suboptimal memory outcome
Maximum memory outcome
The threshold moves up as
the virulence increases.
Duration of memory (G)
104
1000
100
i.e. as virulence increases, the
system is more likely to evolve
to the suboptimal memory outcome.
10
1
0.1
0.01
0.001
0.1
1
Rate of host killing by more virulent pathogen, a2
10
This is because it is more important
to exclude the virulent strain than
to be protected against re-infection
in this situation
Evolutionary cycles?
one pathogen strain => maximum memory duration
allows invasion of more virulent strain(s).
costly for the host
reduce duration of memory
exclude virulent strain(s)
Some thoughts on biological implications
•difficult to test because duration of memory not well studied
•Need to compare pathogen that exists as a diverse population to
pathogen that exists as a homogeneous population
Perhaps the common cold, with its 100 serotypes
Immune protection relies largely on IgA in nasal secretions
But: the titer of rhinovirus specific IgA declines faster than other
antibody titers, and protection is may not last for life but for a few years
-> perhaps it helps exclude more virulent strains??
Vaccination may backfire: if protection is increased by vaccination, it may allow
for the emergence of more virulent strains, and this could be costly for the
host population
Final thoughts: How can duration of
memory be modulated?
Experiments indicate that infection with a heterologous virus can lead to a
decline of previously established memory against a first infection
If pathogen exists as a diverse population and the host can
frequently be infected by different strains of the pathogen,
memory may be relatively short lived.
Adaptive??
People
Alun Lloyd (NC State) on the models of rhinovirus drug resistance
Marc Collett (Viropharma)
Dan Pevear (Viropharma)