Evolution of Virulence
Matthew H. Bonds
The François-Xavier Bagnoud Center for Health and Human Rights
Harvard School of Public Health
Partners in Health
Outline of Presentation
1. Background to Disease Evolution
- Evolution of virulence
- Antibiotic resistance
- Disease emergence
2. Evolutionary Stable Strategies (ESS)
3. Evolution of Virulence
- single infection
- multiple infections
Background to Disease Evolution
1. Evolution of Virulence
2. Antibiotic Resistance
3. Disease Emergence
Background to Disease Evolution
1. Evolution of Virulence
2. Antibiotic Resistance
3. Disease Emergence
Background to Disease Evolution
1. Evolution:
A change in genetic material in a population
from generation to the next.
- We say that organisms evolve to “maximize
their fitness”
Background to Disease Evolution
1. Evolution:
A change in genetic material in a population
from generation to the next.
- We say that organisms evolve to “maximize
their fitness”
2. Fitness ≅ Reproductivity
Background to Disease Evolution
1. Evolution:
A change in genetic material in a population
from generation to the next.
- We say that organisms evolve to “maximize
their fitness”
2. Fitness ≅ Reproductivity = number of
surviving offspring or number of reproductive
offspring
Background to Disease Evolution
1. Evolution:
A change in genetic material in a population
from generation to the next.
- We say that organisms evolve to “maximize
their fitness”
2. Fitness ≅ Reproductivity = number of
surviving offspring or number of reproductive
offspring
Evolutionarily Stable Strategy
Evolutionarily Stable Strategy (ESS):
A strategy which, if adopted by a population,
cannot be invaded by any alternative strategy
that is initially rare.
An ESS is a kind of Nash equilibrium.
What is the ESS for a Pathogen?
What is the ESS for a Pathogen?
A strategy adopted by some kind of pathogen, for
which an alternative (mutant) strategy, cannot
invade.
What is the ESS for a Pathogen?
A strategy adopted by some kind of pathogen, for
which an alternative (mutant) strategy, cannot
invade.
dI
 SI  (  v)I
dt

What is the ESS for a Pathogen?
A strategy adopted by some kind of pathogen, for
which an alternative (mutant) strategy, cannot
invade.
dI
 SI  (  v)I  0
dt

What is the ESS for a Pathogen?
A strategy adopted by some kind of pathogen, for
which an alternative (mutant) strategy, cannot
invade.
S *
 1  RI  I *
v

What is the ESS for a Pathogen?
A strategy adopted by some kind of pathogen, for
which an alternative (mutant) strategy, cannot
invade.

v

 R0
What is the ESS for a Pathogen?
A strategy adopted by some kind of pathogen, for
which an alternative (mutant) strategy, cannot
invade.

v
 R0
A strategy that maximizes the Basic Reproductive Ratio
is evolutionarily stable (Anderson and May, 1982)

ESS for a Pathogen?

v
 R0
What are the evolutionary tradeoffs faced by pathogens?

ESS for a Pathogen?

v
 R0
What are the evolutionary tradeoffs faced by pathogens?
Pathogens should evolve to maximize the transmission
rate
 and minimize the disease-induced death rate.
ESS for a Pathogen?

v
 R0
What are the evolutionary tradeoffs faced by pathogens?
Pathogens should evolve to maximize the transmission
rate
 and minimize the disease-induced death rate.
There must be a tradeoff between transmission and
virulence! ?
ESS for a Pathogen?
 (v)
 R0
v

ESS for a Pathogen?
 (v)
 R0
v
 (v)  v


ESS for a Pathogen?
 (v)
 R0
v
 (v)  v

Tradeoff between transmission and killing the host

 (v)

v
ESS for a Pathogen?
v
 R0
v
Maximize Ro with respect to v


dR0
0
dv
 (v)
v*  

*


v*
v
ESS for Multiple Pathogens?
v
 R0
v
Maximize Ro with respect to v


dR0
0
dv
 (v)
v*  

*


v*
v
ESS for Multiple Pathogens?
 (v)
 R0
v

ESS for Multiple Pathogens?
 (v1)
  v1  v 2

 R0
ESS for Multiple Pathogens?
v1
 R10
  v1  v 2


gv 2
  v2
 R02
  v1  v 2
ESS for Multiple Pathogens?
v1
 R10
  v1  v 2
gv 2
  v2
 R02
  v1  v 2
Maximize Ro with respect to v



dR10
0

dv1
dR02
0
dv 2


v1*    v2
v 2*   (  v1 )
ESS for Multiple Pathogens?


dR10
0
dv1
dR02
0
dv 2


v1*    v2
v 2*   (  v1 )
ESS for Multiple Pathogens?
dR10
0
dv1
dR02
0
dv 2


v2

v1*    v2
v 2*   (  v1 )

v1(v2 )



v *1
v1
ESS for Multiple Pathogens?
dR10
0
dv1
dR02
0
dv 2


v2


v1*    v2
v 2*   (  v1 )

v1(v2 )
v2 (v1)





v *1
v1
ESS for Multiple Pathogens?
dR10
0
dv1
dR02
0
dv 2


v2

v1*    v2
v 2*   (  v1 )

v1(v2 )
v *2



v2 (v1)




v *1
v1
ESS for Multiple Pathogens?
dR10
0
dv1
dR02
0
dv 2


v2

v1*    v2
v 2*   (  v1 )

CoESS
v1(v2 )
v *2



v2 (v1)




v *1
v1
Summary
The evolutionarily stable strategy for a pathogen is the
strategy that maximizes its basic reproductive ratio
Typically, the phenotype that we consider to be evolving is
the disease-induced mortality rate (virulence)
There may be a tradeoff between virulence and
transmission
The ESS level of virulence depends on coinfection.
The host represents a common property resource, and the
Co-evolutionarily stable strategy is the outcome of a
prisoner’s dilemma.