population genetics of infectious diseases
TRANSCRIPT
Population genetics of infectious disease
Rosemary McCloskey
November 13, 2014
Rosemary McCloskey Infectious diseases November 13, 2014 1 / 20
Outline
Infectious disease: disease caused by presence of a pathogenicorganism in the host (bacteria, virus)
1 How does the concept of effective population size apply to aninfectious disease?
2 How do epidemics get started?
3 Why is it ever advantageous for a pathogen to kill its host?
Rosemary McCloskey Infectious diseases November 13, 2014 2 / 20
Pathogens evolve quickly
5× 10−10
(Drake 1991)
E. coli
3× 10−10
(Chase 2011)
M. tuberculosis
3× 10−5
(Mansky 1995)
HIV
2× 10−3
(Ogata 1997)
HCV
9× 10−5
(Schrag 1999)
MeVRosemary McCloskey Infectious diseases November 13, 2014 3 / 20
Population level factors
Chambers, Henry F., and Frank R. DeLeo. “Waves of resistance: Staphylococcus aureus in the antibioticera.” Nature Reviews Microbiology 7.9 (2009): 629-641.
Rosemary McCloskey Infectious diseases November 13, 2014 4 / 20
Individual host level factors
Fischer, Will, et al. “Transmission of single HIV-1 genomes and dynamics of early immune escaperevealed by ultra-deep sequencing.” PloS one 5.8 (2010): e12303.
Rosemary McCloskey Infectious diseases November 13, 2014 5 / 20
Effective population size
Rosemary McCloskey Infectious diseases November 13, 2014 6 / 20
Typical disease course
Haase, Ashley T. “Perils at mucosal front lines for HIV and SIV and their hosts.” Nature ReviewsImmunology 5.10 (2005): 783-792.
Rosemary McCloskey Infectious diseases November 13, 2014 7 / 20
Ne within a host
Shinzawa, Naoaki, et al. “p38 MAPK-DependentPhagocytic Encapsulation Confers InfectionTolerance in Drosophila.” Cell host & microbe 6.3(2009): 244-252.
Recall
N =1
1t
∑i
1Ni
.
Consider N in units of 10,000CTU’s. For wild-type w1118,
N = 0.01, 2, 9, 9.4, 9.6, 6, 4.2
N = 0.07.
Ne is two orders of magnitudesmaller than N due to thetransmission bottleneck.
Rosemary McCloskey Infectious diseases November 13, 2014 8 / 20
Ne within a host
Shinzawa, Naoaki, et al. “p38 MAPK-DependentPhagocytic Encapsulation Confers InfectionTolerance in Drosophila.” Cell host & microbe 6.3(2009): 244-252.
Recall
N =1
1t
∑i
1Ni
.
Consider N in units of 10,000CTU’s. For wild-type w1118,
N = 0.01, 2, 9, 9.4, 9.6, 6, 4.2
N = 0.07.
Ne is two orders of magnitudesmaller than N due to thetransmission bottleneck.
Rosemary McCloskey Infectious diseases November 13, 2014 8 / 20
Ne within a host
Shinzawa, Naoaki, et al. “p38 MAPK-DependentPhagocytic Encapsulation Confers InfectionTolerance in Drosophila.” Cell host & microbe 6.3(2009): 244-252.
Recall
N =1
1t
∑i
1Ni
.
Consider N in units of 10,000CTU’s. For wild-type w1118,
N = 0.01, 2, 9, 9.4, 9.6, 6, 4.2
N = 0.07.
Ne is two orders of magnitudesmaller than N due to thetransmission bottleneck.
Rosemary McCloskey Infectious diseases November 13, 2014 8 / 20
Ne within a host
Shinzawa, Naoaki, et al. “p38 MAPK-DependentPhagocytic Encapsulation Confers InfectionTolerance in Drosophila.” Cell host & microbe 6.3(2009): 244-252.
Recall
N =1
1t
∑i
1Ni
.
Consider N in units of 10,000CTU’s. For wild-type w1118,
N = 0.01, 2, 9, 9.4, 9.6, 6, 4.2
N = 0.07.
Ne is two orders of magnitudesmaller than N due to thetransmission bottleneck.
Rosemary McCloskey Infectious diseases November 13, 2014 8 / 20
Ne in an epidemic (Dearlove & Wilson, 2013)
Dearlove, Bethany, and Daniel J. Wilson.“Coalescent inference for infectious
disease: meta-analysis of hepatitis C.”Phil. Trans. R. Soc. B 368.1614 (2013):
20120314.
Wakeley, John. “Metapopulation modelsfor historical inference.” Mol. Ecol. 13.4
(2004): 865-875.
pathogens in isolated hosts are nothomogeneously mixed
epidemic as a metapopulation
Ne =D
2(e0 +m)F
D ⇔ number of infected hosts
e0 ⇔ rate of primary transmission
m⇔ rate of secondary transmission
F ⇔ inbreeding coefficient within ahost
Rosemary McCloskey Infectious diseases November 13, 2014 9 / 20
Ne in an epidemic (Dearlove & Wilson, 2013)
Dearlove, Bethany, and Daniel J. Wilson.“Coalescent inference for infectious
disease: meta-analysis of hepatitis C.”Phil. Trans. R. Soc. B 368.1614 (2013):
20120314.
Wakeley, John. “Metapopulation modelsfor historical inference.” Mol. Ecol. 13.4
(2004): 865-875.
pathogens in isolated hosts are nothomogeneously mixed
epidemic as a metapopulation
Ne =D
2(e0 +m)F
D ⇔ number of infected hosts
e0 ⇔ rate of primary transmission
m⇔ rate of secondary transmission
F ⇔ inbreeding coefficient within ahost
Rosemary McCloskey Infectious diseases November 13, 2014 9 / 20
Ne in an epidemic (Dearlove & Wilson, 2013)
Dearlove, Bethany, and Daniel J. Wilson.“Coalescent inference for infectious
disease: meta-analysis of hepatitis C.”Phil. Trans. R. Soc. B 368.1614 (2013):
20120314.
Wakeley, John. “Metapopulation modelsfor historical inference.” Mol. Ecol. 13.4
(2004): 865-875.
pathogens in isolated hosts are nothomogeneously mixed
epidemic as a metapopulation
Ne =D
2(e0 +m)F
D ⇔ number of infected hosts
e0 ⇔ rate of primary transmission
m⇔ rate of secondary transmission
F ⇔ inbreeding coefficient within ahost
Rosemary McCloskey Infectious diseases November 13, 2014 9 / 20
Ne in an epidemic (Dearlove & Wilson, 2013)
Dearlove, Bethany, and Daniel J. Wilson.“Coalescent inference for infectious
disease: meta-analysis of hepatitis C.”Phil. Trans. R. Soc. B 368.1614 (2013):
20120314.
Wakeley, John. “Metapopulation modelsfor historical inference.” Mol. Ecol. 13.4
(2004): 865-875.
pathogens in isolated hosts are nothomogeneously mixed
epidemic as a metapopulation
Ne =D
2(e0 +m)F
D ⇔ number of infected hosts
e0 ⇔ rate of primary transmission
m⇔ rate of secondary transmission
F ⇔ inbreeding coefficient within ahost
Rosemary McCloskey Infectious diseases November 13, 2014 9 / 20
Ne in an epidemic (Dearlove & Wilson, 2013)
Dearlove, Bethany, and Daniel J. Wilson.“Coalescent inference for infectious
disease: meta-analysis of hepatitis C.”Phil. Trans. R. Soc. B 368.1614 (2013):
20120314.
Wakeley, John. “Metapopulation modelsfor historical inference.” Mol. Ecol. 13.4
(2004): 865-875.
pathogens in isolated hosts are nothomogeneously mixed
epidemic as a metapopulation
Ne =D
2(e0 +m)F
D ⇔ number of infected hosts
e0 ⇔ rate of primary transmission
m⇔ rate of secondary transmission
F ⇔ inbreeding coefficient within ahost
Rosemary McCloskey Infectious diseases November 13, 2014 9 / 20
Ne in an epidemic (Dearlove & Wilson, 2013)
Dearlove, Bethany, and Daniel J. Wilson.“Coalescent inference for infectious
disease: meta-analysis of hepatitis C.”Phil. Trans. R. Soc. B 368.1614 (2013):
20120314.
Wakeley, John. “Metapopulation modelsfor historical inference.” Mol. Ecol. 13.4
(2004): 865-875.
pathogens in isolated hosts are nothomogeneously mixed
epidemic as a metapopulation
Ne =D
2(e0 +m)F
D ⇔ number of infected hosts
e0 ⇔ rate of primary transmission
m⇔ rate of secondary transmission
F ⇔ inbreeding coefficient within ahost
Rosemary McCloskey Infectious diseases November 13, 2014 9 / 20
Ne in an epidemic (Dearlove & Wilson, 2013)
Dearlove, Bethany, and Daniel J. Wilson.“Coalescent inference for infectious
disease: meta-analysis of hepatitis C.”Phil. Trans. R. Soc. B 368.1614 (2013):
20120314.
Wakeley, John. “Metapopulation modelsfor historical inference.” Mol. Ecol. 13.4
(2004): 865-875.
pathogens in isolated hosts are nothomogeneously mixed
epidemic as a metapopulation
Ne =D
2(e0 +m)F
D ⇔ number of infected hosts
e0 ⇔ rate of primary transmission
m⇔ rate of secondary transmission
F ⇔ inbreeding coefficient within ahost
Rosemary McCloskey Infectious diseases November 13, 2014 9 / 20
How do epidemics get started?
Rosemary McCloskey Infectious diseases November 13, 2014 10 / 20
Basic reproductive number (Anderson & May, 1979)
R0: “average number of secondary infections produced when oneinfected individual is introduced into a host population where everyoneis susceptible” (May et al. 2001).
R0 > 1⇒ epidemic
R0 < 1⇒ disappearance
May, Robert M., Sunetra Gupta, and Angela R. McLean.“Infectious disease dynamics: what characterizes a
successful invader?.” Phil. Trans. R. Soc. B. 356.1410(2001): 901-910.
Rosemary McCloskey Infectious diseases November 13, 2014 11 / 20
Basic reproductive number (Anderson & May, 1979)
R0: “average number of secondary infections produced when oneinfected individual is introduced into a host population where everyoneis susceptible” (May et al. 2001).
R0 > 1⇒ epidemic
R0 < 1⇒ disappearance
May, Robert M., Sunetra Gupta, and Angela R. McLean.“Infectious disease dynamics: what characterizes a
successful invader?.” Phil. Trans. R. Soc. B. 356.1410(2001): 901-910.
Rosemary McCloskey Infectious diseases November 13, 2014 11 / 20
Basic reproductive number (Anderson & May, 1979)
R0: “average number of secondary infections produced when oneinfected individual is introduced into a host population where everyoneis susceptible” (May et al. 2001).
R0 > 1⇒ epidemic
R0 < 1⇒ disappearance
May, Robert M., Sunetra Gupta, and Angela R. McLean.“Infectious disease dynamics: what characterizes a
successful invader?.” Phil. Trans. R. Soc. B. 356.1410(2001): 901-910.
Rosemary McCloskey Infectious diseases November 13, 2014 11 / 20
Basic reproductive number (Anderson & May, 1979)
R0: “average number of secondary infections produced when oneinfected individual is introduced into a host population where everyoneis susceptible” (May et al. 2001).
R0 > 1⇒ epidemic
R0 < 1⇒ disappearance
May, Robert M., Sunetra Gupta, and Angela R. McLean.“Infectious disease dynamics: what characterizes a
successful invader?.” Phil. Trans. R. Soc. B. 356.1410(2001): 901-910.
Rosemary McCloskey Infectious diseases November 13, 2014 11 / 20
Calculating R0
N hosts
R = number of infected peopledue to first guy
βN new people are infected
αR infected people die of thedisease
νR infected people recover
µR infected people die ofsomething else
R′ = R+ βN − αR− νR− µR
R0 =βN
α+ µ+ ν.
Rosemary McCloskey Infectious diseases November 13, 2014 12 / 20
Calculating R0
N hosts
R = number of infected peopledue to first guy
βN new people are infected
αR infected people die of thedisease
νR infected people recover
µR infected people die ofsomething else
R′ = R+ βN − αR− νR− µR
R0 =βN
α+ µ+ ν.
Rosemary McCloskey Infectious diseases November 13, 2014 12 / 20
Calculating R0
N hosts
R = number of infected peopledue to first guy
βN new people are infected
αR infected people die of thedisease
νR infected people recover
µR infected people die ofsomething else
R′ = R+ βN − αR− νR− µR
R0 =βN
α+ µ+ ν.
Rosemary McCloskey Infectious diseases November 13, 2014 12 / 20
Calculating R0
N hosts
R = number of infected peopledue to first guy
βN new people are infected
αR infected people die of thedisease
νR infected people recover
µR infected people die ofsomething else
R′ = R+ βN − αR− νR− µR
R0 =βN
α+ µ+ ν.
Rosemary McCloskey Infectious diseases November 13, 2014 12 / 20
Calculating R0
+
N hosts
R = number of infected peopledue to first guy
βN new people are infected
αR infected people die of thedisease
νR infected people recover
µR infected people die ofsomething else
R′ = R+ βN − αR− νR− µR
R0 =βN
α+ µ+ ν.
Rosemary McCloskey Infectious diseases November 13, 2014 12 / 20
Calculating R0
+
N hosts
R = number of infected peopledue to first guy
βN new people are infected
αR infected people die of thedisease
νR infected people recover
µR infected people die ofsomething else
R′ = R+ βN − αR− νR− µR
R0 =βN
α+ µ+ ν.
Rosemary McCloskey Infectious diseases November 13, 2014 12 / 20
Calculating R0
+
N hosts
R = number of infected peopledue to first guy
βN new people are infected
αR infected people die of thedisease
νR infected people recover
µR infected people die ofsomething else
R′ = R+ βN − αR− νR− µR
R0 =βN
α+ µ+ ν.
Rosemary McCloskey Infectious diseases November 13, 2014 12 / 20
Calculating R0
+
N hosts
R = number of infected peopledue to first guy
βN new people are infected
αR infected people die of thedisease
νR infected people recover
µR infected people die ofsomething else
R′ = R+ βN − αR− νR− µR
R0 =βN
α+ µ+ ν.
Rosemary McCloskey Infectious diseases November 13, 2014 12 / 20
Some basic reproductive numbers
H5N1 2 (Ward 2009)
Ebola 2 (Stadler 2014)
Spanish Flu 1.5, 3.75 (Chowell 2006)
Malaria 115 (Smith 2007)
Chlamydia 0.5 (Potterat 1999)
Rosemary McCloskey Infectious diseases November 13, 2014 13 / 20
Some basic reproductive numbers
H5N1 2 (Ward 2009)
Ebola 2 (Stadler 2014)
Spanish Flu 1.5, 3.75 (Chowell 2006)
Malaria 115 (Smith 2007)
Chlamydia 0.5 (Potterat 1999)
Rosemary McCloskey Infectious diseases November 13, 2014 13 / 20
Some basic reproductive numbers
H5N1 2 (Ward 2009)
Ebola 2 (Stadler 2014)
Spanish Flu 1.5, 3.75 (Chowell 2006)
Malaria 115 (Smith 2007)
Chlamydia 0.5 (Potterat 1999)
Rosemary McCloskey Infectious diseases November 13, 2014 13 / 20
Some basic reproductive numbers
H5N1 2 (Ward 2009)
Ebola 2 (Stadler 2014)
Spanish Flu 1.5, 3.75 (Chowell 2006)
Malaria 115 (Smith 2007)
Chlamydia 0.5 (Potterat 1999)
Rosemary McCloskey Infectious diseases November 13, 2014 13 / 20
Some basic reproductive numbers
H5N1 2 (Ward 2009)
Ebola 2 (Stadler 2014)
Spanish Flu 1.5, 3.75 (Chowell 2006)
Malaria 115 (Smith 2007)
Chlamydia 0.5 (Potterat 1999)
Rosemary McCloskey Infectious diseases November 13, 2014 13 / 20
Why kill the host?
Rosemary McCloskey Infectious diseases November 13, 2014 14 / 20
Why kill the host?
counterintuitive: host death ⇒ pathogen death
conventional wisdom: parasites evolve towards commensalism ormutualism
R0 =βN
α+ µ+ ν
Anderson & May 1982: trade-off hypothesis
if β increases with high α, observe increased α (eg. cholera)
if β is decreases with high α, observe moderate α (eg. influenza)
Rosemary McCloskey Infectious diseases November 13, 2014 15 / 20
Why kill the host?
counterintuitive: host death ⇒ pathogen death
conventional wisdom: parasites evolve towards commensalism ormutualism
R0 =βN
α+ µ+ ν
Anderson & May 1982: trade-off hypothesis
if β increases with high α, observe increased α (eg. cholera)
if β is decreases with high α, observe moderate α (eg. influenza)
Rosemary McCloskey Infectious diseases November 13, 2014 15 / 20
Why kill the host?
counterintuitive: host death ⇒ pathogen death
conventional wisdom: parasites evolve towards commensalism ormutualism
R0 =βN
α+ µ+ ν
Anderson & May 1982: trade-off hypothesis
if β increases with high α, observe increased α (eg. cholera)
if β is decreases with high α, observe moderate α (eg. influenza)
Rosemary McCloskey Infectious diseases November 13, 2014 15 / 20
Why kill the host?
counterintuitive: host death ⇒ pathogen death
conventional wisdom: parasites evolve towards commensalism ormutualism
R0 =β(α)N
α+ µ+ ν(α)
Anderson & May 1982: trade-off hypothesis
if β increases with high α, observe increased α (eg. cholera)
if β is decreases with high α, observe moderate α (eg. influenza)
Rosemary McCloskey Infectious diseases November 13, 2014 15 / 20
Why kill the host?
counterintuitive: host death ⇒ pathogen death
conventional wisdom: parasites evolve towards commensalism ormutualism
R0 =β(α)N
α+ µ+ ν(α)
Anderson & May 1982: trade-off hypothesis
if β increases with high α, observe increased α (eg. cholera)
if β is decreases with high α, observe moderate α (eg. influenza)
Rosemary McCloskey Infectious diseases November 13, 2014 15 / 20
Why kill the host?
counterintuitive: host death ⇒ pathogen death
conventional wisdom: parasites evolve towards commensalism ormutualism
R0 =β(α)N
α+ µ+ ν(α)
Anderson & May 1982: trade-off hypothesis
if β increases with high α, observe increased α (eg. cholera)
if β is decreases with high α, observe moderate α (eg. influenza)
Rosemary McCloskey Infectious diseases November 13, 2014 15 / 20
Example: bacteriophage (Messenger et al. 1999)
two E. coli cultures infectedwith bacteriophage f1
L1 culture: new cells every day
L8 culture: new cells every 8days
predict higher virulence in theL1 culture
Messenger, Sharon L., Ian J. Molineux, and J. J.Bull. “Virulence evolution in a virus obeys a tradeoff.” Proceedings of the Royal Society of London.
Series B: Biological Sciences 266.1417 (1999):397-404.
Rosemary McCloskey Infectious diseases November 13, 2014 16 / 20
Example: bacteriophage (Messenger et al. 1999)
two E. coli cultures infectedwith bacteriophage f1
L1 culture: new cells every day
L8 culture: new cells every 8days
predict higher virulence in theL1 culture
Messenger, Sharon L., Ian J. Molineux, and J. J.Bull. “Virulence evolution in a virus obeys a tradeoff.” Proceedings of the Royal Society of London.
Series B: Biological Sciences 266.1417 (1999):397-404.
Rosemary McCloskey Infectious diseases November 13, 2014 16 / 20
Example: bacteriophage (Messenger et al. 1999)
two E. coli cultures infectedwith bacteriophage f1
L1 culture: new cells every day
L8 culture: new cells every 8days
predict higher virulence in theL1 culture
Messenger, Sharon L., Ian J. Molineux, and J. J.Bull. “Virulence evolution in a virus obeys a tradeoff.” Proceedings of the Royal Society of London.
Series B: Biological Sciences 266.1417 (1999):397-404.
Rosemary McCloskey Infectious diseases November 13, 2014 16 / 20
Example: bacteriophage (Messenger et al. 1999)
two E. coli cultures infectedwith bacteriophage f1
L1 culture: new cells every day
L8 culture: new cells every 8days
predict higher virulence in theL1 culture
Messenger, Sharon L., Ian J. Molineux, and J. J.Bull. “Virulence evolution in a virus obeys a tradeoff.” Proceedings of the Royal Society of London.
Series B: Biological Sciences 266.1417 (1999):397-404.
Rosemary McCloskey Infectious diseases November 13, 2014 16 / 20
Example: bacteriophage (Messenger et al. 1999)
two E. coli cultures infectedwith bacteriophage f1
L1 culture: new cells every day
L8 culture: new cells every 8days
predict higher virulence in theL1 culture
Messenger, Sharon L., Ian J. Molineux, and J. J.Bull. “Virulence evolution in a virus obeys a tradeoff.” Proceedings of the Royal Society of London.
Series B: Biological Sciences 266.1417 (1999):397-404.
Rosemary McCloskey Infectious diseases November 13, 2014 16 / 20
Example: malaria (Mackinnon & Read, 1999)
Plasmodium chaubaudi : mouseparasite similar to humanmalaria
obtained isolates from wildThamnomys rutilans
infected lab mice, measuredbody weight, blood celldensity, infectivity tomosquitoes, parasitemia
Mackinnon, Margaret J., and Andrew F. Read.“Genetic relationships between parasite virulence
and transmission in the rodent malaria Plasmodiumchabaudi.” Evolution (1999): 689-703.
Rosemary McCloskey Infectious diseases November 13, 2014 17 / 20
Example: malaria (Mackinnon & Read, 1999)
Plasmodium chaubaudi : mouseparasite similar to humanmalaria
obtained isolates from wildThamnomys rutilans
infected lab mice, measuredbody weight, blood celldensity, infectivity tomosquitoes, parasitemia
Mackinnon, Margaret J., and Andrew F. Read.“Genetic relationships between parasite virulence
and transmission in the rodent malaria Plasmodiumchabaudi.” Evolution (1999): 689-703.
Rosemary McCloskey Infectious diseases November 13, 2014 17 / 20
Example: malaria (Mackinnon & Read, 1999)
Plasmodium chaubaudi : mouseparasite similar to humanmalaria
obtained isolates from wildThamnomys rutilans
infected lab mice, measuredbody weight, blood celldensity, infectivity tomosquitoes, parasitemia
Mackinnon, Margaret J., and Andrew F. Read.“Genetic relationships between parasite virulence
and transmission in the rodent malaria Plasmodiumchabaudi.” Evolution (1999): 689-703.
Rosemary McCloskey Infectious diseases November 13, 2014 17 / 20
Example: malaria (Mackinnon & Read, 1999)
Plasmodium chaubaudi : mouseparasite similar to humanmalaria
obtained isolates from wildThamnomys rutilans
infected lab mice, measuredbody weight, blood celldensity, infectivity tomosquitoes, parasitemia
Mackinnon, Margaret J., and Andrew F. Read.“Genetic relationships between parasite virulence
and transmission in the rodent malaria Plasmodiumchabaudi.” Evolution (1999): 689-703.
Rosemary McCloskey Infectious diseases November 13, 2014 17 / 20
Example: optimal virulence (Anderson & May 1982)
Virulence and recovery rate of six myxoma virus strains in Australianrabbits (Fenner & Ratcliffe, 1966).
0.00 0.02 0.04 0.06 0.08 0.10
0.00
0.01
0.02
0.03
0.04
0.05
virulence α
reco
very
rat
e ν
0.00 0.02 0.04 0.06 0.08 0.10
2.0
2.5
3.0
3.5
4.0
virulence α
basi
c re
prod
uctiv
e nu
mbe
r R
0
Constant β, exponentially decaying ν ⇒ optimal equilibrium virulence.
Rosemary McCloskey Infectious diseases November 13, 2014 18 / 20
Example: optimal virulence (Anderson & May 1982)
Virulence and recovery rate of six myxoma virus strains in Australianrabbits (Fenner & Ratcliffe, 1966).
0.00 0.02 0.04 0.06 0.08 0.10
0.00
0.01
0.02
0.03
0.04
0.05
virulence α
reco
very
rat
e ν
0.00 0.02 0.04 0.06 0.08 0.102.
02.
53.
03.
54.
0virulence α
basi
c re
prod
uctiv
e nu
mbe
r R
0
Constant β, exponentially decaying ν ⇒ optimal equilibrium virulence.
Rosemary McCloskey Infectious diseases November 13, 2014 18 / 20
Example: optimal virulence (Anderson & May 1982)
Virulence and recovery rate of six myxoma virus strains in Australianrabbits (Fenner & Ratcliffe, 1966).
0.00 0.02 0.04 0.06 0.08 0.10
0.00
0.01
0.02
0.03
0.04
0.05
virulence α
reco
very
rat
e ν
0.00 0.02 0.04 0.06 0.08 0.102.
02.
53.
03.
54.
0virulence α
basi
c re
prod
uctiv
e nu
mbe
r R
0
Constant β, exponentially decaying ν ⇒ optimal equilibrium virulence.
Rosemary McCloskey Infectious diseases November 13, 2014 18 / 20
It’s not that simple
Medica, D. L., and M. V. K. Sukhdeo. “Estimatingtransmission potential in gastrointestinal nematodes(Order: Strongylida).” J. Parasitol. 87.2 (2001):442-445.
not always observed inexperimental studies
vaccines reduce β, but noreduction in α
confounding factorsI mode of transmission
(counterintuitive for STDs)I host immune factorsI age of host when infected
alternatives: short-sightedevolution, co-incidentalevolution
Rosemary McCloskey Infectious diseases November 13, 2014 19 / 20
It’s not that simple
Medica, D. L., and M. V. K. Sukhdeo. “Estimatingtransmission potential in gastrointestinal nematodes(Order: Strongylida).” J. Parasitol. 87.2 (2001):442-445.
not always observed inexperimental studies
vaccines reduce β, but noreduction in α
confounding factorsI mode of transmission
(counterintuitive for STDs)I host immune factorsI age of host when infected
alternatives: short-sightedevolution, co-incidentalevolution
Rosemary McCloskey Infectious diseases November 13, 2014 19 / 20
It’s not that simple
Medica, D. L., and M. V. K. Sukhdeo. “Estimatingtransmission potential in gastrointestinal nematodes(Order: Strongylida).” J. Parasitol. 87.2 (2001):442-445.
not always observed inexperimental studies
vaccines reduce β, but noreduction in α
confounding factorsI mode of transmission
(counterintuitive for STDs)I host immune factorsI age of host when infected
alternatives: short-sightedevolution, co-incidentalevolution
Rosemary McCloskey Infectious diseases November 13, 2014 19 / 20
It’s not that simple
Medica, D. L., and M. V. K. Sukhdeo. “Estimatingtransmission potential in gastrointestinal nematodes(Order: Strongylida).” J. Parasitol. 87.2 (2001):442-445.
not always observed inexperimental studies
vaccines reduce β, but noreduction in α
confounding factorsI mode of transmission
(counterintuitive for STDs)I host immune factorsI age of host when infected
alternatives: short-sightedevolution, co-incidentalevolution
Rosemary McCloskey Infectious diseases November 13, 2014 19 / 20
Thank you!
Rosemary McCloskey Infectious diseases November 13, 2014 20 / 20