Clinically-Immune Hosts as a Refuge for Drug-Sensitive
Malaria Parasites
Eili Y. KleinResources for the Future and Princeton University
David L. SmithDept. of Zoology & Emerging Pathogens Institute
University of Florida
Maciek F. BoniResources for the Future and Princeton University
Ramanan LaxminarayanResources for the Future
Outline
Malaria Parasite Life-CycleEvolution of Resistance to MalariaPopulation Genetics ModelsHistory of Epidemiological Models Two-stage model for transmission of drug-resistant malaria parasites
Parasite Life-Cycle
Basic Reproductive Number (R0)
Basic Reproductive NumberThe expected number of infected mosquitoes
that will eventually arise from one infected mosquitoafter one complete generation of the parasite.
2
0
gnma bceRrg
−
=
Plasmodium falciparumParasite Rate (PfPR)
Plasmodium falciparumParasite Rate (PfPR)
Proportion of Humans Infected
Sporozoite RateProportion of Mosquitos
that are Infectious
Entomological Inoculation Rate
Entomological Inoculation RateThe Number of Infectious bites received per day by a human
Malaria Immunity
PREVENTS INFECTIONInfection Blocking: infection of humansTransmission Blocking: infection of mosquitoes
PROTECTS AGAINST CLINICAL MALARIAPremunition: asymptomatic infectionAcute-Phase: recent clinical episodeFunctional Immunity: age & exposureBlood Stage Immunity: age & exposure
Evolution of ResistanceDe novo mutation rate
World Malaria Report, WHO 2005 Pay
ne 1
987
Par
asito
logy
Tod
ay; W
oote
n et
al 2
002
Nat
ure
Spread of resistant parasites
Population Genetics ModelsReasons for resistance emergence in
low transmission settingsA higher frequency of resistant alleles (mutation-selection balance)
(Hastings Parasitology (1997) 115:133-141)
More drug treatment (per parasite)(White and Pongatavornpinyo Proc R Soc Lond B (2003) 270:545-554)
More selfing(Dye and Williams Proc R Soc Lond B (1997) 264:61-67; Hastings Parasitology (1997) 115:133-141)
Mutant parasites are less likely to survive a host immune response when immunity is better developed
(Gatton et al Parasitology (2001) 123:537-46)
Epidemiological models
Ross – 1910 Macdonald – 1957
The Garki Model
ImmuneNegative
Non-InfectiousPositive
Recovering Slowly
Non-Immune Negative
IncubatingIncubating
Infectious Positive
Non-InfectiousPositive
Recovering Fast
SIR Model
Susceptible Infected(Sensitive)
Human Population
Infectious
Immune
Mosquito Population
Infected Susceptible
Koella and Antia, Malaria Journal 2003, 2:3
SIR Model with Resistance
Susceptible
Infected(Resistant)
Infected(Sensitive)
Human Population
Infectious
Immune
Mosquito Population
Infected Susceptible
Koella and Antia, Malaria Journal 2003, 2:3
Immune Individuals Are Infected
Dietz, K et al. Bull Wld Hlth Org (1974) 50:347-357
Prevalence of P. falciparum (trophozoites/gametocytes) by age and season
Immune Individuals Transmit
Githeko, AK et al Trans R Soc Trop Med Hyg ( 1992) 86, 355-358
Infectiousness to Mosquitos by Age
Two-Stage SIS Model
Susceptible(non-immune)
Infected(non-immune)
Infected(non-immune)
Resistant Infections
Infected(semi-immune)
Infected(semi-immune)
Susceptible(semi-immune)
θ
θ
γ
rx2
ρ2+rw2ρ1+rw1
rx1
hw(1-ξ1) hw(1-ξ2)
hxhx
Sensitive Infections
Model Equations
1 2 1 1 1 1 1( ) ( (1 ) )w w x x w xS B S I r I r S h hγ ρ ξ μ= + + + + − − + +&
1 1 1 1 1(1 ) ( )w w w wI S h I rξ ρ θ μ= − − + + +&
1 1 1( )x x x xI S h I r θ μ= − + +&
2 2 2 2 2 2( ) ( (1 ) )w w x x w xS I r I r S h hρ ξ γ μ= + + − − + + +&
2 2 2 1 2 2(1 ) ( )w w w w wI S h I I rξ θ ρ μ= − + − + +&
2 2 1 2 ( )x x x x xI S h I I rθ μ= + − +&
(1)
Model With No Resistance
Model With No Resistance
R0 – Again!
Basic Reproductive Number (R0)The expected number of infected humans that will
eventually arise from one infected human after one complete generation of the parasite.
The Replacement Number (RX)The expected number of infected humans that will
eventually arise from one infected human after one complete generation of the parasite when the
prevalence of infection is X.
A Refuge for Sensitive Parasites
R0 resistantparasite
R resistant parasite
Immune sensitiveindividuals
Log of Vectorial Capacity
The
Rep
lace
men
t N
um
ber
Fitness cost of Resistance
Conclusion
Asymptomatic semi-immune individuals provide a refuge for sensitive parasites and can prevent the spread of resistant parasites at high transmission levels assuming a great enough fitness costImplications for control strategies aimed at reducing the transmission level (ITNs, IRS)Unlike models of antibiotic resistance (Bonhoeffer, Lipsitch et al. 1997), the parasite with the highest R0 may not predominateAllows for coexistence of both sensitive and resistant parasites