document

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