Low recovery rates stabilize malaria endemicity in areas of lowtransmission in coastal Kenya

Weidong Gu a,*, Charles M. Mbogo b, John I. Githure c, James L. Regens d,Gerry F. Killeen g, Chris M. Swalm e, Guiyun Yan f, John C. Beier a

a Department of Tropical Medicine, School of Public Health and Tropical Medicine, Tulane University Health Sciences Center, New

Orleans, LA 70112, USAb Kenya Medical Research Institute (KEMRI), Kilifi, Kenya

c International Centre of Insect Physiology and Ecology (ICIPE), Nairobi, Kenyad Institute for Science and Public Policy, University of Oklahoma, Norman, OK 73019, USA

e Energy Spatial Analysis Research Laboratory, Tulane University Health Sciences Center, New Orleans, LA 70112, USAf Department of Biological Science, State University of New York, Buffalo, NY 14260, USA

g Department of Public Health and Epidemiology, Swiss Tropical Institute, Basel, Switzerland

Received 3 September 2002; received in revised form 10 September 2002; accepted 12 December 2002

Abstract

The prevalence of Plasmodium falciparum malaria in African communities can be high and stable even in areas of

relatively low transmission where people expose to only a few infectious bites per year. We show in this field study

conducted in 30 sites along the coastal Kenya that prevalence in school children was consistently high, although there

were many sites where transmission intensity measured by exposure to infectious bites was less than 10 per year.

Statistical analyses revealed that prevalence was significantly correlated with the infectious exposure occurring 10�/11

months previously, suggesting that long-lived infections were commonplace and one of the major contributors for the

stability of malaria in these sites. Using mechanistic models of malaria transmission, we found that the association of

high prevalence and low transmission could be due to low recovery rates. Therefore, significant reductions of malaria

prevalence and burden require substantial reductions of the duration of acquired infections, even in areas that have

quite low transmission intensities by the standards of sub-Saharan Africa. Infection control featured by active detection

and drug treatment as well as vector control is critical to combat malaria in areas of relatively low transmission

intensity.

# 2003 Elsevier Science B.V. All rights reserved.

Keywords: Epidemiology; Model; Logistic regression; Infection control; Case detection and drug treatment

1. Introduction

Over 90% of the global morbidity and mortality

caused by Plasmodium falciparum parasites occurs

in sub-Saharan Africa (Breman et al., 2001; Sachs

* Corresponding author. Present address: Medical

Entomology, Illinois Natural History Survey, 607 E Peabody

Drive, Champaign, IL 61820, USA. Tel.: �/1-217-333-1186; fax:

�/1-217-333-2359.

E-mail address: wgu@inhs.uiuc.edu (W. Gu).

Acta Tropica 86 (2003) 71�/81

www.elsevier.com/locate/actatropica

0001-706X/03/$ - see front matter # 2003 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0001-706X(03)00020-2

and Malaney, 2002). Over the past two decades,malaria has deteriorated and mortality doubled or

more in most part of the continent (Trape et al.,

2002). It is increasingly realized that control

programs should be tailored to local epidemiolo-

gical and socioeconomic characteristics (Toure

and Coluzzi, 2000; Hamoudi and Sachs, 1999).

One of the important factors characterizing ma-

laria epidemiological patterns is transmission in-tensity (Beier et al., 1999). The intensity of

transmission is commonly defined as the average

number of infectious bites received during a given

period of time by an individual living in the area,

known as the entomological inoculation rate

(EIR). In practice, EIR is estimated as the product

of the proportion of mosquitoes with sporozoites

in their salivary glands and human-biting rateexperienced by exposed individuals. In Asia and

South America, people are exposed to low levels of

transmission. In contrast, Africa or Papua New

Guinea is the only part of the world where

transmission intensity is high enough to be mea-

sured directly with standard entomological meth-

ods. Although EIR levels often reach hundreds

and sometimes exceed a thousand infectious bitesper year in Africa, it is noteworthy that a

significant proportion of African communities

seems to have relatively low levels of transmission

represented by EIRs of 10 infectious bites per year

or less (Hay et al., 2000). Hereafter in the paper,

we refer low transmission to the situations where

EIR is less than 10 infectious bites per year,

although such levels would be regarded as extre-mely high almost anywhere outside of tropical

Africa.

P. falciparum prevalence in human usually

exceeds 20% in African settings where transmis-

sion is undetectable or below one infectious bite

per year and rapidly increases to exceed 50% at

annual EIRs of 15 or more (for review, see Beier et

al., 1999). In many arid parts of Africa, malariaparasites maintain high prevalence by surviving

and remaining infectious in their human hosts for

the duration of the long dry season, during which

there is little or no transmission (Babiker, 1998;

Theander, 1998; Zwetyenaga et al., 1999; Thomas

and Lindsay, 2000). The association of high

prevalence with low transmission indicates that

malaria control is extremely difficult because aconsiderable reduction in transmission is required

to have a significant impact on prevalence (Beier et

al., 1999).

We therefore sought to further examine the

relationship between malaria prevalence and ex-

posure history in the coastal Kenya which has

been traditionally categorized as hyper-endemic

(Marsh, 1992) while experiencing relatively lowtransmission (Mbogo et al., 1995). Our primary

aims were to better understand the factors respon-

sible for the association of high prevalence and low

transmission, and to identify strategies that might

overcome some of these obstacles and allow such

communities to roll back malaria more success-

fully.

2. Material and methods

2.1. Entomological and parasitological field surveys

in Kenya

Thirty sites along the coast of Kenya (Fig. 1)

were selected for entomological and epidemiologi-

cal surveys during June 1997�/May 1998. This areahas been considered a typical hyper- to holo-

endemic area where the main vectors are mosquito

species in the Anopheles gambiae complex (A.

gambiae , A. arabiensis , and A. merus) and A.

funestus (Marsh, 1992; Mbogo et al., 1995). The

detailed description of the field study is presented

in another paper (Mbogo et al., accepted manu-

script). Briefly, indoor-resting mosquitoes weresampled using the pyrethrum spray collection

(PSC) method at each site once in every 2 months

inside 10 randomly selected houses situated within

a 2-km radius surrounding a primary school. At

the time of mosquito collection, the number of

individuals who slept in the house the previous

night was recorded. The heads and thoraces of all

anopheline mosquitoes were tested using P. falci-

parum sporozoite ELISA. Annual EIR for each

site was estimated as the product of the human-

biting rate and the proportion of sporozoite-

positive mosquitoes averaged over the whole study

period. The human-biting rate was calculated by

dividing the total number of blood-fed and half-

W. Gu et al. / Acta Tropica 86 (2003) 71�/8172

gravid mosquitoes caught in PSC catches by the

number of persons sleeping in the house the night

preceding the collection.

A cross-sectional parasitological survey was

carried out at 30 primary schools in the study

area in May 1998 after obtaining informed consent

from parents and teachers. Thick and thin blood

smears were collected from approximately 100

school children 6�/12 years of age. The thick smear

blood slides were stained with Giemsa and the

number of parasites were counted per 200 leuco-

cytes, and the parasite density was calculated

based on a mean leukocyte count of 8000 per

microliter of blood. A blood film was declared

negative if no parasites were found in 200 micro-

scopic fields of the thick smear examined.

2.2. Temporal correlation between prevalence and

previous exposure

The bimonthly entomological sampling preced-

ing the cross-sectional survey of prevalence al-

lowed us to examine temporal correlations

between prevalence and previous exposure to

infectious bites. We modeled the proportion of

infections in school children as logistic function oflagged exposures measured by EIR. For each site,

the data were aggregated for the periods of June�/

July, August�/October, and November�/December

in 1997, and January�/May in 1998 according to

transmission seasonality on the coastal Kenya

(Fig. 2). The exposure was estimated as the EIRs

averaged during these periods in each site, i.e.

E10�11, E7�9, E5�6, and E1�4 corresponding to thelagged exposures of 10�/11, 7�/9, 5�/6, and 1�/4

months for children in May 1998 (Table 1).

Prevalence (pi) of school children in site i is

logit(pi)�b0�b1Ei;10�11�b2Ei;7�9�b3Ei;5�6

�b4Ei;1�4;

where logit(pi )�/log(pi /(1�/pi)). The parameters

of b0,1,. . .,4 were estimated using the maximum

likelihood method. Note that the estimates of the

proportion of sporozoite infection for a particular

period were made separately based on the mos-

Fig. 1. The annual EIRs from 30 study sites sampled on the

coast of Kenya in East Africa from June 1997 to May 1998.

Fig. 2. Seasonal variation in average EIR over the 30 sites

located on the coast of Kenya.

W. Gu et al. / Acta Tropica 86 (2003) 71�/81 73

quito samples collected during the corresponding

period. The estimates of annual EIR were, how-

ever, obtained from the estimates based on all

mosquito samples aggregated for the whole study

period.

2.3. Mechanistic models of malaria transmission

We further examined the relationship between

malaria prevalence and transmission intensity

using Macdonald’s (1957) models. Human hosts

Table 1

Exposure to EIR from A. gambiae and A. funestus , and logistic regression of prevalence of school children on lagged exposure in some

study sites in coastal Kenya

Site code Prevalence (%) Previous exposure (infectious bites)

Ei ,10 � 11 Ei ,7 � 9 Ei ,5 � 6 Ei ,0 � 4 Annual (Ei ,0 � 11)

AMA 73 72.24 0.75 0.00 10.93 121.06

BAR 65 4.50 2.96 1.76 3.33 16.29

CHA 40 0.00 0.00 0.00 0.00 0.00

DAB 38 0.00 0.00 0.56 0.00 0.58

DIN 60 14.15 5.02 27.30 2.00 52.98

DUM 82 21.95 0.00 0.00 0.46 28.00

GAR 79 7.92 0.89 12.04 1.27 21.78

GAZ 60 0.00 0.83 5.78 0.00 6.18

JAR 55 13.38 2.37 3.26 5.84 30.12

KAG 73 0.00 12.23 11.73 0.00 24.98

KIS 69 9.77 1.54 7.20 0.00 33.13

KIT 71 0.00 0.00 0.00 0.00 0.00

MAG 82 29.64 7.78 5.51 27.18 74.65

MAJ 59 0.00 7.35 15.92 4.70 40.01

MAS 65 3.54 6.69 18.40 3.71 39.67

MAZ 48 0.00 6.70 7.23 0.00 13.09

MBC 60 0.00 0.00 1.57 0.00 1.67

MJA 49 0.00 9.52 3.63 3.18 17.44

MJB 64 0.00 0.00 7.33 3.08 10.64

MJJ 74 10.08 5.42 15.46 3.89 36.81

MOY 78 7.17 0.00 0.00 5.13 14.42

MTE 84 22.77 2.63 0.00 2.71 36.38

MWA 51 1.94 0.00 0.00 0.00 2.12

PAZ 71 0.00 3.54 1.55 1.03 7.69

SHA 54 0.71 0.00 0.26 0.00 1.11

TAK 52 0.00 0.00 0.00 0.00 0.00

TSU 68 14.87 10.46 0.00 7.12 42.36

VIN 66 5.12 0.00 11.84 7.16 26.66

VUG 44 0.00 0.00 7.65 0.00 7.81

ZIW 59 1.97 0.00 0.00 0.00 4.00

Proportion of exposure (%) 0.41 0.15 0.28 0.16

Logistic regression

b 0.017 0.009 0.006 0.018

bS.D. 0.004 0.012 0.006 0.011

Wald statistic 4.370 0.749 0.919 1.725

P -value B/0.001 0.45 0.36 0.08

Annual EIRs were estimated by averaging proportion of sporozoite infection in mosquito samples over the entire period of the

study.

W. Gu et al. / Acta Tropica 86 (2003) 71�/8174

are categorized as either susceptible or infected.Assuming that human�/mosquito contact occurs

randomly, susceptible human become infected at a

rate of b EIR, where b is a constant representing

transmission efficiency between infectious mosqui-

toes and susceptible individuals. Infected indivi-

duals clear their infections and become susceptible

again at a constant daily recovery rate (r),

equivalent to the reciprocal of mean infectionperiod. Thus, the change in malaria prevalence

over time is modeled as (Macdonald, 1957)

dy

dt�b EIR(1�y)�ry: (1)

The relationship between prevalence (y*) and EIR

at equilibrium (i.e. dy /dt�/0) is

y��b EIR

b EIR � r: (2)

This simplistic model suggests that the relationship

between prevalence and EIR is dictated by the

recovery rate. The smaller the r , the higher is

prevalence, no matter what values of b and EIR

are. In reality, both b and r vary as a function of

exposure history, reflecting the effects of immunity(Dietz et al., 1974; Bekessy et al., 1976; Molineaux

and Gramiccia, 1980). We assume constant b and

r for school children living in the study areas and

thus ignore the influence of acquired immunity.

These simplifications are necessary to derive the

general relationship between prevalence and trans-

mission intensity in low transmission areas, while

we nevertheless recognize that the consistentlyhigh prevalence observed at these sites is asso-

ciated with considerable levels of acquired immu-

nity against clinic incidence of malaria (Mbogo et

al., 1995; Gupta et al., 1999). It is difficult to

estimate b or r from experimental studies. For

coefficient b , it was reported that only less than

20% bites from gland-positive mosquitoes pro-

duced infections in residents of endemic areas (Pulland Grab, 1974). Experimental infection by A.

stephensi on volunteers demonstrated that 5 of 10

volunteers developed parasitamae after challenged

by one or two infective mosquitoes (Rickman et

al., 1990). Empirical studies suggested similar

patterns of transmission of sporozoites between

A. stephensi and A. gambiae (Beier et al., 1991).Therefore, we approximated b as 0.5. With the

value of b fixed, we could explore what possible

values of r fitted to our field observations using

Eq. (2). We did not statistically estimate the

recovery rate because our focus was to explore

the factors responsible for the observed pattern of

association of high prevalence with low transmis-

sion rather than to accurately estimate r using thissimplistic model.

Since estimating EIR needs data on human-

biting rates and proportions of sporozoite infec-

tions in mosquitoes, it is not commonly available

and difficult to estimate because the proportion of

sporozoite infection in mosquito populations is

often low even for the most efficient African

vectors, especially in areas of low transmissionwhere it is often difficult to obtain sufficient

mosquito samples for analysis (Gu, 1995). For

example, in Sudan where malaria is endemic and

highly prevalent, it was reported that only one

infected mosquito was identified during a survey

lasted for several years (Theander, 1998). We

further investigated the relationship between pre-

valence and the human-biting rate that was oftensurveyed in many epidemiological studies. We

used Macdonald’s (1952) model of sporozoite

infection in mosquitoes that involved explicitly

modeling transmission dynamics in mosquito

populations. The proportion (s ) of sporozoites’

infection in mosquitoes is modeled as

s�pnacy

acy � loge p; (3)

where a is human-biting habit, c the transmissioncoefficient between an infected person and a

susceptible mosquito, p the daily survival rate of

mosquitoes, and n the number of days taken for

completion of extrinsic parasite development in

mosquitoes.

Since EIR is a product of human-biting rate

(ma) and s , substituting Eq. (3) into Eq. (1) and

solving for the equilibrium prevalence in human,we obtain

y��ma2 bcpn � r loge p

ma2 bcpn � rac: (4)

W. Gu et al. / Acta Tropica 86 (2003) 71�/81 75

The relationship between prevalence and the hu-man-biting rate is shaped by many parameters

governing the transmission. Empirical data were

available for some of these parameters on the coast

of Kenya (Mbogo et al., 1996), and the values of

the other parameters were extracted from other

studies in which A. gambiae and A. funestus were

involved and ideally conducted on the Kenyan

coast. Specifically, a was set as 0.4 because theoviposition cycle was estimated to be 2 days

(Ijumba et al., 1990; Mutero and Birley, 1987)

and human blood indices for A. gambiae on the

coastal Kenya is consistently greater than 80%

(Mbogo et al., 1996); p was estimated to be 0.85

based on a parous rate of ca. 0.65 for A. gambiae

and A. funestus in the study areas (Mbogo et al.,

1996) and an oviposition cycle of 2 days; and theextrinsic incubation period n was set to be 10 days

(Lines et al., 1991). The infectious reservoir is

usually estimated to be around 5% of the whole

population in areas with stable endemic malaria

(Drakeley et al., 2000; Graves et al., 1988; Haji et

al., 1996; Killeen et al., 2000). We therefore set c as

0.15, reflecting the approximate mean infectious-

ness of infected individuals that would be requiredto maintain typical levels of infectiousness in the

population as a whole at the levels of prevalence

observed here. By fixing the values of a , b , c , p ,

and n as 0.4, 0.5, 0.15, 0.85, and 10, respectively,

we could examine how the relationship between

prevalence and human-biting rates (ma) is affected

by the recovery rate using Eq. (4). Although the

specific curves of the predictions do change inresponse to adjustments to the values of these

parameters, exploring the parameter space shows

that our conclusions are valid to reasonable ranges

in these values of the parameters most likely

encountered in the field.

3. Results

Transmission intensity on the coast of Kenya

varied widely from place to place with annual

EIRs ranging from B/1 to 121 infectious bites,

with several adjacent sites experiencing consider-

ably different transmission levels (Fig. 1). There

were 16 sites with annual EIRs of less than 20, and

12 sites of less than 10. Malaria parasite transmis-

sion was detected all year-round with two peaks

appearing during June�/July and November�/De-

cember (Fig. 2). P. falciparum malaria infection

prevalence was consistently high in school children

at all 30 sites, regardless of local EIR estimates

(Fig. 3a). The average prevalence from the sites

with annual EIR values of less than 5 was 53%.

Compared to the three orders of magnitude

variation in annual EIR among the 30 sites, the

variation in prevalence was relatively small.

The summaries of sporozoite infection in A.

gambiae and A. funestus for each period are

tabulated (Table 2). Logistic regression of preva-

lence to previous exposure shows that prevalence

Fig. 3. The relationships between malaria prevalence and

transmission intensity, measured by annual EIR (a) and the

man-biting rate (b) under various recovery rates: (*/ - - */)

0.005; (*/ - */) 0.01; (. . .) 0.02; (*/) 0.05, and (m) the

observations in the coast of Kenya.

W. Gu et al. / Acta Tropica 86 (2003) 71�/8176

was only significantly related to the exposure that

lagged 10�/11 months (Table 1). The significant

relationship between prevalence and exposure

taking place more than 10 months previously

suggests long periods of infection for many

children residing in low transmission areas on the

coast of Kenya.

Fig. 3a displays the relationship between pre-

valence and EIR with the estimated parameters

under various recovery rates. This model predicts

that given the estimated recovery rate of 0.005,

substantial reductions of prevalence can only

occur when EIR is reduced below one infectious

bite per year. However, substantial increase in the

recovery rate from 0.005 to 0.05 could significantly

reduce prevalence from 75 to 23% when annual

EIR is 10 (Fig. 3a).

The predicted prevalence as a function of the

human-biting rate is displayed under various

recovery rates (Fig. 3b). The predictions based

on the recovery rate of 0.005 capture the empiri-

cally observed steep rise to high prevalence once

transmission potential exceeds the threshold re-

quired for stable transmission (Beier et al., 1999).

Increasing the recovery rate not only reduces

predicted prevalence but also increases the thresh-

old of transmission. There is an evident bias in the

model fit that predictions with the recovery rate of

Table 2

Summary of sporozoite examination from sampled mosquitoes aggregated for four periods during June 1997�/May 1998 from the 30

sites on the coast of Kenya

Mosquito species Sampling period

June�/July August�/October November�/December 1997 January�/May 1998

A. gambiae

Sites with annual EIRB/10

Positive 5 8 10 2

Total examined 64 197 933 66

Proportion of sporozoites 0.08 0.04 0.11 0.03

Sites with annual EIR�/10

Positive 121 66 93 28

Total examined 1027 531 2215 347

Proportion of sporozoites 0.12 0.12 0.04 0.08

All sites

Positive 126 74 103 30

Total examined 1091 728 3148 413

Proportion of sporozoites 0.12 0.10 0.03 0.07

A. funestus

Sites with annual EIRB/10

Positive 1 1 7 1

Total examined 22 46 386 153

Proportion of sporozoites 0.05 0.02 0.02 0.01

Sites with annual EIR�/10

Positive 48 30 13 28

Total examined 721 595 695 679

Proportion of sporozoites 0.07 0.05 0.02 0.04

All sites

Positive 49 31 20 29

Total examined 743 641 1081 832

Proportion of sporozoites 0.07 0.05 0.02 0.03

W. Gu et al. / Acta Tropica 86 (2003) 71�/81 77

0.005 underestimate prevalence at the low end oftransmission intensity while overestimate preva-

lence at high transmission intensity.

4. Discussion

Previous studies reported discrepancies between

predicted and observed prevalence due to failure

to account for exposure-induced immunity(Koella, 1991). The models we have applied

underestimate prevalence at low EIR values and

overestimate prevalence at high EIR values.

Therefore, infections likely last longer than 200

days at EIRs of 1 or less and shorter periods where

annual EIR�/10. Although sampling errors asso-

ciated with limitations of the indoor PSC catch for

estimating transmission intensity may contributeto these biases, increasing immunity in response to

previous blood-stage infection (Charlwook et al.,

1998) is the most likely explanation for this bias

and indicates that the estimated threshold for

transmission stability is probably overestimated

by our analysis. This is because the estimated rate

of recovery approximates the mean of values

encountered over the range of transmission in-tensity and prevalence observed here. Thus,

although mean recovery rate may be substantially

higher at EIRs of 10 or more, at transmission

intensities of 1 or less, the recovery rate might be

considerably less than 0.005 as indicated by visual

inspection of model fitting (Fig. 3a). Modeling of

the EIR�/prevalence relationship at increasing

rates of recovery demonstrates that substantialreductions in the mean duration of infections

could reduce prevalence in many sites and could

increase the threshold vector density required to

maintain transmission (Fig. 3b).

It should be noted that EIRs are only measur-

able by conventional entomological methods when

they are moderate to high (Theander, 1998). For

areas where people are exposed to only a fewinfectious bites per year, intensive sampling sur-

veys, especially covering most of the transmission

seasons, are required to accurately estimate EIRs.

If transmission is temporally concentrated during

short seasons like that observed on the coast (Fig.

2), the estimates of EIRs with limited sampling

effort are biased, especially in areas of lowtransmission. Therefore, it is not surprising to

find high prevalences in three sites where no

transmission was detected. It is difficult to assess

the effect of the bias on our estimation of the

recovery rate. In this study, we believe that the

results are qualitatively valid in the presence of the

bias. First of all, both logistic regression of

prevalence on previous exposures and fitting thefield data to dynamical models (Eqs. (2) and (4))

generated consistently low recovery rates. Addi-

tionally, the model (Eq. (4)) without estimates of

EIR displayed a consistent pattern.

Substantial transmission had occurred on the

coastal Kenya during the short rains of

November�/December in 1997. The significant

association between prevalence and exposure dur-ing the previous long rains, almost a whole year

previously, indicates that long-lived infections are

important features on the coast of Kenya as they

are in more arid parts of Africa (Babiker, 1998;

Theander, 1998; Zwetyenaga et al., 1999). Long-

term persistence of infections may be one of the

major mechanisms for P. falciparum that enables

it to maintain high stable prevalence across muchof its range where transmission is seasonal or

intermittent.

The pattern of high prevalence in areas of

relatively low transmission and low recovery rates

of untreated malaria infections in Africa is not

uncommon to malaria epidemiologists. By exam-

ining the link between these two characteristics of

malaria epidemiology, here we have further ex-plored its implications for public health policy to

identify strategies that could enable drastic reduc-

tions of malaria burden in many parts of Africa

where transmission intensity is relatively low by

the standards of this most malaria-afflicted con-

tinent. The implication of this result for malaria

control is that we should reconsider our long-term

goals and control strategies for African commu-nities where, for example, EIR is below 10

infectious bites per year. Besides conventional

vector control to reduce transmission intensity,

aggressive and sustained efforts to increase recov-

ery rates through active case detection and drug

treatment should also be considered in these areas.

By developing an individual-based model, we were

W. Gu et al. / Acta Tropica 86 (2003) 71�/8178

able to incorporate effects of immunity on bothsusceptibility and recovery rate as a function of

individuals’ exposure history (Gu et al., 2003). The

results of the individual-based model are indicative

that infection control characterized by active

detection and drug treatment as well as vector

control is feasible to eliminate malaria from many

sites on the coast of Kenya (Gu et al., 2003).

Wide accessibility to health cares and effectivetreatment of malaria infections have played a

significant role in reducing malaria morbidity

and mortality in Asian countries (Alles et al.,

1998). In Sri Lanka, point prevalence was less than

1% in areas with EIR of one per annum, whereas

similar inoculation rates in Africa are associated

with much high prevalence (Carter et al., 2000).

Similarly, low prevalences have also been reportedin peri-urban communities in Senegal exposed to

an annual EIR of approximately 14 but who have

good access to screening and treatment (Ver-

cruysse et al., 1983). Furthermore, the successful

interruption of malaria transmission by African

vectors with a combination of rigorous vector

control, and intensive case detection and drug

treatment has been clearly demonstrated on theisland of Mauritius (Julvez, 1995; Kaneko et al.,

2000). The arrival of A. gambiae in Mauritius in

the mid-19th century brought with it catastrophic

epidemics, followed by stable endemic malaria

similar to that experienced by much of mainland

Africa today (Julvez, 1995). During the Global

Malaria Eradication campaign, malaria was suc-

cessfully eradicated from this island with a combi-nation of aggressive vector control and rigorous

case surveillance. Mauritius remains free of ma-

laria today despite the continued presence of

highly efficient vectors, predominantly A. arabien-

sis , because of a relentless system for screening,

treating, and following immigrants from malarious

regions (Julvez, 1995).

Closer examination of Fig. 3b reveals that undercurrent conditions on the coast of Kenya, where

poor access to good clinical facilities and effective

drugs allows most chronic infections to persist for

10 months, vector densities would probably have

to be reduced to less than one bite per week or

possibly less, for transmission to be destabilized

and eliminated. This is clearly beyond the reach of

vector control methods currently applied in Kenyaand available more broadly in Africa (Mbogo et

al., 1995; Molineaux and Gramiccia, 1980; Killeen

et al., 2000). Conversely, even increasing the mean

recovery rate so that most infections are cleared in

50 days more or less is similarly unlikely to

destabilize transmission at vector densities of

more than one bite per person per day. In reality,

malaria is likely to be even more intransigent thanindicated by these steady-state models because

they assume homogenous, random mixing of the

vector and human populations. In the real-world

of malaria transmission, exposure and transmis-

sion are highly aggregated in space and time,

resulting in greatly stabilized transmission and

the concentration of most transmission within

foci which are much more intense than the localaverage and considerably more robust to control

(Carter et al., 2000; Woolhouse et al., 1997; Dye

and Hasibeder, 1986). Furthermore, strategies

aiming at elimination of malaria are sensitive to

introduction of new infections into infection-free

communities and even a single introduced infec-

tion can cause an epidemic in an infection-free

community (Arez et al., 1999; Gu et al., 2003).Thus, it seems that if our ambitions for malaria

control in Africa are to go beyond clinical manage-

ment of cases and partial reductions of incidence,

both intensive vector control and active suppres-

sion of human infection prevalence will be re-

quired, even in areas where transmission intensity

is considered relatively low by African standards.

Macdonald developed the theory of malariastability that emphasized the role of mosquito-

related parameters in characterizing malaria sta-

bility such as survival rate and human-biting habit

(Macdonald, 1952, 1957). The emphasis on ma-

laria-related parameters is derived from the gen-

eral understanding that these parameters are

subject to greater variation in nature than the

recovery rate (Macdonald, 1952). This is notsurprising since most of the studies upon which

that observation was based do have high levels of

transmission (Molineaux and Gramiccia, 1980).

This mosquito-oriented characterization of ma-

laria stability has led to the generalization that

malaria is unstable in areas of low and seasonal

transmission. However, malaria transmission in

W. Gu et al. / Acta Tropica 86 (2003) 71�/81 79

Africa is clearly very stable even where transmis-sion is relatively low due to slow recovery from

infection. Unless substantial reductions of trans-

mission intensity and increases in the recovery rate

of human are both achieved and immigrants

monitored, stable malaria will continue unabated

in Africa, even in areas where transmission poten-

tial is relatively moderate. We suggest that our

long-term goals for effective control of malaria inAfrica must therefore go beyond bednets and

clinical case management to include active case

detection, treatment, and rigorous follow-up of

asymptomatic infections so that the reservoir of

parasites to initiate new infections can be substan-

tially reduced without forcing the emergence of

drug resistance.

Acknowledgements

We thank A. Spielman, P. Carnevale, and C.Rogier for inspiring discussions about malaria

epidemiology that led to the present work. Special

thanks are due to A. Saul, V. Robert, and J. Lines

for their critical and constructive suggestions.

Financial support came from NIH (U19

AI45511, D43 TW01142, D43 TW00920) and

NSF (DEB-0083602).

References

Alles, H.K., Mendis, K.N., Carter, R., 1998. Maleria mortality

rates in South Asia and in Africa: implications for malaria

control. Parasitol Today 14, 369�/375.

Arez, A.P., Snounou, G., Pinto, J., Sousa, C.A., Modiano, D.,

Ribeiro, H., Franco, A.S., Alves, J., Rosario, V.E., 1999. A

clonal Plasmodium falciparum population in an isolated

outbreak of malaria in the Republic of Cabo Verde.

Parasitology 118, 347�/355.

Babiker, H.A., 1998. Unstable malaria in Sudan: the influence

of the dry season. Plasmodium falciparum population in the

unstable malaria area of eastern Sudan is stable and

genetically complex. Trans. R. Soc. Trop. Med. Hyg. 92,

585�/589.

Beier, J.C., Davis, J.R., Vaughan, J.A., Noden, B.H., Beier,

M.S., 1991. Quantitation of Plasmodium falciparum spor-

ozoites transmitted in vitro by experimentally infected

Anopheles gambiae and Anopheles stephensi . Am. J. Trop.

Med. Hyg. 44, 564�/570.

Beier, J.C., Killeen, G.F., Githure, J.I., 1999. Entomologic

inoculation rates and Plasmodium falciparum malaria pre-

valence in Africa. Am. J. Trop. Med. Hyg. 61, 109�/113.

Bekessy, A., Molineaux, L., Storey, J., 1976. Estimation of

incidence and recovery rates of Plasmodium falciparum

parasitaemia from longitudinal data. Bull. World Health

Organ. 54, 685�/693.

Breman, J.G., Egan, A., Keusch, G.T., 2001. The intolerable

burden of malaria: a new look at the numbers. Am. J. Trop.

Med. Hyg. Suppl. 64, 4�/7.

Carter, R., Mendis, K.N., Roberts, D., 2000. Spatial targeting

of interventions against malaria. Bull. World Health Organ.

78, 1401�/1411.

Charlwook, J.D., Smith, T., Lyimo, E., Kitua, A.Y., Masanja,

H., Booth, M., Alonso, P.L., Tanner, M., 1998. Incidence of

Plasmodium falciparum infection in infants in relation to

exposure to sporozoite-infected anophelines. Am. J. Trop.

Med. Hyg. 59, 243�/251.

Dietz, K., Molineaux, L., Thomas, A., 1974. A malaria model

tested in the African Savannah. Bull. World Health Organ.

50, 347�/357.

Drakeley, C.J., Akim, N.I.J., Sauerwein, R.W., Greenwood,

B.M., Targett, G.A.T., 2000. Estimates of the infectious

reservoir of Plasmodium falciparum malaria in the Gambia

and in Tanzania. Trans. R. Soc. Trop. Med. Hyg. 94, 472�/

476.

Dye, C., Hasibeder, G., 1986. Population dynamics of mos-

quito-borne disease: effects of flies which bite some people

more frequently than others. Trans. R. Soc. Trop. Med.

Hyg. 80, 69�/77.

Graves, P.M., Burkot, T.R., Carter, R., Cattani, J.A., Lagog,

M., Parker, J., Brabin, B.J., Gibson, F.D., Bradley, D.J.,

Alpers, M.P., 1988. Measurement of malarial infectivity of

human populations to mosquitoes in the Madang area,

Papua New Guinea. Parasitology 96, 251�/263.

Gu, W., 1995. Estimating sporozoite rates by examining pooled

samples of mosquitoes. Trans. R. Soc. Trop. Med. Hyg. 89,

359�/360.

Gu, W., Killeen, G.F., Mbogo, C.M., Regens, J.L., Githure,

J.I., Beier, J.C., 2003. An individual-based model of

Plasmodium falciparum malaria transmission on the coast

of Kenya. Trans. R. Soc. Trop. Med. Hyg. 97, 1�/8.

Gupta, S., Snow, R.W., Donnelly, C.A., Marsh, K., Newbold,

C., 1999. Immunity to non-cerebral severe malaria is

acquired after one or two infections. Nat. Med. 5, 340�/343.

Haji, H., Smith, T., Meuwissen, J.T., Sauerwein, R., Charl-

wood, J.D., 1996. Estimation of the infectious reservoir of

Plasmodium falciparum in natural vector populations based

on oocyst size. Trans. R. Soc. Trop. Med. Hyg. 90, 494�/

497.

Hamoudi, A., Sachs, J.D., 1999. The changing global distribu-

tion of malaria: a review. Working Papers. Center for

International Development at Harvard University.

Hay, S.I., Rogers, D.J., Toomer, J.F., Snow, R.W., 2000.

Annual Plasmodium falciparum entomological inoculation

rates (EIR) across Africa: literature survey, internet access

and review. Trans. R. Soc. Trop. Med. Hyg. 94, 113�/127.

W. Gu et al. / Acta Tropica 86 (2003) 71�/8180

Ijumba, J.N., Mwangi, R.W., Beier, J.C., 1990. Malaria

transmission potential of Anopheles mosquitoes in the

Mwea-Tebere irrigation scheme, Kenya. Med. Vet. Ento-

mol. 4, 425�/432.

Julvez, J., 1995. History of insular malaria in the southwestern

Indian Ocean: an eco-epidemiological approach. Sante 5,

353�/358.

Kaneko, A., Taleo, G., Kalkoa, M., Yamar, S., Kobayakawa,

T., Bjorkman, A., 2000. Malaria eradication on islands.

Lancet 356, 1560�/1564.

Killeen, G.F., McKenzie, F.E., Foy, B.D., Schieffelin, C.,

Billingsley, P.F., Beier, J.C., 2000. The availability of

potential hosts as a determinant of feeding behaviours and

malaria transmission by African mosquito populations.

Am. J. Trop. Med. Hyg. 62, 545�/551.

Koella, J.C., 1991. On the use of mathematical models of

malaria transmission. Acta Trop. 49, 1�/25.

Lines, J.D., Wilkes, T.J., Lyimo, E.O., 1991. Human malaria

infectiousness measured by age-specific sporozoite rates in

Anopheles gambiae in Tanzania. Parasitology 102, 167�/177.

Macdonald, G., 1952. The analysis of equilibrium in malaria.

Trop. Dis. Bull. 49, 813�/828.

Macdonald, G., 1957. The Epidemiology and Control of

Malaria. Oxford University Press, London.

Marsh, K., 1992. Malaria*/a neglected disease. Parasitology

104, S53�/S69.

Mbogo, C.N., Snow, R.W., Khamala, C.P., Kabiru, E.W.,

Ouma, J.H., Githure, J.I., Marsh, K., Beier, J.C., 1995.

Relationships between Plasmodium falciparum transmission

by vector populations and the incidence of severe disease at

nine sites on the Kenyan coast. Am. J. Trop. Med. Hyg. 52,

201�/206.

Mbogo, C.N., Baya, N.M., Ofulla, A.V.O., Githure, J.I., Snow,

R.W., 1996. The impact of permethrin-impregnated bednets

on malaria vectors of the Kenyan coast. Med. Vet.

Entomol. 10, 251�/259.

Mbogo, C.N., Mwangangi, J.M., Nzovu, J., Gu, W., Yan, G.,

Gunter, J., Swalm, C., Keating, J., Regens, J.L., Shililu, J.I.,

Githure, J.I., Beier, J.C., accepted manuscript. Spatial and

temporal heterogeneity of Anopheles mosquitoes and Plas-

modium falciparum transmission along the Kenyan coast.

Am. J. Trop. Med. Hyg.

Molineaux, L., Gramiccia, G., 1980. The Garki Project. World

Health Organization, Geneva.

Mutero, C.M., Birley, M.H., 1987. Estimation of the survival

rate and oviposition cycle of field populations of malaria

vectors in Kenya. J. Appl. Ecol. 24, 853�/863.

Pull, J.H., Grab, B., 1974. A simple epidemiological model for

evaluating the malaria inoculation rate and the risk of

infection in infants. Bull. World Health Organ. 51, 507�/516.

Rickman, L.S., Jones, T.R., Long, G.W., Paparello, S.,

Schneider, I., Paul, C.F., Beaudoin, R.L., Hoffman, S.L.,

1990. Plasmodium falciparum -infected Anopheles stephensi

inconsistently transmit malaria to humans. Am. J. Trop.

Med. Hyg. 43, 441�/445.

Sachs, J., Malaney, P., 2002. The economic and social burden

of malaria. Nature 415, 680�/685.

Theander, T.G., 1998. Malaria in areas of unstable and

seasonal transmission: lessons from Daraweesh. Trans. R.

Soc. Trop. Med. Hyg. 92, 589�/592.

Thomas, C.J., Lindsay, S.W., 2000. Local-scale variation in

malaria infection amongst rural Gambian children esti-

mated by satellite remote sensing. Trans. R. Soc. Trop.

Med. Hyg. 94, 159�/163.

Toure, Y.T., Coluzzi, M., 2000. The challenges of doing more

against malaria. Bull. World Health Organ. 78, 1376.

Trape, J.-F., Pison, G., Spiegel, A., Enel, C., Rogier, C., 2002.

Combating malaria in Africa. Trends Parasitol. 18, 224�/

230.

Vercruysse, J., Jancloes, M., van de Velden, L., 1983. Epide-

miology of seasonal falciparum malaria in an urban area of

Senegal. Bull. World Health Organ. 61, 821�/831.

Woolhouse, M.E.J., Dye, C., Etard, J.-F., Charlwood, J.D.,

Garnett, G.P., Hagan, P., Hil, J.L.K., Ndhlovu, P.D.,

Quinnell, R.J., Watts, C.H., Chandiwana, S.K., Anderson,

R.M., 1997. Heterogeneities in the transmission of infec-

tious agents: implications for the design of control pro-

grams. Proc. Natl. Acad. Sci. USA 94, 338�/342.

Zwetyenaga, J., Rogier, C., Spiegel, A., Fontenille, D., Trape,

J.-F., Mercereau-Puijalon, O., 1999. A cohort study of

Plasmodium falciparum diversity during the dry season in

Ndiop, a Senegalese village with seasonal, mesoendemic

malaria. Trans. R. Soc. Trop. Med. Hyg. 93, 375�/380.

W. Gu et al. / Acta Tropica 86 (2003) 71�/81 81