Understanding the link between malaria
risk and climate
Krijn P. Paaijmansa,1, Andrew F. Reada,b, and Matthew B. Thomasa
Center for Infectious Disease Dynamics,aDepartment of Entomology, Chemical Ecology Laboratory, andbDepartment of Biology, Mueller Laboratory,
Pennsylvania State University, University Park, PA 16802
Edited by Burton H. Singer, Princeton University, Princeton, NJ, and approved June 8, 2009 (received for review March 27, 2009)
The incubation period for malaria parasites within the mosquito is
exquisitely temperature-sensitive, so that temperature is a major
determinant of malaria risk. Epidemiological models are increas-
ingly used to guide allocation of disease control resources and to
assess the likely impact of climate change on global malaria
burdens. Temperature-based malaria transmission is generally in-
corporated into these models using mean monthly temperatures,
yet temperatures fluctuate throughout the diurnal cycle. Here we
use a thermodynamic malaria development model to demonstrate
that temperature fluctuation can substantially alter the incubation
period of the parasite, and hence malaria transmission rates. We
increases in mean temperature. Diurnal temperature fluctuation
around means >21°C slows parasite development compared with
constant temperatures, whereas fluctuation around <21°C speeds
development. Consequently, models which ignore diurnal varia-
tion overestimate malaria risk in warmer environments and un-
derestimate risk in cooler environments. To illustrate the implica-
tions further, we explore the influence of diurnal temperature
fluctuation on malaria transmission at a site in the Kenyan High-
lands. Based on local meteorological data, we find that the annual
epidemics of malaria at this site cannot be explained without
invoking the influence of diurnal temperature fluctuation. More-
over, while temperature fluctuation reduces the relative influence
of a subtle warming trend apparent over the last 20 years, it
nonetheless makes the effects biologically more significant. Such
effects of short-term temperature fluctuations have not previously
been considered but are central to understanding current malaria
transmission and the consequences of climate change.
basic reproductive rate ? climate change ? diurnal temperature
fluctuations ? extrinsic incubation period ? Plasmodium falciparum
In part this is because transmission of disease is determined by
a suite of other socioeconomic, environmental and behavioral
factors that can exacerbate or negate climatic influences (2–4).
But even leaving these nonclimatic issues aside, the effect of
climate itself on the intrinsic probability of transmission remains
controversial (1, 3, 5).
The influence of climate on vector-borne disease can be
the number of cases of a disease that arise from one case of the
disease introduced into a population of susceptible hosts (1). R0
is determined by a range of entomological and epidemiological
parameters. Among these, the extrinsic incubation period (EIP)
of the parasite within the mosquito, also referred to for malaria
as the period of sporogony, is one of the most critical as this
influences R0in an exponential fashion (6). Hence, even small
changes in the EIP can have a large effect on R0; this is because
it greatly influences the number of infected mosquitoes that live
long enough to become infectious. During the EIP, malaria
parasites go through various developmental stages and very
many replication cycles before migrating to the salivary glands
he dynamics and distribution of malaria are strongly deter-
mined by climatic factors (1). However, the exact influence
where they can be transmitted to humans. The speed of this
development depends on host, parasite and environmental fac-
tors, but estimates are on the order of 10–14 days in areas of high
malaria transmission (7, 8). In those same areas, 90% of the
female mosquitoes die within 12 days (7) and are therefore
unlikely to contribute to malaria transmission.
The extrinsic incubation period is extremely temperature
sensitive (9, 10). For Plasmodium falciparum, the major malaria
species throughout much of Africa, the relationship between
ambient temperature (T) and the EIP is approximated by EIP ?
111/(T-16), describing the iconic Detinova curve (11, 12). Use of
this equation is ubiquitous, with the vast majority of studies
deriving EIP using measures of average monthly temperature to
predict current malaria risk, and hence identify priority areas for
allocation of resources for disease control and to assess the
impact of climate change on global malaria burdens (8, 13–19).
However, mosquitoes and the developing malaria parasites do
not experience ‘average temperatures,’ but are exposed to
highlight how diurnal temperature fluctuation has the potential
to dramatically alter the rate of parasite development and hence
Our approach utilizes a common thermodynamic model (20),
which characterizes the nonlinear influence of temperature on
and Fig. S1). This model enables us to determine cumulative
growth of the malaria parasite inside the mosquito over set time
intervals (e.g., every 30 min) for different fluctuating tempera-
ture regimes, including temperatures approaching the thresholds
for malaria development. We determine air temperature using a
minimum-maximum temperature model in which temperature
follows a sinusoidal progression during daytime and a decreasing
exponential curve during the night (21, 22). This model produces
realistic diurnal temperature patterns for different maxima and
minima (see Methods and Fig. S2), and can be used to explore
the influence of day length, so enabling us to consider effects
such as latitude and seasonality. We find that temperature
fluctuations have important impacts on the time until mosqui-
toes will become infectious and hence on R0. Proper under-
standing of the influence of environment on disease risk both
now and under future climate change scenarios requires that we
incorporate temperature fluctuations into climate-based
Author contributions: K.P.P., A.F.R., and M.B.T. designed research; K.P.P. performed re-
search; K.P.P. analyzed data; and K.P.P., A.F.R., and M.B.T. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
Freely available online through the PNAS open access option.
See Commentary on page 13645.
1To whom correspondence should be addressed at: 19a Chemical Ecology Lab, University
Park, PA 16802. E-mail: email@example.com.
This article contains supporting information online at www.pnas.org/cgi/content/full/
August 18, 2009 ?
vol. 106 ?
The predicted effect of diurnal temperature range (DTR) on the
extrinsic incubation period of P. falciparum for a 12:12 day:night
cycle is shown in Fig. 1; the effects predicted under 10:14 and
14:10 day:night cycles are shown in Fig. S3. Temperature fluc-
tuation alters the length of the EIP compared with estimates
day length shaping the relationship. In areas with means of
20–22°C, the effects of fluctuation are generally small. However,
in areas with means below 20°C, the effect of fluctuation is very
much larger, with extrinsic incubation period reduced by many
days as DTR increases. For instance, at a constant 18°C, EIP is
completed within 46 days, but under a diurnal fluctuation of ?
7°C, parasites become infectious nearly a fortnight earlier. The
reason is that exposure to warmer temperatures for at least part
of the day provides something of a rescue effect, increasing
development rate relative to the cooler mean temperatures. This
mechanism can even result in parasites being able to develop at
average temperatures below the currently assumed minimum
threshold temperature. In contrast, at mean temperatures above
c.22°C, and especially above 24°C, DTR has the reverse effect
leading to a relative increase in the incubation period. Here,
periodic exposure to cooler temperatures, and/or hot tempera-
tures that exceed the optimum, leads to longer incubation
periods than expected. Day length exacerbates these influences
as expected, so that in transmission seasons with longer day
lengths, for example, around a low mean temperature the rescue
effects of high temperature occur for longer each day, further
speeding development. All these conclusions are qualitatively
robust to changes in high and low threshold temperatures for
parasite development (Fig. S4).
period on absolute R0 requires data on a suite of entomological
parameters. However, it is possible to assess the expected relative
change if we hold all parameters constant and vary EIP only (see
Methods). Importantly, adult mosquito survival is largely insensitive to
we follow others and assume a median daily survivorship of 0.860 (24)
and a maximum mosquito lifespan of 56 days (13). The result is that
small changes in EIP due to temperature fluctuation can have a large
relative effect on R0with, again, the extent of DTR and day length
S3 C and D). When we compare our model with Detinova’s equation
(12) we see that at mean temperatures less than or equal to 20°C, the
the resulting estimate of R0. This means that risk models based on the
intensity under cooler conditions. At mean temperatures greater than
than halve estimates of R0, suggesting that current risk models are
would still leave R0below the threshold for establishment. However,
there will be cases where a doubling will result in R0exceeding 1, and
in already endemic areas, any changes are important in terms of
quantifying actual transmission intensity. A doubling of R0from 50 to
a particular control measure and/or allocation decisions about the
resources necessary to control or even locally eradicate malaria (25).
In addition to revealing the importance of temperature fluc-
tuation for estimating transmission intensity under existing
conditions, Fig. 1A also enables us to explore likely effects of
climate change. In general, increasing mean temperature results
in a shortening of the incubation period (although at high mean
temperatures and large DTR the reverse is possible). However,
as DTR increases, the sensitivity of EIP to warming declines (the
contours in Fig. 1A get further apart as DTR increases). Thus,
the relative effects of increases in mean temperature are likely
temperature ranges (0–16°C). (B) The relative change in R0(%, right hand bar) across a range of mean temperatures (18–28°C) and diurnal temperature ranges
(0–16°C), comparing R0estimates derived from the length of EIP shown in Fig. 1A with estimates as predicted by the iconic equation of Detinova (12). Models
are run with 12:12 day:night cycle.
Changes in the extrinsic incubation period of malaria parasites and in the basic reproductive number as a consequence of temperature fluctuation. (A)
Paaijmans et al.PNAS ?
August 18, 2009 ?
vol. 106 ?
no. 33 ?
to be less than expected when daily temperature fluctuation is
taken into account. However, there is a further complication as
global warming is unlikely to result in a symmetrical shift in
maximum and minimum temperatures. Several studies predict
proportionately greater increases in daily minima than in daily
maxima, resulting in decreases in DTR (26–28), although the
reverse is possible at local scales (28, 29). Defining the nature of
these changes at particular sites will be important for predicting
local changes in disease burdens because changes in DTR can
exacerbate or mitigate the influence of increases in mean
temperatures, depending on initial starting conditions (Fig. 1A).
To explore these arguments further we examine the predicted
influence of temperature fluctuation on seasonal malaria at
Kericho, a site in the Kenyan Highlands that has been at the
centre of the debate on whether climate change has already
impacted on malaria dynamics (6, 30–35). We derived estimates
of mean daily temperatures and DTR from the Kericho mete-
orological station data (obtained from the National Climatic
Data Center) for the main malaria transmission season for the
years 1987–2005 (see Methods). These data indicate mean
14.9–20.5°C, with DTR from 9.0–17.5°C (Fig. 2A and B). With
these mean temperatures, the Detinova curve (12) predicts EIP
to last between 24 and 1,475 days (Fig. 2C). Given mosquito
mortality rates of 10–20% per day and an upper limit for survival
of 56 days (13), these incubation periods make transmission
unlikely (and often impossible) in all but 16 of a total of 82
potential transmission months for which data are available (Fig.
2C). Assuming that transmission is not possible in years where
EIP falls below maximum mosquito longevity for less than 1
month (unless the EIP itself is less than a month), this translates
at the annual level to transmission during only 6 of the 17 years
(Fig. 2C). Yet seasonal malaria epidemics have occurred annu-
ally throughout the 17 years (36). This mismatch between theory
and observation can be rectified by incorporating the observed
DTR, which reduces the length of the EIP considerably to 22–72
days (Fig. 2D). These shorter periods of the EIP now make
of the total; a result consistent with the frequency of epidemics
observed at Kericho during this period (36).
Simple linear regressions fitted to the Kericho temperature data
reveal a marginally positive trend in the mean temperatures (R2?
19-year time period. Conventional extrapolation from the Detinova
curve would lead to the conclusion that the warming would have
too long to make the change biologically meaningful. Including the
influence of fluctuation together with the modest decline in DTR
reduces the magnitude of the relative change, with the EIP reduced
from 42 to 36 days. However, although smaller, this relative change is
now within biologically meaningful limits for mosquito survival, and
Our analysis reveals that diurnal temperature fluctuation will
alter the length of parasite incubation compared with estimates
based on the equivalent means, with both DTR and day length
shaping the relationship. Under warmer conditions, for example,
of short-term exposure to sub- and superoptimum temperatures.
Consequently, in areas with mean temperatures in the range of
22–28°C (representative of large parts of sub-Saharan Africa),
implementation of temperature fluctuation. (A) The mean air temperature and (B) the mean diurnal temperature range during malaria transmission seasons
(March–July) between 1986 and 2006 in Kericho, and the corresponding length of the extrinsic incubation period of Plasmodium falciparum based on (C)
Detinova’s equation (12) and (D) the thermodynamic model described in the current paper, allowing temperature fluctuations.
Actual temperature conditions in a Kenyan highland area and the predicted length of malaria parasite development with and without the
www.pnas.org?cgi?doi?10.1073?pnas.0903423106Paaijmans et al.
estimates of R0, or other metrics of malaria risk, based solely on
measures of mean temperature could be too high so that by
extension, malaria may be potentially more controllable than
currently assumed. The effect is likely to be greatest for mean
temperatures ?26°C, which tend to be representative of areas
with high transmission intensities. A more pronounced effect,
however, occurs at lower temperatures, where malaria transmis-
sion is more likely to be epidemic rather than endemic. In these
transition environments, EIP becomes markedly shorter as day
enable parasites to complete development within the lifespan of
their vector at lower mean temperatures than previously pre-
dicted. Hence, in areas with mean temperatures below 20°C,
current estimates of risk could be too low.
This latter point is supported by the data from Kericho. The
relatively low mean temperatures revealed at Kericho over the
last c.20 years are similar to those reported by Zhou et al. (31)
from meteorological station data at 4 East African Highland
sites (including Kericho) for the period 1978–1998, and by
Shanks et al. (35) from a separate station at Kericho for the
period 1966–1995. The malaria developmental period estimated
from the Detinova curve (12) for the cool mean temperatures at
Kericho is too long to allow malaria transmission in most years.
However the regular malaria epidemics observed there since the
1980s can be explained by the observed diurnal temperature
fluctuations; at these cooler altitudes, there is nonetheless
sufficient heat during part of the day to allow EIP to be routinely
completed within the lifespan of adult Anopheles mosquitoes.
surroundings (37). Incorporating this source of temperature vari-
and An. funestus, the principal malaria vectors in Kericho (39, 40),
spend time feeding and resting indoors (41–46). Other studies
suggest a tendency for outdoor biting and resting, or no clear
preference between environments (43, 45, 47, 48). In addition, the
ability of anopheline mosquitoes to maintain steady-body temper-
atures by behavioral thermoregulation is limited (49). The impor-
tance of temperature fluctuation we have shown here makes a
strong case for trying to determine how mosquito behavior impacts
on the temperature conditions actually experienced by developing
malaria parasites, and further emphasizes that mean monthly
temperature is but one determinant of the thermal regime deter-
mining malaria transmission.
In previous studies of climate change in the East African
Highlands (e.g., 32, 34) mean temperatures were estimated using
the global 0.5 ? 0.5o[?55 ? 55 km at the equator (32)] gridded
Research Unit, Norwich, U.K.). These interpolated means ap-
pear 2–4°C higher than actual mean temperatures derived from
site specific meteorological stations [see (35) for explicit com-
parison and also (30)]. Although the extent of these differences
will depend in part of the exact location (especially altitude) of
the meteorological stations, the deviations from actual temper-
ature data [shown to be significant by Shanks et al. (35)] raise
questions over use of global gridded data for any quantitative
evaluations influenced by absolute temperature.
Beyond helping to explain the presence of malaria under cool
conditions, the role of temperature fluctuations appear central
for interpreting the consequences of climate change. The trends
in the Kericho data, for example, suggest a marginal increase in
the mean temperatures and a marginal decrease in DTR during
the transmission season over the last 20 years. The changes are
small, and we acknowledge that alternative analyses could reveal
different patterns and that additional factors, such as intermonth
or interannual variability (51), can also be important. Even so,
an increase in mean temperature is consistent with the analysis
of Pascual et al. (34) and predicted for the region using general
circulation models (52). Moreover, our aim is not to argue for or
against the presence of a climate change signal (31, 32, 34, 30),
but rather, to ask how daily temperature fluctuation might affect
the biological significance of any change that might have already
occurred, or which will do so in the future. From mean temper-
ature alone, the increase from 16.8–17.8°C seen at Kericho (Fig.
2A) is predicted to halve the extrinsic incubation period, an
long for parasite development to be completed within the
mosquito lifespan, so the probability of transmission remains
effectively nil. Hence, this large predicted effect of climate
change on EIP will have little biological significance. When the
effects of diurnal temperature fluctuation are included, the
predicted shortening in incubation period for that same 1°C
change in mean temperature is relatively smaller (Fig. 2B).
Nonetheless, because the baseline EIP is already much shorter
due to the effects of temperature fluctuation, even this more
developing fast enough to transmit routinely. This result sup-
ports the argument for a recent climate-induced increase in
malaria transmission intensity in the Kenyan Highlands (34).
The influence of short-term temperature fluctuation suggests
an important but largely unexplored mechanism via which
environmental temperature can affect disease transmission, and
adds a layer of complexity to the potential influence of climate
change on dynamics of vector-borne diseases such as malaria. In
general, diurnal temperature fluctuation reduces the impact of
a change in mean temperature, although the nonlinearities,
together with possible changes in DTR, make patterns complex.
For example, if we consider a 3°C rise in temperature [the
median increase in terrestrial temperature predicted by the
IPCC for the months March–May in East-Africa by 2100 (52)]
then for a site with a current mean temperature of 18°C, the
standard Detinova equation (12) predicts a shortening of EIP of
34 days (from 56 to 22 days). However, allowing for a typical
DTR of 12°C, the reduction in EIP would only be 13 days (from
34 to 21). Whether DTR changes simultaneously over this range
is relatively unimportant as 21°C is on the linear part of the
development curve (Fig. S1) and so daily temperature variation
has negligible effect on ultimate EIP (Fig. 1). Alternatively, if we
consider an equivalent 3°C increase in temperature for a hypo-
thetical malaria-free area with a current mean of just 14°C, then
although EIP is predicted to be reduced dramatically, malaria
transmission would remain extremely unlikely based on mean
mosquitoes. However, with a DTR of 12°C, EIP is reduced to 42
days making malaria transmission theoretically possible. If DTR
was to simultaneously increase at this transition site by 2°C, then
EIP would be reduced to 37 days, further increasing risk of
transmission. On the other hand, if warming reduced DTR by
2°C, then EIP would increase to 47 days, lessening the effect of
the increase in mean temperature.
development within the mosquito is sensitive to short-term varia-
this effect; a substantial knowledge gap that needs to be filled and
tested. However, the so-called Kaufmann-effect (53), whereby
biological processes appear to be faster under fluctuating low
temperatures, and slower under fluctuating high temperatures, has
long been recognized and the influence of diurnal temperature
variation established in a range of other host/vector-pathogen/
general (61). As such, there is every reason to expect malaria parasite
development to be affected by temperature fluctuation and recipro-
cally, little empirical support for the prevailing use of mean
monthly (or even annual) temperatures for estimating disease
risk. Indeed, the effects we describe result only from basic rate
Paaijmans et al. PNAS ?
August 18, 2009 ?
vol. 106 ?
no. 33 ?
summation of the generic nonlinear development model and
take no account of additional physiological mechanisms, which
(61). Furthermore, while our focus has been on the extrinsic
incubation period, the effects of daily temperature dynamics
have not been thoroughly explored for any of the key entomo-
logical parameters (e.g., development rate, adult size, length of
feeding cycle, biting rate, adult longevity) that combine to
determine vectorial capacity and R0, and are likely highly
dynamic, especially in environments where malaria is seasonal
[see (34)]. Analysis of these nonequilibrium conditions will
require development of models beyond the standard Ross-
MacDonald framework. In either case, given the need to
understand malaria dynamics for setting operational control
objectives and for predicting consequences of climate change,
this study highlights an urgent need to develop a better
mechanistic understanding of vector-parasite interactions with
improved integration of the biological and environmental
diurnal rhythm of the air temperature (T) is given by a sinusoidal progression
during daytime and a decreasing exponential curve during the night (21, 22):
T ? Tmin? ?Tmax? Tmin?sin??
t ? 12 ? D/2
D ? 2p?
trise? t ? tset
T ?Tmin? Tsetexp??N/?? ? ?Tset? Tmin?exp???t ? tset?/??
1 ? exp??N/??
tset? t ? trise
where Tminand Tmax(oC) are the minimum and maximum daily air tempera-
duration between solar noon and maximum air temperature, trise(hours) the
time of sunrise, tset(hours) the time of sunset, Tset(oC) the temperature at
sunset, N (hours) the duration of the night and ? the nocturnal time constant.
This model accurately predicts the daily temperature progression as ob-
served during clear days in a lowland (Kisian; 1,126 m above mean sea level)
and highland site (Fort Ternan: 1,552 m amsl) in western Kenya [Fig. S2; data
from (62), D ? 12]. The observed average temperatures were 23.0°C (model
prediction 23.3°C) and 20.3°C (model prediction 20.6°C) in the lowland and
highland site, respectively.
temperature - diurnal temperature range combinations. Mean temperatures
varied from 12 to 28°C and the DTR from 0 to 16°C. To assess the effect of
Extrinsic Incubation Period. The development of a malaria parasite within its
have been used to describe the relationship between malaria development
development [Detinova’s formula (12)] or, we feel, do not accurately mimic
the pattern generally observed in cold-blooded species (63). Therefore we
a set of empirical data (64–69) and the appropriate linear range derived from
the Detinova function (12) (Fig. S1) to give:
r?T? ? 0.000112T?T ? 15.384? ??35 ? T??R2? 0.924?
Development rate was calculated at 30-min intervals using the temperature
model described above. Growth rates were accumulated until they reached a
value of 1, which defines the completion of the extrinsic incubation period.
This type of approach has been widely used to explore a number of
temperature-dependent rate effects for insects (e.g., 20, 70–72) and more
fundamentally for exploring the effect of temperature on a wide range of
ecological and evolutionary questions (e.g., 59, 73, 74). Brie `re’s model is just
one of the possible models that captures the characteristic nonlinear and
asymmetric influence of temperature, with a sharper decline in development
at temperatures above the optimum than below. Other alternative functions
such as those proposed by Logan (70) and Lactin (71) are more complex and
provide no better fit to the available data. While having equivalent fit alone
does not ensure identical model behavior (61), exploring the effects of tem-
perature fluctuations on EIP with an alternative thermodynamic model for
Plasmodium falciparum (63), produces qualitatively similar results (Fig. S4A
and B) due to the fundamental nature of the rate summation effect with
nonlinear development functions (61).
Basic Reproduction Rate. The mean number of secondary cases a single infec-
tious person will cause in a population is important for setting proper disease
control targets. R0is determined by a range of entomological and epidemi-
where r is the recovery rate of hosts from infection, m the vector:host ratio,
a the biting rate of the vector, b the transmission coefficient from verte-
brate to vector, c the transmission coefficient from vector to vertebrate, p
the daily survival rate of the vector and EIP, the extrinsic incubation period
or development time of the parasite within the vector. The relative con-
sequences of changes in extrinsic incubation period on R0can be assessed
using the relationship between EIP and p derived from the R0equation:
pEIP/-lnp. We assume that all other parameters in the R0equation (10) are
similar and can therefore be omitted; that is, estimates based on the mean
and estimates based on a fluctuating temperature regime only affect the
duration of EIP in this study.
Temperature Data from Kericho. The Kericho district ranges from 1,600–3,000
m (40). Available daily surface data for the years 1986–2006, including mini-
mum, maximum, and mean air temperatures, were obtained from the Na-
tional Climatic Data Center (http://www.ncdc.noaa.gov/oa/mpp/freeda-
ta.html). The meteorological station is situated at an altitude of 2,184 m. We
restrict our analysis to data from March to July, the months of the main
transmission season. The approach of focusing on the transmission season
differs from most other studies that tend to consider conditions across the
African Highlands is not holoendemic (35) and entomological surveys in
Kericho indicate the principal mosquito vectors are largely restricted to a
4–5-month window (39, 40). Thus, from the perspective of mosquito-parasite
biology, it is most relevant to consider conditions during this discrete season.
Months with less than 7 days of temperature data were omitted from the
analysis (May 2002, April 2004, and June 2005).
and to the 2 anonymous referees for constructive inputs. Supported by a
Netherlands Organisation for Scientific Research (NWO) grant to KPP and, in
part, by a grant with the Pennsylvania Department of Health using Tobacco
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