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\begin{document}

\title{Exploring the thermal limits of malaria transmission in the western
Himalaya}



\author[1]{Farhina Mozzafer}%
\author[1]{Gautam Menon}%
\author[2]{Farah Ishtiaq}%
\affil[1]{The Institute of Mathematical Sciences}%
\affil[2]{Tata Institute for Genetics and Society}%


\vspace{-1em}



  
  \date{May 17, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
Environmental temperature is a key driver of malaria transmission
dynamics. Using detailed temperature records from four sites
(1800-3200m) in the western Himalaya, we model how temperature regulates
parasite development rate (the inverse of the extrinsic incubation
period, EIP) in the wild. Using a Bri\selectlanguage{ngerman}ére parametrization of the EIP,
combined with Bayesian parameter inference, we study the thermal limits
of transmission for avian (\emph{P. relictum}) and human Plasmodium
parasites (\emph{P. vivax} and \emph{P. falciparum}) as well as for two
malaria-like avian parasites, Haemoproteus and Leucocytozoon. We
demonstrate that temperature conditions can substantially alter the
incubation period of parasites at high elevation sites (2600-3200m)
leading to restricted parasite development or long transmission windows.
We then compare estimates of EIP based on measures of mean temperature
versus hourly temperatures to show that EIP days vary in cold versus
warm environments. We found that human \emph{Plasmodium} parasites
experience a limited transmission window at 2600m. In contrast, for
avian \emph{Plasmodium} transmission was not possible between September
to March at 2600m. In addition, temperature conditions suitable for both
\emph{Haemoproteus} and \emph{Leucocytozoon} transmission were obtained
from June to August and in April, at 2600m. Finally, we use temperature
projections from a suite of climate models to predict that by 2040, high
elevation sites (\textasciitilde{} 2600 m) will have a temperature range
conducive for malaria transmission, albeit with a limited transmission
window. Our study highlights the importance of accounting for fine-scale
thermal effects in the expansion of the range of the malaria parasite
with global climate change.%
\end{abstract}\selectlanguage{ngerman}%



\sloppy


Abstract

Environmental temperature is a key driver of malaria transmission
dynamics. Using detailed temperature records from four sites
(1800-3200m) in the western Himalaya, we model how temperature regulates
parasite development rate (the inverse of the extrinsic incubation
period, EIP) in the wild. Using a Bri\selectlanguage{ngerman}ére parametrization of the EIP,
combined with Bayesian parameter inference, we study the thermal limits
of transmission for avian (\emph{P. relictum} ) and
human\emph{Plasmodium} parasites (\emph{P. vivax} and \emph{P.
falciparum} ) as well as for two malaria-like avian parasites,
\emph{Haemoproteus} and\emph{Leucocytozoon} . We demonstrate that
temperature conditions can substantially alter the incubation period of
parasites at high elevation sites (2600-3200m) leading to restricted
parasite development or long transmission windows. We then compare
estimates of EIP based on measures of mean temperature versus hourly
temperatures to show that EIP days vary in cold versus warm
environments. We found that human\emph{Plasmodium} parasites experience
a limited transmission window at 2600m. In contrast, for avian
\emph{Plasmodium} transmission was not possible between September to
March at 2600m. In addition, temperature conditions suitable for both
\emph{Haemoproteus} and\emph{Leucocytozoon} transmission were obtained
from June to August and in April, at 2600m. Finally, we use temperature
projections from a suite of climate models to predict that by 2040, high
elevation sites (\textasciitilde{} 2600 m) will have a temperature range
conducive for malaria transmission, albeit with a limited transmission
window. Our study highlights the importance of accounting for fine-scale
thermal effects in the expansion of the range of the malaria parasite
with global climate change.

\textbf{Key words:} Climate change, Extrinsic Incubation Period,
Malaria, Western Himalaya



\textbf{Introduction}

Changes in climate are shifting the geographic ranges of species (e.g.,
birds; Chen \emph{et al} . 2011, Freeman \emph{et al} . 2018). These
have a significant influence on parasite transmission dynamics, either
by exposing immunologically naïve hosts to longer transmission seasons
or bridging novel host-parasite interactions (Patz \emph{et al} . 2001).
Among vector-borne pathogens, malaria parasites have remained the most
virulent group, with high sensitivity to climatic factors which continue
to threaten both human and many wild animal populations (van
Riper\emph{et al} . 1999).

Temperature is the key environmental driver influencing the transmission
dynamics and distribution of malaria parasites. The rate of malaria
parasite transmission and intensity of infection is strongly determined
by the extrinsic incubation period (EIP: also known as the duration of
sporogony), the time it takes for a parasite to develop within a
mosquito and become transmissible (Ohm \emph{et al} . 2018). Therefore,
the EIP determines the parasite development rate in the midgut after
many replication cycles before it migrates as a sporozoite (infective
stage) in the salivary glands of an arthropod vector. The development
rate of a parasite depends on host, parasite, and environmental
conditions. These conditions must be conducive for transmission of the
parasite. For example, the EIP of human \emph{Plasmodium} is dependent
on temperature and the parasite generally takes 8--14 days to develop,
so if adult \emph{Anopheles} mosquitoes die before or within a 12-day
period, they are unlikely to contribute to parasite transmission
(Killeen \emph{et al} . 2000, Paijmans \emph{et al} . 2009, Ohm \emph{et
al} . 2018). In addition, temperature plays a central role in regulating
mosquito population dynamics, age-structure in a population,
life-history traits, fitness and phenology of vectors and parasites,
leading to complex spatial and temporal patterns of distribution
(Beck-Johnson \emph{et al} . 2013).

Most mechanistic models of human \emph{Plasmodium} transmission are
based on the degree-day model of Detinova (Detinova 1962). The Detinova
model assumes a linear relationship between ambient temperature
(\emph{T} ) and the parasite development rate (PDR). For example,
for\emph{Plasmodium falciparum} the following relationship is assumed to
hold: EIP (in days) =111/(\emph{T} -16), where 111 is the cumulative
number of degree-days required for the parasite to complete
development,\emph{T} is the average ambient environmental temperature,
and the relationship assumes that the temperature threshold below which
development cannot occur is 16°C. However, although this equation is
used in many studies, it fails to capture daily temperature fluctuations
which could potentially alter the rate of parasite development and
malaria transmission in a population. Other thermodynamic models propose
a nonlinear relationship between temperature and growth or development
(Paaijmans \emph{et al} . 2009). These models can be generalised to
consider temperature fluctuations which alter the length of parasite
incubation period and malaria transmission rates. Therefore,
epidemiological models should benefit from combining local
meteorological data and diurnal temperature fluctuations to understand
the biological significance of temperature in shaping parasite
transmission dynamics.

Temperature is considered as the main driver for mosquito emergence and
spring phenology (e.g., budburst, leaf-out, and flowering) in temperate
regions (e.g., H\selectlanguage{russian}ӓllfors \emph{et al} . 2020). In the context of
epidemiology of avian malaria, the overlap in seasonal emergence of
vectors produces spring relapses in chronic infections (parasite
phenology) and new infections in breeding host populations (Applegate
1970, Beaudoin \emph{et al} . 1971). However, the implications of
temperature variation for avian malaria parasite development across
temperate regions are less understood.

The western Himalayas are a species-rich and highly seasonal ecosystem
with distinct physiographic climatic conditions which drives bird
migration, spring phenology and vector emergence (Barve \emph{et
al.}2016, Ishtiaq and Barve 2018). In general, birds harbour a huge
diversity of three genera of haemosporidian parasites \selectlanguage{english}-\emph{Plasmodium,
Haemoproteus} and \emph{Leucocytozoon,} which are more ubiquitous and
cosmopolitan (except Antarctica) (Valkin\selectlanguage{polish}ũ\selectlanguage{english}as 2005). These parasites are
transmitted by dipteran insects, e.g., mosquitoes (\emph{Plasmodium} ),
biting midges (\emph{Haemoproteus} ) and black flies
(\emph{Leucocytozoon} ) and have significant negative effects on the
host survival and longevity (Asghar \emph{et al} . 2015), reproductive
success and body condition (Marzal \emph{et al} . 2005). In this montane
system, birds exhibit two migration strategies; species are either
year-round high elevation residents (sedentary) or seasonal elevational
migrants. Elevational migrants winter at low elevations or in the plains
([?] 1500 m above sea level; a.s.l.) and move to breeding grounds at
higher elevations (2600--4000 m a.s.l. or even higher) during the summer
season (Dixit \emph{et al} . 2016). The elevational migrants are exposed
to a large suite of parasites and vector fauna, especially in low
elevations and move to high elevation breeding grounds only during the
summer season (``migratory escape'', Loehle 1995). By contrast,
sedentary counterparts potentially experience little or no exposure to
parasites at high elevations in winters. Given that a competent vector
and optimal thermal conditions are present, elevational migrants could
act as `bridge hosts' of parasite species and potentially increase
transmission risk between wintering and breeding areas. This potentially
increases the risk of infection to na\selectlanguage{ngerman}ïve resident birds at high
elevations which might not have evolved to cope with parasite infection.
In addition, the emergence of insect vectors (e.g., \emph{Culicoides} )
is driven by temperature and does not coincide with peak bird breeding
season (April-May) in a high elevation environment suggesting a mismatch
in phenology of vectors and avian hosts (Ishtiaq \emph{et al.} unpubl.,
e.g., Gethigs \emph{et al} . 2015). This mismatch potentially alters the
degree of interaction between host and vector species, thereby
influencing parasite transmission dynamics. Only if the arrival of
infected birds (with infective stages in the bloodstream) coincides with
the peak of vector abundance, can transmission of pathogens from
migratory birds to vectors be facilitated. There are currently no
studies undertaken to understand the influence of environmental factors
on vector phenology and what changes in parasites' distribution ranges
are expected with climate change.

In this study we model the change in temperature and parasite
transmission dynamics in four western Himalayan sites across an
elevational gradient. Using fine-scale meteorological data, we explore
limits of parasite transmission as a function of temperature in the
western Himalayan landscape. Specifically, we ask the following
questions:

(i) Is parasite transmission restricted by temperature in high elevation
environments?

(ii) Is there spatial and temporal variation in parasite transmission
dynamics?

(iii) How will climate change affect the distribution of malaria and the
parasite transmission window?

\textbf{MATERIALS AND METHODS}

\textbf{Study area and collection of temperature data}

For micro-climate data, we deployed the Thermochron iButton (Maxim
Integrated Products, http://www.maxim-ic.com/) to record temperature
data every hour on a round-the-clock basis at each sampling site from
2014\selectlanguage{english}-2015: Mandal {[}1800m: N30.44685deg E79.27328deg{]}, Anusuya
{[}2000-2200m: N30.47888degE79.28503deg{]}, Kanchula {[}2600m: N30.45913deg
E79.22744deg{]} and Shokharakh {[}3100-3400m: N30.47860degE79.217980deg;
Figure 1.{]} in the western Himalaya, Uttarakhand state, India.

\textbf{Quantifying the effects of environmental temperature on parasite
development (Extrinsic Incubation Period)}

The extrinsic incubation period is the reciprocal of the parasite
development rate (PDR). A convenient representation of the PDR follows
from the Briere equation (Briere \emph{et al} . 1999)

PDR\textsubscript{parasite} (T) = c * T * (T -- T\textsubscript{min}) *
\selectlanguage{english}[?] (T\textsubscript{max} -- T) (1)

where T\textsubscript{min} and T\textsubscript{max} are the minimum and
maximum temperatures that can sustain

parasite development and c is a constant, the scaling parameter. These
parameters must

be estimated or fit against experimental data. This model was based on
thermodynamic

principles and shown to capture accurately the form of the EIP
in\emph{Plasmodium falciparum} and \emph{Plasmodium vivax} as described
previously by others (Paaijmans \emph{et al} . 2009, Cator \emph{et
al.}2013).

\textbf{A Bayesian approach to the calculation of the extrinsic
incubation period}

Given the Briere equation (Briere \emph{et al} . 1999) we first use
Bayesian methods to find the best estimates for the parameters
T\textsubscript{min,} T\textsubscript{max} and c (Gelman \emph{et al} .
2013, Bolstad \emph{et al} . 2016, McElreath 2016). Bayesian inference
approach allows us to incorporate prior knowledge into a description of
data, capturing parameter uncertainties. It also provides a consistent
framework for including prior information, while accounting for
uncertainty in inferred parameters.

We used thermodynamic models to estimate the influence of both mean and
diurnal temperature fluctuation on malaria transmission
(Paaijmans\emph{et al} . 2009). Specifically, we selected parasite
species that have been recorded in the western Himalayan birds. We
extracted the temperature dependent EIP values for two human malaria
parasites -\emph{P. falciparum} , \emph{P. vivax} and avian parasites in
the genus\emph{Plasmodium} (\emph{Plasmodium relictum} ),
\emph{Haemoproteus} and\emph{Leucocytozoon} using parasite specific
temperature data summarised in Suppl. Table 1. Specifically, for
\emph{Haemoproteus} , we choose the average (midpoint of the range) as
only temperature ranges were available (Suppl. Table 1).

To estimate the EIP of a parasite species, two main parameters are
required: the lifespan of arthropod vectors and temperature data. The
two human malaria parasites - \emph{P. falciparum} , \emph{P. vivax} are
transmitted by species of \emph{Anopheles} mosquito. The avian
malaria,\emph{P. relictum,} is primarily transmitted by \emph{Culex
quinquefasciatus} . It takes the malaria parasite 56 days to develop in
the mosquito at 18degC which is longer than the lifespan of the
mosquitoes. At 22degC it takes only 19 days and at 30degC only 8 days
(Githeko 2007). The upper limit of longevity of mosquitoes can be up to
56 days as used in previous studies (Craig \emph{et al} . 1999,
Paaijmaans \emph{et al} . 2009) depending upon environmental conditions.
We considered an upper threshold for the EIP for mosquitoes as 56 days.
The vectors of \emph{Haemoproteus} sp. are biting midges
(\emph{Culicoides} sp.) and black flies (simulids)
for\emph{Leucocytozoon} . The lifespan of biting midges is
\textasciitilde{}10 to 20 days (Sick \emph{et al} . 2019) whereas black
flies can survive for two to three weeks (Adler 2004). We thus
considered the upper threshold for the EIP for both biting midges and
black flies to be 20 days.

We describe our methods in more detail in subsections below:

\textbf{(i) \emph{Estimation of model parameters}}

We estimate the parameters \selectlanguage{greek}θ \selectlanguage{english}=
\{T\textsubscript{min},T\textsubscript{max}, c, \selectlanguage{greek}σ\selectlanguage{english}\} using Bayesian
inference methods (Gelman \emph{et al} . 2013, Bolstad \emph{et al} .
2016, McElreath 2016) implemented using the available data. The
parameters T\textsubscript{min}, T\textsubscript{max} and c have been
defined earlier. The quantity \selectlanguage{greek}σ \selectlanguage{english}provides the scale factor for the width
of the likelihood between observed data and model.

Our implementation of the inference strategy uses STAN
(https://mc-stan.org/), a platform for statistical modelling and
high-performance statistical computation. STAN performs Bayesian
statistical inference with Markov Chain Monte Carlo (MCMC) sampling. It
also provides diagnostic tools to evaluate the accuracy and convergence
of the MCMC while allowing for posterior predictive checks.

\textbf{(ii) \emph{Prior distribution}}

Bayesian approaches incorporate prior knowledge about the parameters
into the model. Our choices for these distributions are summarised in
(Suppl. Table 2) below for each parasite. We choose a common prior for
Sigma, 1/gamma (0.0001,0.0001) and scale parameter (c), gamma (1,10), in
all cases. We selected a flat prior for T\textsubscript{min} and
T\textsubscript{max} within a defined range. We used a gamma
distribution as both the scaling parameter and sigma are non-negative
continuous positive values.

\textbf{(iii)} Likelihood

We choose a normal distribution with mean parameter \selectlanguage{greek}μ \selectlanguage{english}given by the
Bri\selectlanguage{ngerman}ére equation (Briére \emph{et al} . 1999) as the likelihood of the
data and standard deviation \selectlanguage{greek}σ. \selectlanguage{english}We run STAN (\emph{https://mc-stan.org/})
for four chains of 1000 iterations each, discarding 500 iterations in
each case for warmup. \(\hat{R}\), the convergence statistic
reported by STAN, is close to 1 (\textless{} 1.05), indicating the 4
Markov chains are in close agreement with one another.

\textbf{Calculation of the extrinsic incubation period (EIP)}

The EIP was calculated using mean daily temperature and mean hourly
temperature for \emph{P. falciparum} , \emph{P. vivax} , \emph{P.
relictum} , \emph{Leucocytozoon} and \emph{Haemoproteus} parasites. The
mean hourly temperature is used to estimate the effect of diurnal
temperature fluctuation on EIP. The diurnal temperature range (DTR)
variation across these four sites is the difference between maximum and
minimum temperatures on each day of the month at each site. This was
done for each day of the month for all four sites. Since all four sites
are at different elevations, it is possible that for a few days of a
month, the temperature was marginally above the minimum threshold
temperature for the development of parasites. The EIP calculated using
these temperatures can thus become anomalously high. We thus set the EIP
to 90 days whenever the computed EIP exceeded that number. We calculated
the mean EIP using both the mean daily temperature as well as mean
hourly temperatures for the month with the following procedure: We
calculate the EIP using the mean temperature for each day of the month.
We then average this EIP over the entire month. We use a similar
procedure for the mean hourly temperature. We set the upper threshold
temperature to about 5\textsuperscript{o}C above the maximum threshold
temperature (T\textsubscript{max}) following Hu and Appel (2004) and
Cator \emph{et al} . (2013). The upper threshold temperature is lethal
for parasite development. Once the temperature exceeds this lethal
temperature the development of parasites does not occur and no estimate
of EIP is possible.

\textbf{Modelling future parasite range expansion with warming climate}

We used a series of climate-based models to predict the change in
parasite range with temperature. First, we extracted monthly values for
minimum temperature and maximum temperature for the year 2021-2040 for
four Himalayan sites. We used Madhmaheshwar as a nearby site (30\selectlanguage{ngerman}°38\selectlanguage{english}'13\selectlanguage{english}"N
79deg12\selectlanguage{english}'58\selectlanguage{english}"E) as an alternative to Shokharakh due to non-availability of
data.

We used data from eight global climate models available on WorldClim
(\emph{www.worldclim.org)} . These global climate models (GCM) are
BCC-CSM2-MR, CNRM-CM6-1, CNRM-ESM2-1, CanESM5, IPSL-CM6A-LR, MIROC-ES2L,
MIROC6, MRI-ESM2-0. We extracted temperature data for the year 2021-2040
at a spatial resolution of 2.5 minutes to estimate the effect of future
climate change on malaria transmission. A set of scenarios have been
chosen to provide a range of distinct end of century climate change
outcomes by the energy modelling community, which mainly deals with
greenhouse gas emission scenarios driven by different socioeconomic
assumptions. We considered the shared socioeconomic pathway SSP2-4.5,
which provides one scenario for global emissions, consistent with
certain assumptions about how socio-economic trends might evolve in the
future. We selected SSP2-4.5 because it represents a ``middle of the
road'' scenario i.e., the world follows a path in which social,
economic, and technological trends do not shift markedly from historical
patterns.

To extract the minimum temperature and maximum temperature for the year
2021-2040 values, we use the GIS software QGIS (https://www.qgis.org).
We compute the average of predicted monthly mean temperature across all
eight GCM models.

\textbf{Comparison of EIP calculated using local meteorological data and
WorldClim data}

The temperature collected from data loggers is the real temperature
experienced by the malaria vectors in the field. Therefore, data from
loggers can be expected to provide more precise and local results as
compared to the weather station temperature data. To understand
variation in temperature modelling based on the local temperature
records and WorldClim (\emph{www.worldclim.org}) data, we calculated the
EIP using mean temperature collected from both datasets from May to
April 2014 to 2015.

\textbf{Results}

We estimated the extrinsic incubation temperature of
three\emph{Plasmodium} and two malaria-like
parasites-\emph{Haemoproteus} and\emph{Leucocytzoon} using one-year
field-collected data across four sites in the western Himalaya. Mean
daily temperatures were warmest (18degC) for the low elevation site at
1800m (Mandal), followed by the mid elevation site (13degC). The two high
elevation sites at 2600m (Kanchula) and 3200m (Shokharakh) had the
coolest temperatures, 10degC and 8degC, respectively (as shown in Figure 2).

\textbf{Explicit formulae for the Extrinsic incubation period}

The EIP of each parasite, in the Briere parametrization, requires three
parameters to be specified. The distributions of these parameters must
be obtained using prior knowledge and the available data, together with
statistical methods. We obtained parameter values describing the EIP
using the Bayesian methods described above, for \emph{P. relictum,
Haemoproteus} and \emph{Leucocytozoon.} The parameter values obtained
together with the appropriate confidence interval are shown in Table
1\emph{.} We display our results in Figure. 3, together with those
derived earlier for \emph{P. falciparum} and \emph{P. vivax} by
Cator\emph{et al} . (2013).

For \emph{P. falciparum} and \emph{P. vivax,} we rederived the forms
obtained by Cator \emph{et al} . (2013) through these Bayesian methods.
The work of Cator \emph{et al} . (2013) used an alternative method
involving simple curve-fitting using SPSS (IBM SPSS v20). We find exact
consistency with these earlier results, demonstrating the validity of
our numerical methods. Our results extrapolate from the limited data
available, together with non-informative estimates of the relevant
priors, to obtain what appear to be reasonable fits to the data,
together with uncertainty bounds.

\textbf{Effects of environmental temperature on parasite development
(Extrinsic Incubation Period)}

Using the thermodynamic parasite development model, we estimated the
effect of using the mean daily temperature and mean hourly temperature
on the calculation of the EIP for each site (1800-3200m). Our methods
described the rate of parasite development for \emph{Plasmodium} species
(two human and one avian \emph{Plasmodium} ), \emph{Haemoproteus} ,
and\emph{Leucocytozoon} parasites (Figure 3) at varying temperatures.
For high elevation sites (3200m), the EIP estimates for all parasites
using both measures suggested that transmission was not possible
throughout the year. Below, we describe where results from both measures
coincide, for other elevations and parasites, as well as where they
differ in detail. We find that both measures, based on either the
diurnal temperature range or the mean temperature, very largely give
similar results for the periods of the year where the EIP is within the
allowable range for transmission. However, for specific months, it is
possible that transmission is possible within one scheme but not within
the other (Figure 4).

For the 2600m site, there was no parasite transmission predicted using
the EIP based on both temperature measures for \emph{P. falciparum}
and\emph{P. vivax} from May to March. However, in June, the mean
temperature range predicted no transmission of \emph{P. vivax} whereas
the EIP days of 46.9+-15.71 using the diurnal temperature range. In
April, the EIP days for \emph{P. vivax} were longer by 13.95 days using
the diurnal temperature range (EIP days: 36.08+-3.5) than the mean
temperature (EIP days: 22.13+-4.04). The EIP days for \emph{P.
falciparum} were 5.62 days shorter using mean temperature measures (EIP
days:40.29+- 12.11) than the diurnal temperature (EIP days: 45.91+-10.64)
in April.

For avian \emph{Plasmodium relictum} , using both mean temperature and
diurnal temperature range, September to March was predicted as no
transmission period and May to August and April as predicted
transmission, at 2600m. In April, the EIP was 18.7 days longer using the
diurnal temperature range (EIP days:32.95+-16.29) than the mean
temperature range (EIP days:14.25+-2.25). For two malaria-like avian
parasites, \emph{Haemoproteus} and \emph{Leucocytozoon} , September to
March were predicted as no transmission period and June to August was
predicted as the transmission period (\textless{} 1 day difference in
EIP estimates) using both temperature measures. However, diurnal
temperature range predicted no parasite transmission in April whereas
mean temperature range estimated the EIP days of 8.27+-1.1 and 5.62+-0.75,
for \emph{Haemoproteus} and \emph{Leucocytozoon} , respectively.

For the 2000m site (Anusuya), October to March was predicted to have no
transmission period for \emph{P. falciparum} and \emph{P. vivax} using
both temperature measures. In April, using the mean temperature
predicted EIP days of 37.12+-27.34 for \emph{P. falciparum} and
34.73+-9.66 for \emph{P. vivax} , however no transmission was obtained
using the diurnal temperature range. Using the mean temperature, there
was no \emph{P. falciparum} transmission predicted for May and
September. However, the diurnal temperature range approach predicted EIP
days of 51.7+-17.94 in May and 50.7+-17.02 in September.

Among avian parasites, \emph{P. relictum} transmission window was
predicted from May to September using both temperature measures.
However, there was no \emph{P. relictum} transmission predicted in
October using mean temperatures while the diurnal temperature range
method estimated EIP days of (47.4+-19.46). In March, use of the diurnal
temperature range predicted no \emph{P. relictum} transmission whereas
the mean temperature range measure suggested EIP days of 46.03+-17.43. In
April, both temperature measures predicted \emph{P.
relictum}transmission, however, EIP days using diurnal temperature range
were 3.06 longer than for the mean temperature. For two malaria-like
parasites, \emph{Haemoproteus} and \emph{Leucocytozoon,} transmission
was predicted from June to September using both temperature measures.
There was no \emph{Haemoproteus} transmission predicted for October to
April using both temperature measures. In May, \emph{Haemoproteus}showed
no transmission using mean temperature whereas, using the diurnal
temperature, transmission was predicted with showed EIP days of
15.44+-8.54. However, \emph{Leucocytozoon} transmission was not predicted
from November to February, while only the mean temperature supported EIP
days of 17.71+-13.56 in March and April. The diurnal temperature range
method indicated transmission in October with EIP days of 19.81+-7.8.

For the lowest elevation site (1800m), \emph{P. falciparum} and \emph{P.
vivax} showed no transmission from December to February using both
measures, the DTR and the mean temperature. An exception was for
P.\emph{vivax} where the use of the diurnal temperature range showed an
EIP of 51.6+-10.72 days in the month of February\emph{.} The effect of
daily temperature variations on \emph{P. falciparum} and \emph{P.
vivax}predicted a transmission window from May to October, March, and
April. In November, there was no transmission using the mean temperature
for both \emph{P. falciparum} and \emph{P. vivax.} The use of the
diurnal temperature range predicted transmission for both parasites in
that month, with EIP more than 45 days in both cases.

In contrast, for \emph{P. relictum} , use of the diurnal temperature
range suggested transmission throughout the year. However, the use of
the mean temperature showed no transmission across the months December
to February. For the two malaria-like parasites, transmission months
ranged from May to October for \emph{Haemoproteus} and May to November,
as well as April, for \emph{Leucocytozoon.} The exceptions were: using
the mean temperature led to transmission in March while using the
diurnal temperature range led to transmission in April
for\emph{Haemoproteus} . In March, there was no transmission predicted
using the diurnal temperature range while mean temperature range
predicted EIP days of 12.79+-11.96 for \emph{Leucocytozoon} .

Our comparisons of mean temperature collected using experimental logger
data and WorldClim data from 2014-2015 showed threshold temperature not
supporting parasite transmission at the high elevation site (3200m)
throughout the year (Suppl. Fig. S1). However, at the 2600 m
site,\emph{P. vivax} transmission was predicted from May to September
and April whereas experimental data suggested only in April. For avian
parasites, \emph{P. relictum} , \emph{Haemoproteus}
and\emph{Leucocytozoon} the window in which transmission is predicted is
largely similar using these two source datasets, albeit leading to
longer EIP days with experimental data, with the only exception for the
month of April where this systematics are reversed. This larger pattern
was reversed at 1800 m, with shorter EIP days with experimental data as
compared to using WorldClim data, with the only exception again being
for the month of April. The 2000m site showed closely similar
transmission patterns for all parasites using both datasets, again
except for the months of March and April, for \emph{P. relictum}
and\emph{Leucocytozoon} .

\textbf{Predicting parasite range expansion}

Using computed monthly mean temperatures extracted from global climate
projections (2021-2040) and our field data collected from 2014-2015, we
compared the EIP for avian as well as the human malaria parasites across
the four Himalayan sites (Figure 5). The main point was that for
virtually all parasites, climate change scenarios lead to an expansion
of the transmission period in which parasite survival is guaranteed as
well as the lower EIP. The only exception was the low elevation site,
Mandal (1800m) where a decrease in average temperature is predicted
leading to an increase in EIP. The effects of climate change are known
to be inhomogeneous, in general, even as there is a secular increase in
overall mean temperatures. This counterexample to the general trend
supports that observation.

\textbf{Comparison of EIP using historical and future climate data}

To understand the effect of climate change with the historical and
future climate temperature on the EIP, we have used average temperature
for the year 2000-2018 (historical temperature data) and average
temperature of 2021-2040 (future temperature data), using data from
WorldClim (\emph{www.worldclim.org} ). The EIP calculated using both
these data is shown in Figure 6. The effects of global warming are
clearly seen, i.e., with high temperature for the year 2021-2040, the
EIP is shorter as compared to the lower temperatures across the period
2000-2018.

\textbf{Discussion}

Understanding how changing global temperature affects the period during
which parasite development can occur is crucial to modelling how the
range of viability of the malaria parasite changes with time. We explore
these questions using a thermodynamic model that describes the nonlinear
relationship between developmental rate and temperature, for five
blood-borne parasites and their arthropod hosts. For this we use a
parametrization of the EIP proposed by Briere \emph{et al} . (1999),
using Bayesian inference methods to estimate the relevant parameters
using prior knowledge assembled using an extensive literature search.
For avian haemosporidia -- \emph{P. relictum} ,
\emph{Leucocytozoon}spp., \emph{Haemoproteus} spp. - we are not aware of
any prior attempt to obtain the constants defining the EIP as
parameterized for the Briere equation. We believe this calculation
presents those results for the first time

Using measures of mean temperature versus the diurnal fluctuating
temperature in the field, we demonstrated both spatial and temporal
variation in malaria transmission risk in the western Himalayan region.
Both human malaria and avian malaria prevalence vary with season and
intensity across these sites. We showed that for all five vector-borne
parasites transmission was most strongly constrained by temperature in
high elevation (3200 m) environments throughout the year, and that
different models provided largely consistent results for lower
elevations.

Whilst the temperature and transmission windows we calculate could fit
within the lifespan of \emph{Anopheles} species in general, it is
important to note here that our study was primarily designed for the
forested habitat with no records of \emph{Anopheles} species (FI
unpublished data). Malaria incidence has been reported from human
dominated hilly areas below 2000 m with high prevalence
for\emph{Anopheles} mosquitoes incriminated as prime malaria vectors
(Shukla \emph{et al} . 2007). Our analysis showed that the temperature
conditions are not conducive for malaria transmission in the current
scenario and the diurnal temperature fluctuation has no effect on
malaria transmission biology. In line with the Government of India's
National Framework for Malaria Elimination in India 2016--2030 Program
(NVBDCP 2016), it is crucial now to apply such approaches for
identification of hotspots using fine-scale data which can help in
addressing the ecological drivers of malaria transmission
(Mishra\emph{et al} . 2016). These temperature estimates have
implications on defining the parasite transmission limits across
spatio-temporal scales: i) EIP responds in a non-linear fashion to
temperature and is sensitive to small changes in temperature which could
have significant effects on the parasite transmission window (e.g.,
Blanford \emph{et al} . 2013); ii) hourly fluctuations in temperature
are experienced in the field by both mosquito and parasite which could
provide site-specific insights into parasite transmission range at a
small spatial scale. While our data do capture these effects explicitly
using mean versus DTR measures, we emphasised that using site-specific
data is important for deriving insights into malaria transmission range.
Our comparisons of EIP calculated using local meteorological data and
WorldClim data showed that relying on weather station data might
underestimate the parasite development in a highly seasonal ecosystem
with distinct physiographic climatic conditions.

The changing climate has rapidly influenced the rainfall, temperature,
and vegetation phenology. These changes are causing shifts in the timing
of species activity. For example, a surge in temperature has shifted
timing and length of breeding season in birds (Hallfors \emph{et al} .
2020) leading to mismatch with optimal resource abundance which is vital
for reproductive success. For short-lived ectotherms, the spread of
mosquito species to new habitats in high elevations, short generation
times, high population growth rates and strong temperature-imposed
selection could lead to fast adaptation (Couper \emph{et al} . 2021).

In the western Himalayan context, the thermodynamic model showed that
the EIP days do not support transmission of avian haemosporidians
parasites at high elevation sites (3200m). However, EIP days have
limited transmission windows for \emph{Plasmodium} ,
\emph{Haemoproteus}and \emph{Leucocytozoon} from 1800-2000 m. This
further implies that low to mid elevation sites have optimal conditions
and lack thermal constraints for parasite transmission during peak
breeding season (April-May). Ishtiaq and Barve (2018) showed that the
probability of infection with \emph{Plasmodium} parasite declines
steeply with elevation. In contrast, \emph{Leucocytozoon} spp. infection
risk increases with elevation, however, most of these infections were
sub microscopic in high elevation in breeding season (April-May). This
contrasts with studies on the ecology of haemosporidia in temperate
regions where birds with latent infections return to the breeding
grounds and experience a relapse, with increase in parasites visible in
the blood stages (Applegate 1970, Becker \emph{et al} . 2020). In
general, parasite intensity showed a significant decline with elevation
in the breeding season (April-May) and an increase across mid-elevations
in the nonbreeding season. The absence of gametocytes (infective stage)
in the blood during spring season or late emergence of vectors due to
environmental conditions could lead to the disruption of transmission
cycles (migratory mismatch).

Our data support the hypothesis that avian \emph{Plasmodium}
,\emph{Haemoproteus} and \emph{Leucocytozoon} are currently restricted
by thermal gradient and provide an ecological explanation for absence of
gametocytes in breeding season at high elevation. This further implies
that fledgelings might be at the risk of haemosporidian
(\emph{Haemoproteus} ) infections from June-August which coincides with
peak emergence of \emph{Culicoides} spp. in 2000-2600 m sites (Ishtiaq
et al. unpublished data). Using a thermodynamic model, we supported
the\emph{Plasmodium relictum} transmission scenario in Hawaiian Islands
using Degree-day models with 13degC as minimum temperature and 30deg C as
maximum temperature threshold to complete sporogonic development
(LaPointe \emph{et al} . 2010).

We used climate models to interrogate how changing temperature from
2021-2040 could potentially lead to an expansion of the temperature
range conducive for malaria transmission in high elevation zones. Using
mean temperature data, we found low elevation sites (1800m) might
experience unsuitable conditions for parasite transmission in the future
which suggests that some habitats that are currently too cool to sustain
vector populations may become more favourable in the future, whereas
others that are drying may become less conducive to vector reproduction.
Therefore, the geographic ranges of mosquitoes may expand or be reduced,
which may cause parallel changes in the population of malaria pathogens
they transmit. Such expansion also increases the time window of malaria
transmission resulting in a larger number of generations of parasites
per year that can positively affect parasite abundance (Schroder\emph{et
al} . 2008).

One of the limitations of our study is the use of one year data to
define these thermal effects at a small spatial scale. To quantify these
temperature effects at a fine scale, we need long-term data across
multiple sites. Nevertheless, the mean temperature variation using field
data and WorldClim records exhibited similar patterns in parasite
transmission range. Furthermore, our modelling using mean versus hourly
temperatures captures the EIP variation which is corroborated by the
prevalence and intensity of parasites characterised in avian hosts. Our
data illustrates the contrasting thermal environments that can exist
across relatively small spatial scales within a region and can have
divergent effects on parasite development.

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\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\emph{Figure 1. Daily temperature sampling site of the western Himalaya
Mandal (1800 m), Anusuya (2000 m), Kanchula (2600 m) and Shokharakh
(3200 m). We have used the Madhmaheshwar site as an alternative to
Shokharakh for modelling future parasite range expansion, as explained
in the main text.}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\emph{Figure 2. Daily temperature records at an hour interval across
four sites in the western Himalaya. Mean temperature (upper panel) and
DTR (Diurnal temperature range) (Lower panel) for all four sites. Each
point shown in colour represents a value of daily temperature
(in\textsuperscript{O}C, right hand bar) from May 2014 to April 2015 of
that site. The solid lines represent average temperature. The black
vertical bar represents standard deviation.}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\selectlanguage{ngerman}\emph{Figure 3: Relationship between temperature and parasite
development rate for P. falciparum, P. vivax, P. relictum, Haemoproteus
and Leucocytozoon obtained using Bayesian modelling as described in the
text. The available empirical data (circle), summarised in the Suppl.
Table 1, is fitted to the Briére equation. The prior distributions for
all the estimated parameters are provided in Suppl. Table 2. The solid
line is the fit to the empirical data. The bands show the uncertainty
(confidence interval) in inferred parameters.}

\emph{}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\emph{Figure 4: Extrinsic incubation period (EIP) in days of P.
falciparum, P. vivax, P. relictum, Haemoproteus and Leucocytozoon for
four sites of the western Himalaya. These are calculated using mean
temperature (circle) and diurnal temperature range (DTR) (star) from May
2014 to April 2015. Bar represents the standard deviation.}

\emph{}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\emph{Figure 5: Comparison of extrinsic incubation period (EIP) in days
of P. falciparum, P. vivax, P. relictum, Haemoproteus and Leucocytozoon
for four sites of the western Himalaya. using mean temperature data (May
2014 to April 2015, circle) and future climate data (2021 to 2040,
triangle). Bar represents the SD.}

\emph{}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

\emph{Figure 6: Comparison of extrinsic incubation period (EIP) in days
of P. falciparum, P. vivax, P. relictum, Haemoproteus and Leucocytozoon
for four sites of the western Himalaya. using mean temperature data (May
2000 to April 2018, hexagon) and future climate data (2021 to 2040,
triangle).}

\emph{}\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
\textbf{Parasite} & \vtop{\hbox{\strut \textbf{T\textsubscript{min}
(\textsuperscript{o}C)}}\hbox{\strut \textbf{(2.5, 97.5) \%CI}}} &
\textbf{T\textsubscript{max} (\textsuperscript{o}C) (2.5,97.5) \%CI} &
\textbf{C (2.5,97.5) \%CI} & \selectlanguage{greek}\textbf{σ (2.5, 97.5) \%CI}\selectlanguage{english}\tabularnewline
P. falciparum & \vtop{\hbox{\strut 15.624}\hbox{\strut (15.02, 17.09)}}
& \vtop{\hbox{\strut 34.921}\hbox{\strut (33.38, 36.97)}} &
\vtop{\hbox{\strut 0.000116}\hbox{\strut (9.6e-5, 1.5e-4)}} &
\vtop{\hbox{\strut 0.01}\hbox{\strut (9.0e-3, 0.03)}}\tabularnewline
P. vivax & \vtop{\hbox{\strut 13.51}\hbox{\strut (13.02, 14.58)}} &
\vtop{\hbox{\strut 34.08}\hbox{\strut (31.97, 36.81)}} & 0.000122
(9.8e-5, 1.5e-4) & \vtop{\hbox{\strut 0.02}\hbox{\strut (0.01,
0.03)}}\tabularnewline
P. relictum & \vtop{\hbox{\strut 12.56}\hbox{\strut (9.06, 14.41)}} &
\vtop{\hbox{\strut 34.46}\hbox{\strut (31.38, 37.72)}} & 0.000157
(1.0e-4, 2.2e-4) & \vtop{\hbox{\strut 0.01}\hbox{\strut (6.3e-3,
0.03)}}\tabularnewline
\emph{Haemoproteus} \textbf{spp.} &
\vtop{\hbox{\strut 12.01}\hbox{\strut (11.04, 13.79)}} &
\vtop{\hbox{\strut 29.48}\hbox{\strut (28.03, 31.78)}} & 0.000299
(1.4e-4, 4.7e-4) & \vtop{\hbox{\strut 0.08}\hbox{\strut (0.05,
0.16)}}\tabularnewline
\emph{Leucocytozoon} \textbf{spp.} &
\vtop{\hbox{\strut 11.92}\hbox{\strut (11.03, 12.94)}} &
\vtop{\hbox{\strut 29.95}\hbox{\strut (28.1, 31.94)}} & 0.000425
(1.9e-4, 7.0e-4) & 0.11 (0.05, 0.23)\tabularnewline
\bottomrule
\end{longtable}

\emph{Table 1. Estimated parameter values of minimum and maximum
temperature, scaling parameter c and sigma using Bayesian method for all
parasites. \% CI is the confidence interval.}

\selectlanguage{english}
\FloatBarrier
\end{document}

