Exploring the thermal limits of malaria transmission in the western Himalaya

Abstract Environmental temperature is a key driver of malaria transmission dynamics. Using detailed temperature records from four sites: low elevation (1800), mid elevation (2200 m), and high elevation (2600–3200 m) 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 Briére parametrization of the EIP, combined with Bayesian parameter inference, we study the thermal limits of transmission for avian (Plasmodium relictum) and human Plasmodium parasites (P. vivax and 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 (2600–3200 m) leading to restricted parasite development or long transmission windows. The thermal limits (optimal temperature) for Plasmodium parasites were 15.62–34.92°C (30.04°C) for P. falciparum, 13.51–34.08°C (29.02°C) for P. vivax, 12.56–34.46°C (29.16°C) for P. relictum and for two malaria‐like parasites, 12.01–29.48°C (25.16°C) for Haemoproteus spp. and 11.92–29.95°C (25.51°C) for Leucocytozoon spp. 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 Plasmodium parasites experience a limited transmission window at 2600 m. In contrast, for avian Plasmodium transmission was not possible between September and March at 2600 m. In addition, temperature conditions suitable for both Haemoproteus and Leucocytozoon transmission were obtained from June to August and in April, at 2600 m. Finally, we use temperature projections from a suite of climate models to predict that by 2040, high elevation sites (~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.


| INTRODUC TI ON
Changes in climate, especially temperature and precipitation, are shifting the geographic ranges of species (e.g., birds ;Chen et al., 2011;Freeman 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 & Reisen, 2001). Among vectorborne pathogens, malaria parasites have remained the most virulent group, with high sensitivity to climatic factors, which continue to threaten humans, avian species, and non-human primates (van Riper et al., 1986).
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 are 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 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 (Beck-Johnson et al., 2013;Paaijmans et al., 2009). These conditions must be conducive for transmission of the parasite. For example, the EIP of human Plasmodium is dependent on temperature and the parasite generally takes 8-14 days to develop under optimal conditions of temperature (20°-25°C), so if adult Anopheles mosquitoes die before or within a 12-day period, they are unlikely to contribute to parasite transmission (Killeen et al., 2000;Ohm et al., 2018;Paaijmans et al., 2009). 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 et al., 2013).
Until 2010, most mechanistic models of human Plasmodium transmission were based on the degree-day model of Detinova (Detinova, 1962). More recently, multiple mechanistic models explained unimodal or nonlinear relationship between temperature and length of parasite development period (Beck-Johnson et al., 2013;Mordecai et al., 2019;Villena et al., 2022). The Detinova model as- temporal changes in changes in mosquito age structure and population dynamics to predict shift in malaria seasonality and disease risk. Villena et al. (2022) showed that the effect of temperature on parasite transmission could vary by mosquito species-the upper thermal limits varied significantly between the parasite transmission by the same mosquito species (An. stephensi) and between mosquitoes carrying P. falciparum. Other thermodynamic models propose a nonlinear relationship between temperature and growth or development (Paaijmans et al., 2009). These models can be generalized to consider temperature fluctuations, which alter the length of parasite incubation period and malaria transmission rates. Therefore, epidemiological models should improve from combining local micro-climate data using loggers by teasing apart 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., Hällfors 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 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 drive bird migration, spring phenology, and vector emergence Ishtiaq & Barve, 2018). In general, birds harbor a huge diversity of three genera of haemosporidian parasites-Plasmodium, Haemoproteus, and Leucocytozoon, which are more ubiquitous and cosmopolitan (except Antarctica) (Valkiūnas, 2005). These parasites are transmitted by dipteran insects, e.g., mosquitoes (Plasmodium), biting midges (Haemoproteus), and black flies (Leucocytozoon) and have significant negative effects on the host survival and longevity (Asghar et al. 2015), reproductive success, and body condition (Marzal et al., 2005). In this montane system, birds exhibit two

T A X O N O M Y C L A S S I F I C A T I O N
Disease ecology 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 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 naïve resident birds at high elevations, which might not have evolved to cope with parasite infection. In addition, the emergence of insect vectors (e.g., 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 et al. unpublished, e.g., Gethings et al., 2015). This mismatch potentially alters the degree of interaction between host and vector species, thereby influ- 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: N30.47860°E79.217980°; Figure 1] to record detailed temperature records from 2014 to 2015. For micro-climate data, we deployed the Thermochron iButton (Maxim Integrated Products, http://www. maxim -ic.com/) around 2 m above the ground on tree trunk shielded from direct sunlight to record temperature data every hour on a round-the-clock basis at each sampling site.

| 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 Briére equation (Briére et al., 1999).
where T min and T 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 Plasmodium falciparum and Plasmodium vivax as described previously by others (Cator et al., 2013;Paaijmans et al., 2009).

| A Bayesian approach to the calculation of the extrinsic incubation period
Given the Briére equation (Briére et al., 1999), we first use Bayesian methods to find the best estimates for the parameters T min, T max , and c (Bolstad & Curran, 2016;Gelman et al., 2013;McElreath, 2016).
Bayesian inference approach allows us to incorporate prior knowledge into a description of data, capturing parameter uncertainties.
We used thermodynamic models to estimate the influence of both mean and diurnal temperature fluctuation on malaria transmission (Paaijmans 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-P. falciparum, P. vivax, and avian parasites in the genera Plasmodium (Plasmodium relictum), Haemoproteus, and Leucocytozoon using parasite specific temperature data summarized in Table 1. Specifically, for Haemoproteus, we selected the average (midpoint of the range) as only temperature ranges were available (Table 1).
To estimate the EIP of a parasite species, two main parameters are required: the life span of arthropod vectors and temperature data.
The two human malaria parasites-P. falciparum, P. vivax are transmitted by species of Anopheles mosquito. The avian malaria, P. relictum, is primarily transmitted by Culex quinquefasciatus. It takes the malaria parasite 56 days to develop in the mosquito at 18°C, which is longer than the life span of the mosquitoes. At 22°C it takes only 19 days and at 30°C only 8 days (Githeko, 2007). The upper limit of longevity of mosquitoes can be up to 56 days as used in previous studies (Craig et al., 1999;Paaijmans et al., 2009) depending upon environmental conditions. We considered an upper threshold for the EIP for mosquitoes as 56 days. For human Plasmodium, we did not consider any specific Anopheles mosquito species as only three Anopheles species from 300 to 2000 m were reported in the western Himalayan region, and no information on their role in malaria transmission (Devi & Jauhari, 2004). The vectors of Haemoproteus sp. are biting midges (Culicoides sp.) and black flies (simulids) for Leucocytozoon. The life span of biting midges is ~10-20 days (Sick et al., 2019), whereas black flies can survive for 2-3 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:

| Estimation of model parameters
We estimate the parameters θ = {T min , T max , c, σ} using Bayesian inference methods (Bolstad & Curran, 2016;Gelman et al., 2013;McElreath, 2016) implemented using the available data. It also provides diagnostic tools to evaluate the accuracy and convergence of the MCMC while allowing for posterior predictive checks.

| Priors distribution
Bayesian approaches incorporate prior knowledge about the parameters into the model. Our choices for these distributions are summarized in (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 min and T max within a defined range. We used a gamma distribution as both the scaling parameter and sigma are non-negative continuous positive values.

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

| Calculation of the extrinsic incubation period (EIP)
The EIP was calculated using mean daily temperature and mean hourly temperature for P. falciparum, P. vivax, P. relictum, We calculated the mean EIP using both the mean daily temperature and mean hourly temperatures for the month with the following procedure: We calculated the EIP using the mean temperature for each day of the month. We then average this EIP over the entire month.
We used a similar procedure for the mean hourly temperature. We set the upper threshold temperature to about 5°C above the maximum threshold temperature (T max ) following Hu and Appel (2004) and Cator et al. (2013).

| Modeling 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 years 2021-2040 for four Himalayan sites. We used Madhmaheshwar (30°38′13″ N 79°12′58″ E), a nearby site, as an alternative to Shokharakh due to nonavailability of data.
We used data from eight global climate models available on To extract the minimum temperature and maximum temperature for the years 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.

| 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

| RE SULTS
We estimated the extrinsic incubation temperature of three

| 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 P. relictum, Haemoproteus, and Leucocytozoon. The parameter values obtained together with the appropriate confidence interval are shown in Table 3. We display our results in Figure. 3

| 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 (1800-3200 m).

| Predicting parasite range expansion
Using computed monthly mean temperatures extracted from global climate projections (2021-2040) and our field data collected from 2014 to 2015, we compared the EIP for avian as well as the human malaria parasites across the four Himalayan sites ( Figure 6). 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 (1800 m), 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.

| 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 years 2000-2018 (historical temperature data) and average temperature of 2021-2040 (future temperature data), using data from WorldClim. The EIP calculated using both these data is shown in Figure 7. The effects of global warming are clearly seen, i.e., with high temperature for the years 2021-2040, the EIP is shorter as compared with the lower temperatures across the period 2000-2018.

| DISCUSS ION
Understanding how changing global temperature affects the parasite development rate is crucial to modeling the range of viability of the malaria parasite changes with time. We explore these ques-  (Devi & Jauhari, 2004). Given that thermal tolerance differs by mosquito species when transmitting the same pathogen (Villena et al., 2022) and could change spatial extent of suitability of parasite transmission, our parasite development rate could change if mosquito species were considered as the main factor. Nonetheless, malaria incidence has been reported from human dominated hilly areas below 2000 m in western Himalayan region with high prevalence for Anopheles mosquitoes incriminated as prime malaria vectors (Shukla 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 2016-2030Program (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 et al., 2016).
These temperature estimates have implications on defining the parasite transmission limits across spatiotemporal scales: (i) EIP responds in a nonlinear fashion to temperature and is sensitive to small changes in temperature, which could have significant effects on the parasite transmission window (e.g., Blanford 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 emphasized 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 (e.g., Ishtiaq & Barve, 2018;Srinivasan et al., 2018). It is important to highlight those two temperature datasets will also affect other life-history traits of mosquitos (e.g., survival, feeding frequency, vector competence, emergence, etc.), which are important in driving the parasite transmission biology (Lalubin et al., 2013). Temperature is consid-  (Lalubin et al., 2013). Vector phenology and abundance are mainly driven by ambient temperatures that trigger larval development (Beck-Johnson et al., 2013;Jarošík et al., 2011) and precipitation that provides egg-laying opportunities. However, vector populations respond nonlinearly to both temperature and precipitation, e.g., increasing temperatures and precipitation favor reproduction and may result in higher abundances, but this will be reversed when exceeding the thermal optimum or a precipitation threshold (Mordecai et al., 2019).
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 (Hällfors 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 et al., 2021).

F I G U R E 3
Relationship between temperature and parasite development rate for P. falciparum, P. vivax, P. relictum, Haemoproteus, and Leucocytozoon obtained using Bayesian modeling as described in the text. The available empirical data (circle), summarized in Table 1 in the blood stages (Applegate, 1970;Becker et al., 2020). We used climate models to interrogate how changing temperature from 2021 to 2040 could potentially lead to an expansion of the temperature range conducive for malaria transmission in highelevation zones. Using mean temperature data, we found lowelevation sites (1800 m) 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 favorable 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 & Schmidt, 2008).
One of the limitations of our study is the use of 1-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 modeling using mean versus hourly temperatures captures the EIP variation, which is corroborated by the prevalence and intensity of parasites characterized in avian hosts. Our data illustrate the contrasting thermal environments that can exist across relatively small spatial scales within a region and can have divergent effects on parasite development. Our modeling approach can be applied to other life-history traits of parasites or vectors.

ACK N OWLED G M ENTS
This work was supported by the DBT/Wellcome Trust India Alliance Fellowship (IA/I[S]/12/2/500629) awarded to FI.

CO N FLI C T O F I NTE R E S T S
Authors declare no conflict of interest.

DATA AVA I L A B I L I T Y S TAT E M E N T
Data and codes are archived in github link https://github.com/fmozaf fer/Malar ia-EIP/.