Current estimates of malaria basic reproduction number underestimate parasite transmission efficiency due to multiple blood feeding

Background: Despite significant control efforts based on the large-scale distribution of insecticide treated nets, malaria cases have not declined in recent years. Mathematical models are used to predict the impact of these and other control interventions, but complex mosquito behaviors— such as repeated blood feedings—are generally not incorporated. Here, we examine how malaria transmission dynamics are impacted when infected mosquitoes feed a second time, as is typical in natural field settings. Methods: We performed sporozoite time course analyses to measure the Plasmodium falciparum extrinsic incubation period (EIP) in Anopheles gambiae females blood fed once or twice. We incorporated these findings into a model of the basic reproduction number R0, a measure of transmission potential, using current population and monthly mean temperature data across sub-Saharan Africa. Findings: A second blood feed drastically shortens the EIP and increases the average R0 by 12.2% (range: 10.2%-56.5%), impacting hundreds of millions of people. Moreover, parasite growth is further accelerated in mosquitoes with reduced reproductive capacity, which mimic genetic modifications currently proposed in population suppression gene drives. Interpretation: Our findings suggest that transmission efficiency is systematically underestimated in malaria models, particularly in elimination settings. Due to a shorter EIP, younger mosquitoes and mosquitoes with reduced reproductive ability may provide a larger contribution to infection, with important consequences for insecticide-based interventions and gene drive strategies. These findings call for an urgent reassessment of current and future control campaigns. Funding: Howard Hughes Medical Institute, Bill & Melinda Gates Foundation; National Institutes of Health; National Science Foundation.


Introduction
Malaria remains a devastating disease for tropical and subtropical regions, accounting for an estimated 405,000 deaths and 228 million cases in 2018 1 . Anopheles mosquitoes transmit the causative Plasmodium malaria parasites, and vector control through long-lasting insecticidetreated bed nets (LLINs) and indoor residual spraying (IRS) has greatly decreased the malaria burden in recent decades.
Since the early 20 th century, epidemiological models of malaria have been key to understanding which aspects of the transmission cycle should be targeted by malaria control to provide the most benefit 2,3 . Insecticidal interventions like LLINs are particularly effective in these models because they shorten the average lifespan of the mosquito, as well as lowering mosquito numbers and biting rates. As parasites require a significant amount of time to develop from sexual stages in the blood meal into infectious sporozoites in the salivary glands (a time period known as the extrinsic incubation period or EIP), decreasing mosquito survival curtails onward transmission to humans. The relationship between the EIP and the lifespan of the mosquito is therefore a key driver of malaria.
In most epidemiological studies the Plasmodium falciparum EIP is considered to last 12-14 days as determined through experimental laboratory infections 4 . This is similar to the expected lifespan of the Anopheles female, which although difficult to precisely measure due to the lack of reliable age markers, has been shown to be approximately 2-3 weeks 5,6 . When considered in the context of the basic reproduction number (R0)-the average number of infections resulting from a first case 3 -the EIP has an exponential relationship with transmission, and small changes in this parameter have large effects on malaria 7 . Furthermore, the relationship between the mosquito mortality rate and the parasite EIP is such that changes in one can be compensated by changes in the other. Thus, shortened lifespan can be offset by faster parasite development and result in the same transmission potential.
The biological factors that influence parasite developmental rates are largely unknown. The EIP is dependent on environmental temperature and larval nutrition, with higher temperatures (up to a point) and plentiful nutrients available during larval stages accelerating parasite growth 8 . Our recent studies in Anopheles gambiae have shown the P. falciparum EIP is also dependent on mosquito oogenesis, a process largely orchestrated by the steroid hormone 20-hydroxyecdysone (20E) 9 . Parasite growth is faster in females with impaired oogenesis, detected by the presence of larger oocysts in the midgut and of infectious sporozoites in the salivary glands at earlier time points, reducing the EIP. Accelerated growth rates are likely mediated by nutrients available after blood feeding 10 that become more abundant when egg development is impaired 9 .
Given this unexpected relationship between oogenesis and the P. falciparum EIP, the number of reproductive cycles a female mosquito completes may have important consequences for parasite transmission. There is a wealth of literature showing that many mosquito species, including An. gambiae, undergo multiple reproductive cycles of blood feeding, egg development and egg laying in their lifespan, which can be counted by ovarian dilatations 11,12 . Moreover, multiple feeds may be required even within a single reproductive cycle due to interrupted feeding or to nutrient deprivation during the larval stage (pre-gravid behavior) 13 . Additional blood meals may therefore potentially influence oocyst growth and the EIP, as suggested by reports showing an additional feed can boost P. falciparum oocyst size 14 and salivary gland sporozoite numbers at a given time point 15 .
Here, we examine how the parasite EIP is affected by multiple feedings, and the consequences of these effects in an epidemiological model of malaria transmission. By providing a second uninfected blood meal to females previously infected with P. falciparum, we show a striking boost in oocyst size and a substantially shortened EIP. A model-derived R0 equation parameterized using these data predicts a sizeable underestimate of current malaria transmission potential across sub-Saharan Africa, with over 208 million people living in areas where multiple blood feeding raises average R0 estimates by ≥15%. The speed of parasite development is further enhanced by a second feeding event in reproduction-defective females, suggesting that mosquito control strategies that reduce the reproductive output of Anopheles females-such as population suppression gene drives or chemical sterilants-could actually lead to increased parasite transmission. These data have important implications for generating accurate epidemiological models of malaria transmission and for better estimating the true impact of current and future mosquito control measures.

Rearing of Anopheles gambiae mosquitoes
Anopheles gambiae mosquitoes (wild-type G3 and transgenic strains) were reared in cages at 27°C, 70-80% humidity on a 12 h light:12 h dark cycle. Adults in colony cages were fed on 10% glucose solution ad libitum and weekly on human blood (Research Blood Components, Boston, MA). Males and females were mated in large cages.
Plasmodium falciparum (NF54 strain) was cultured as in 9 and is used under the permissions of a material transfer agreement from the laboratory of Carolina Barillas-Mury, National Institutes of Health, Bethesda, MD, USA.

P. falciparum infections of An. gambiae mosquitoes
Cages of mated female mosquitoes aged 4-6 days (d) were blood fed on ~320 µl P. falciparum culture for 30-60 min via heated membrane feeders and introduced into a custom-built glove box (Inert Technology, Amesbury MA). Feeding behavior was encouraged by starving mosquitoes of 10% glucose solution for 24 h and females not fully engorged were removed. Blood-fed mosquitoes were provided 10% glucose solution for 48 h and then given an oviposition site. Females were fed a second time 3 days after the initial infectious blood meal, using uninfected blood. Blood intake at the second blood meal was encouraged by providing an oviposition site 2 d post infectious blood meal (pIBM) and non-blood fed mosquitoes were removed. Females blood-fed twice and control mosquitoes fed once were provided 10% glucose solution until dissection. At dissection time points, mosquitoes were aspirated into 80% ethanol and transferred to 1X phosphate-buffered saline (PBS) (oocyst stages) or aspirated into ice-cold PBS (sporozoites stages) and beheaded. At least 3 biological replicates of each infection were performed.
Oocyst counts and measurements: At 7 d pIBM, midguts were stained directly in 2 mM mercurochrome (Sigma-Aldrich, St. Louis, MO) for 12 min. Mercurochrome-stained midguts were imaged at 100X on an Olympus Inverted CKX41 microscope, and oocysts were counted and measured using scaled images in FIJI 16 . Burst oocysts were counted but excluded from oocyst size analysis. Mean oocyst size was calculated for each midgut to avoid pseudoreplication.
Sporozoite counts: Mosquitoes were decapitated and the salivary glands of individual females were collected in a small volume of PBS and disrupted using a handheld disposable pestle. Released sporozoites were spun at 8000 g for 10 min at 4˚C and resuspended in a known volume of PBS. Sporozoites in 0.1 µl were counted using a disposable hemocytometer at 200X magnification on an Olympus Inverted CKX41 microscope with phase-contrast microscopy and sporozoite totals for each mosquito were calculated.

Generation of Dzpg females
Zpg and Cas9-carrying mosquito strains were generated previously 9 . Zpg/Cas9 mutant females, hereafter Dzpg mutants, were the F1 progeny of Zpg and Cas9 transgene homozygotes. Zpg controls and Dzpg mutant females did not differ in their ability to take a blood meal.

Statistical analysis
Experimental data were analyzed using JMP 14 Pro statistical software and GraphPad Prism 8.0. JMP 14 Pro was used to construct statistical models to account for variation due to multiple factors in an experiment. Depending on the distribution of the data, a Generalized Linear Model (GLM) (Poisson) or a Standard Least Squares (SLS) Model (Normal) was used and non-significant interaction terms (p>0.05) were removed where possible and models with minimal AICc scores and their effect test outputs are reported (Tables S1 and S2). Graphpad Prism 8.0 was used to calculate logistic regression curves and Fisher's exact and c 2 tests (Tables S3 and S4).

Modeling
We calculated the basic reproductive number, R0, as a function of temperature and population as in 17 using their equation (2) reproduced here as The expression is based on temperature-dependent trait data from Anopheles species that vary with temperature including biting rate (a), vector competence (bc), adult mosquito mortality ( ), parasite development rate (PDR), egg-to-adult survival probability (pEA), mosquito development rate (MDR) and eggs laid per female per day (EFD). Note that adult mortality is calculated through daily adult survival (p) via = -. ; parasite development rate is one over the extrinsic incubation period (EIP); and mosquito development rate is one over the larval development time ( 78 ).
Additionally, human related quantities-human density (N) and recovery rate (r)-are not temperature-dependent. For computation we set r as 1/200 but this does not impact the final ratios as it cancels out. The temperature-dependent traits of biting rate, parasite development rate and mosquito development time are fit to Briere functions, represented by where c, T0 and Tm are constants defined in 17 . The temperature-dependent traits vector competence, daily adult survival, egg-to-adult survival probability and eggs laid per female are fit to quadratic functions, represented by where q, r, and s are constants defined in 17 .
We then modified the basic reproductive number to incorporate a second blood feeding with reduced EIP, which we refer to as " H given by where we scale EIP using the term . We determine as the relative reduction in EIP in the presence of a second blood feed: ( =8.63 (2BF)/10.88 (1BF)=0.793. We then consider the ratio of the modified R0 to the original R0 as To estimate the impact of the EIP reduction on transmission potential, we applied these R0 functions to current population and monthly mean temperature data across Africa to estimate the percent change in R0 under a scenario where mosquitoes blood feed while infected. We incorporated the distribution of the population to quantify the number of people living in regions experiencing particularly high changes in transmission estimates.

Data
We used spatial raster files from multiple sources to map the change in R0 across the continent of Africa. We obtained global monthly mean temperatures for the period 1970-2000 from WorldClim 2.0 18 . We restricted analysis to the area of Africa where the predicted probability of An. gambiae and closely related species (An. gambiae complex) is greater than 5%, using predicted Anopheles distribution maps from the Malaria Atlas Project 19 , under the assumption that the observed effects on the EIP are consistent in these species. Spatial human population distribution for 2015 was obtained from WorldPop 20 . Monthly mean temperature and human population data were aggregated with bilinear resampling to match the projection of the Anopheles geographic extent data at a 5x5 km resolution.

R0 projections
Using these data, we calculated R0 and " H for each 5x5 km grid cell for each month. We set a lower bound for human population of N=250 to avoid exponential growth of R0 that occurs at very low population densities (figure S1). For areas with very low transmission, large ratio changes result from small absolute changes so we excluded data from months where the temperature is too high or too low to sustain transmission-i.e. " H < 1-from both the maps and the following summary calculations. For each month, we took the ratio " H /R0 to show the monthly change in transmission potential under a multiple blood feeding scenario (figure S2). To estimate the maximum and minimum change, we selected the highest and lowest ratio observed for each location. To estimate the average impact, we took the mean of the monthly R0 and " H estimates over the year, excluding months where " H < 1, and examined the ratio of the means.

An additional blood meal accelerates P. falciparum development
To determine whether additional blood feeding events have an effect on parasite development, we fed An. gambiae females on a P. falciparum (NF54) culture, and at 3 days post infectious blood meal (pIBM) we provided them with a second, uninfected blood meal. A control group was instead maintained on sugar after the initial infectious feed ( figure 1A). We dissected females 4 days later (7 d pIBM), and analyzed oocyst numbers and size in both groups. While we detected no effects on the prevalence or intensity of infection (figure 1B, prevalence shown in pie charts), we observed a striking increase in oocyst size in females that had been blood fed a second time ( figure 1C, figure 2A, B). Mean oocyst size was 81% larger in doubly fed females (standard least squares (SLS) model: p<0.0001; #BF: p<0.0001, Table S1), suggesting increased growth rates following an additional blood meal. Moreover, these oocysts already showed increased DNA content (figure 2A, B) and release of mature sporozoites at an early time point (10 d pIBM)(figure 2C), by immunofluorescence microscopy. Together these data show that P. falciparum development is accelerated when females blood feed a second time.

Mosquitoes are infectious sooner following an additional blood meal
We next examined the effect of a second blood meal on the appearance of sporozoites, the infectious stage of parasite development, in the salivary glands. Following a similar protocol of a second blood meal at 3 d pIBM, we detected sporozoites as early as 7 d pIBM, and we observed a significant increase in sporozoite prevalence at early time points after infection (8 and 10 d pIBM) when most of the control females have no sporozoites in their glands ( figure 3A). Doublyfed mosquitoes were 15.0-fold and 7.7-fold, respectively, more likely to have sporozoites in their salivary glands at these time points (Fisher's exact test d8:p=0.0026; d10:p<0.0001). Moreover, the intensity of infection was also increased at 10 d pIBM (generalized linear model (GLM): p=0.0290, #BF:p=0.0085, Table S1)(figure 3B). These observations were not due to a change in the prevalence or intensity of oocyst infection, which were both unaffected as described above ( figure 1B). By 14 d pIBM singly and doubly-fed mosquitoes became equally infected ( figure 3A,  B), with sporozoite prevalence near 100% and no difference in infection intensity (GLM: p=0.0258, #BF:p=0.4032, Table S1).
Based on the above prevalence data we constructed EIP curves using logistic regression to describe how the infectious population changes over time, and calculated the EIP50-the median time to infectiousness-for each of our treatment groups. A second blood feeding significantly shortened the EIP50, with mosquitoes becoming infectious 2.25 days earlier than females fed a single time (Z test: p<0.0001), corresponding to a 20.7% reduction ( figure 3C). Given mosquitoes regularly take multiple (>3) blood meals in the field 5 , this result infers that extensive transmission occurs much sooner and is mediated by considerably younger mosquitoes than previously thought, forcing a reevaluation of malaria transmission dynamics.

Modelled estimates of R0 with a single blood meal underestimate transmission
Using these data, we mapped the consequence of a second blood meal on the distribution of R0 across the continent of Africa, considering all locations where An. gambiae and closely related Anopheles vectors are present (as described in the methods). We chose a simple metric of transmission potential-the basic reproductive number R0, calculated as a function of temperature and population as in 17 -to investigate the impact of revised estimates of the EIP on malaria transmission potential. For each 5x5 km grid cell of the map, we calculated both the standard R0 using EIP50 estimates derived from a single blood feed 17 and the adjusted R0 using the proportional reduction in EIP50 observed after two blood feeds in our experiments (20.7%). We then mapped the ratio of the adjusted to standard R0 in each grid cell across Africa for each month of the year when there is active transmission.
The reduction in EIP50 leads to higher mean R0 throughout the year, with an average increase of 12.2% across Africa (figure 4A, center panel). When analyzed as individual months, the greatest increase in R0 ranges from 10.2-56.5%, depending on geographic location (figure 4A, right panel).
Here, the largest proportional increases in R0 are found where estimated transmission is lower, such as Southern Africa. Importantly, there is a minimum 10.2% rise in all mapped locations (figure 4A, left panel). Together, these results imply a significant underestimate of malaria transmission potential across the continent by current models.
To determine how many people are impacted by the change in transmission potential, we plotted how the R0 increase is distributed across the human population considering the minimum, mean, and maximum mapped scenarios. For 21.6% of the population-equivalent to 208 million people-revising the EIP50 increases the average transmission potential by at least 15% ( figure  4B, mean curve). The entire mapped population, over 950 million people, experiences at least a 10.2% increase in R0 during periods of transmission ( figure 4B, minimum curve). Furthermore, a quarter of the population experiences at least a 25% higher R0 during one month of the year (figure 4B, maximum curve).

Effects of an additional blood meal are exacerbated in females with impaired egg development
As mosquito reproduction is a target of genetic and chemical control strategies currently in the pipeline 21-23 , and we had previously shown that the parasite EIP is substantially shorter in all instances where oogenesis is reduced 9 , we went on to determine whether parasite growth could be further boosted after a second blood meal in females with impaired egg development. To this aim, we used genetically modified An. gambiae mutants that are mosaics of zero population growth (Dzpg), a gene required for germline cell maintenance and therefore egg development 24 . After infecting Dzpg or control females with a P. falciparum culture, we provided an additional blood meal to approximately half of each group to compare parasite development in both feeding regimes, as done above. Mean oocyst size was increased in Dzpg females fed either once or twice when compared to controls (SLS model: p<0.0001; #BF: p<0.0001, genotype: p<0.0001, Table S1)(figure 5A), demonstrating that P. falciparum growth can be further boosted by a second blood meal in this background. Moreover, despite lower oocyst numbers (GLM: p<0.0001; genotype: p<0.0001, Table S1)(figure 5B), oocyst prevalence was not affected in Dzpg mutants (figure 5B pie charts). Sporozoite intensity in the salivary glands at an early time point (10 d pIBM) was higher in both feeding regimes (GLM: p<0.0001; #BF: p<0.0001, genotype: p=0.0013, #BF x genotype: p=0.0407, Tables S1 and S2)(figure 5C). Although sporozoite prevalence at 10 d pIBM was only significantly higher in Dzpg females fed once (figure 5C upper pie charts), cumulative prevalence across both single and double blood feedings was significantly increased (Fisher's exact test: p<0.0001) and these mutants were 3.9-fold more likely to be infected than control mosquitoes (odds ratio; 95% CI: 2.3-6.5 fold)(figure 5C lower pie charts). These results suggest that, even in cases where they may support lower oocyst loads, females with impaired egg development would be more effective at transmitting P. falciparum parasites under either blood feeding regime.

Discussion
The parasite EIP is a key parameter in malaria transmission dynamics. Given the relatively short Anopheles lifespan-estimated to be around 2-3 weeks depending on species and environmental conditions 5,6 -parasites with faster sporogonic development are more likely to be transmitted to the next human host 4 . Here, we demonstrate that multiple blood feedings significantly accelerate parasite development within the mosquito, shortening the time required for sporozoites to appear in the salivary glands. These findings are consistent with studies showing that a second blood meal increases sporozoite intensities 15,25,26 , and with the recent observation of larger oocysts in females fed twice reported in An. gambiae infected with P. falciparum 14 . Our study provides a comprehensive assessment of the effects of a second blood meal on parasite developmental rates, conclusively linking additional blood meals to a shortened EIP.
Incorporating these results into a simple model shows that malaria transmission potential, estimated as R0, may be significantly greater than previously appreciated. Indeed, with a scenario of multiple blood feeding resulting in a shorter EIP than with standard estimates, R0 increases by a minimum of 10.2% across Africa, and up to 56.5% in specific locations. These are substantial effects, with hundreds of millions of people potentially impacted by these findings. The neglected contribution of multiple blood feeding may partly explain high malaria burdens in places and seasons when expected transmission potential is low 27 . Further, the most significant changes to modelled R0 are in regions with relatively low transmission including Southern Africa, suggesting that malaria elimination efforts in these settings may be more challenging than anticipated.
Another key implication of a shortened EIP is that previous R0 calculations may have overestimated the relevance of other parameters of malaria transmission, particularly daily mosquito survival. This is relevant for interventions such as LLINs, which impact standard R0 estimates through the assumed reduction of the average lifespan of mosquitoes in a population. Given the importance of survival and EIP for modelling transmission dynamics, improved data on the nature of daily survival (e.g. constant vs age-dependent decrease) in natural mosquito populations is urgently needed.
One limitation of our work is the choice of the basic reproductive number as our metric. Although widely used, this metric considers mean-field dynamics, without accounting for known heterogeneities such as differences in mosquito lifespan, parasite strain competition and spatial variation 28 . While these heterogeneities play an important role in determining the precise level of transmission, we expect them to similarly affect our transmission estimates under both single and multiple blood feeds, as through our ratio calculation their contributions cancel out.
Another caveat is we measured the effects of an additional blood meal only in An. gambiae and we cannot exclude that the magnitude of the change will be different in other Anopheles vectors. Interestingly, however, in a recent study in the arboviral vector Aedes aegypti, a second blood meal shortened the dengue virus EIP 29 , suggesting that exploiting mosquito resources may be a generalized mechanism for pathogens to plastically accelerate their development and improve their odds of transmission.
Considering females blood feed on average every 2-3 days 5 , and thus may have taken >2 meals by the time they become infectious, our model might represent a conservative estimate of the impact of feeding behavior on the EIP. In support of this hypothesis, our data using Dzpg mutants demonstrates that P. falciparum growth rates are not saturated with two blood feeds and that parasites are capable of undergoing even shorter developmental cycles in the mosquito vector. Additional resources provided by the second blood meal might be responsible for the accelerated parasite growth.
What are the implications of these findings for vector control strategies? Firstly, our data point towards females potentially contributing to malaria transmission from a younger age. Given the observed age-dependent mortality induced by insecticides, with higher resistance levels observed in younger mosquitoes 30,31 , this observation implies that insecticide-based interventions (both LLINs and IRS) may be less impactful than predicted by current models. When combined with the observation that multiple blood feeding increases insecticide resistance in older females of a related species, An. arabiensis 32 , our results suggest that mosquitoes feeding multiple times are more likely to survive to the point when they become infectious.
Secondly, results obtained with Dzpg mutants confirm and expand previous findings that-due to a further increase in parasite growth rates-mosquitoes with reduced reproductive capacity have a significantly higher transmission potential, even in the face of possible lower oocyst numbers. These findings are particularly relevant for control strategies that tamper with mosquito reproduction, such as chemical sterilants 23 or genetically-engineered population suppression gene drives 21,22 . At a time when Anopheles gene drive strains are being tested in semi-field settings for their ability to suppress field mosquito populations, our data call for an urgent and careful evaluation of whether these genetically-modified mosquitoes would contribute to more efficient malaria transmission while the drive is spreading.
Finally, our results emphasize that informed policy decisions on current and future malaria control strategies can only be built on thorough research into the fundamental factors affecting malaria transmission biology.      H using revised estimates of EIP50 (derived from two blood feeds). Standard models underestimate R0 by at least 10.2%, with no areas unchanged (minimum, left). In these same regions, the average change over the year using the shortened EIP ranges from a 10.2% to 56.4% increase, with a mean of 12.2% (mean, center). Some regions see much greater changes during at least one month of the year, ranging from 10.2% to 56.5% (maximum, right). (B) Distribution of R0 increases across the affected population (950 million people). For 21.6% of the population living in these areas-equivalent to 208 million people-revising the EIP parameter increases the modelled average transmission potential by 15% or more (area right of pink dotted line, and below mean line). A quarter of the population experiences at least a 25% higher R0 during one month of the year (area right of purple dotted line, and below maximum line). Note the logarithmic y-axis. We set a lower population bound of N=250 (dotted line) to avoid exponential growth in R0 that occurs at very low population densities due to our formula structure. This cutoff reflects the changing shape of this function across different temperature values, demonstrated using temperatures that allow for higher (25˚C), medium (30˚C) and lower (20˚C) transmission. R0 estimates are highest closer to the optimal temperature of 25˚C 17 .