Abstract
Monitoring malaria transmission is a critical component of efforts to achieve targets for elimination and eradication. Two commonly monitored metrics of transmission intensity are parasite prevalence (PR) and the entomological inoculation rate (EIR). Using geostatistical methods, we investigate the relationship between Plasmodium falciparum PR and EIR using data collected over 38 months in a rural area of Malawi. Our results indicate that hotspots identified through the EIR and PR partly overlapped during high transmission seasons but not during low transmission seasons. The estimated relationship showed a one-month delayed effect of EIR on PR such that at low transmission levels increases in EIR are associated with rapid rise in PR, but at high transmission levels, decreases in EIR do not translate into notable reductions in PR. Our study emphasises the need for integrated malaria control strategies that combines vector and human host managements monitored by both entomological and parasitaemia indices.
Introduction
National malaria control programmes, working in collaboration with global stakeholders, have achieved extensive intervention coverage over the last two decades, leading to significant reductions in morbidity and mortality due to malaria (Bhatt et al., 2015b). However, malaria is still a leading global health problem. The previous successes and current challenges have motivated ambitious, yet feasible, global and national targets towards malaria elimination. A key component of efforts to achieve these targets is surveillance and monitoring, which is critical for continued assessment of intervention effectiveness, identification of areas or groups at the highest risk, and guiding the development and implementation of new intervention strategies (World Health Organization, 2015).
A wide range of metrics exists for monitoring malaria parasite transmission. The strengths and limitations of each metric are related, in part, to the step of the parasite transmission cycle it measures (Tusting et al., 2014). These strengths and weaknesses, including the sensitivity of each metric, which vary across epidemiological settings and as parasite transmission declines within a given setting (The malERA Refresh Consultative Panel on Characterising the Reservoir and Measuring Transmission, 2017). Two of the most commonly monitored metrics are the prevalence of Plasmodium parasites and the entomological inoculation rate (EIR), especially in moderate to high transmission settings.
The prevalence of Plasmodium parasites in the human population at a given time point (i.e. the parasite rate; PR) approximates the reservoir of hosts potentially available to transmit the parasite from humans to mosquitoes. Whereas only the gametocyte stage of the parasite contributes to transmission, it remains relatively expensive to detect this stage of the parasite. Whereas rapid diagnostic tests (RDTs) that primarily detect asexual-stage antigens are inexpensive and easily deployed in large-scale community-based surveys (Poti et al., 2020), their limit of detection (50-200 parasites/µl) is higher than that of expert microscopy or PCR (Chiodini, 2014), so that RDT-based estimates of PR are biased by excluding low-density infections. Despite these limitations, RDT-based cross-sectional surveys to measure PR capture both symptomatic and asymptomatic infections, which is important because both are likely to contribute to transmission (Bousema et al., 2014; Slater et al., 2019), and changes in PR over time can indicate changes in transmission.
EIR provides an estimate of the intensity of parasite transmission from mosquitoes to humans, expressed as the number of infectious bites received per person per unit time. EIR is calculated by multiplying the number of malaria vector bites per person per unit time, also known as the human biting rate (HBR), by the proportion of vectors carrying the infectious sporozoite stage of malaria parasites, referred to as the sporozoite rate (SR) (Onori and Grab, 1980). The accuracy and precision of EIR estimates, therefore, depends on the accuracy and precision with which HBR and SR can be measured (Tusting et al., 2014). Two common methods for measuring HBR are the human landing catch and the Centers for Disease Control and Prevention Light Trap, but inter-individual variation in attractiveness to mosquitoes restricts standardisation across sampling points for both of these methods (Knols et al., 1995; Qiu et al., 2006). Alternative methods for estimating HBR include the Suna trap, which uses a synthetic blend of volatiles found on human skin and carbon dioxide to attract host-seeking Anopheles mosquitoes (Mukabana et al., 2012; Menger et al., 2014; Hiscox et al., 2014). The standardised odour blend allows for reliable comparisons among trapping locations (Mburu et al., 2019). Regardless of the method used to estimate HBR, the precision of SR decreases as the number of mosquitoes collected decreases. Despite these limitations, EIR is a vital metric of malaria parasite transmission because it directly describes human exposure to malaria parasites before post-inoculation factors such as immunity, nutrition, and access to health care (Killeen et al., 2000). Moreover, EIR provides information about the relative contributions of different vector species to transmission, which can impact malaria intervention effectiveness based on interspecies differences in biting behaviours related to time and location, non-human blood-meal hosts, larval ecology, and insecticide resistance profiles (Ferguson et al., 2010).
Malaria parasite transmission is heterogeneous in space and time at fine resolution due to several factors, including the availability of larval mosquito habitat, socioeconomics, human behaviour and genetics, and malaria intervention coverage (Carter et al., 2000; Bousema et al., 2012; McCann et al., 2017b). Repeated cross-sectional surveys continousely carried out in communities can reveal this fine-resolution heterogeneity (Roca-Feltrer et al., 2012), providing timely estimates of malaria control progress at the sub-district level and potentially identifying hotspots of malaria parasite transmission for targeted intervention (Kabaghe et al., 2017; Bousema et al., 2016). However, understanding this heterogeneity and identifying hotspots in a way that is meaningful for control programmes remains challenging (Stresman et al., 2019), in part because hotspot location and size can depend on which metric is used (Stresman et al., 2017). Given that PR and EIR are indicative of components of the parasite transmission cycle that are separated by multiple complex steps, each metric provides partial but useful information about the underlying risk of transmission. Therefore, measuring and mapping both metrics can provide a fuller picture of parasite transmission (Cohen et al., 2017).
Additionally, modelling the functional relationship between EIR and PR can provide further insights into the underlying malaria epidemiology. For example, the functional relationship between EIR and PR can then, for monitoring and evaluation purposes, be used to quantify the average reductions in prevalence that may be gained as a result of reductions in EIR, and conversely, the expected increase in prevalence when the number of infectious mosquito bites increases. Previous studies have modelled the functional relationship between EIR and PR using paired estimates of EIR and PR from sites representing a wide range of EIR and PR in Africa (Beier et al., 1999; Smith et al., 2005). These meta-analyses used one estimate each of EIR and PR per site from studies conducted before 2004 and excluded sites with reported malaria control activities, revealing consistently high PR (above 50%) for sites with EIR greater than 15 infectious bites (ib)/person/year and a steep decrease in PR with decreasing EIR when EIR is below 15 ib/person/year. In the current study, we investigate the EIR-PR relationship over a finer time resolution of one month for 38 months, within a single geographical region. The EIR-PR relationship in this context, therefore, takes into account subannual changes in transmission, likely driven by seasonal weather patterns, and other (year-to-year) spatiotemporal variabilities, likely driven by a combination of climatic variation and changes in malaria control activities.
The joint monitoring of EIR and PR in space and time allows us, in this paper, to investigate and find answers to the following questions. (1) How do spatiotemporal patterns of EIR and PR compare? (2) Do EIR and PR lead to the identification of the same malaria hotspots? (3) How do changes in EIR affect PR at different transmission levels? (4) Does EIR have a lagged effect on PR? (5) Does the EIR-PR relationship vary between women of reproductive age and children between 6 and 60 months of age? To answer these questions, we first map P. falciparum entomological inoculation rate (PfEIR) and P. falciparum parasite prevalence (PfPR) at a high spatiotemporal resolution to identify and compare their spatial heterogeneities and temporal patterns. We then consider several statistical models for the relationship between PfEIR and PfPR, which can be distinguished as follows: mechanistic models that are based on different epidemiological assumptions and empirical models where the data inform the PfEIR-PfPR relationship. Finally, we discuss the possible implications of the estimated relationships for monitoring malaria control strategies.
Methods
Study site
This study was part of the Majete Malaria Project (MMP), an integrated malaria control project in Chikwawa District, Malawi. The catchment area of MMP consisted of three distinct geographical regions, referred to as Focal Areas A, B and C (Figure 1), with a total population of about 25,000 people living in 6,600 households in 65 villages.
Chikwawa experiences highly variable rainfall during its single rainy season, which spans November/December to April/May. Temperatures are generally high, with daily maximum temperatures in December averaging 37.6 °C, and in July averaging 27.6 °C (Joshua et al., 2016). During the rainy season, the Shire and Mwanza rivers, which run near the study area, create marshy habitats, paddies, occasional depressions and watering holes, suitable as larval habitats for Anopheles funestus s.s., Anopheles arabiensis and Anopheles gambiae s.s. (Spiers et al., 2002). Dry season larval habitats consist primarily of burrow pits and pools of standing water along seasonal stream beds.
Malaria control in the district is implemented through the Chikwawa District Health Offce. During the study period, interventions applied throughout the study area included the continuous provision of insecticide-treated nets (ITNs) to pregnant women and children under five years old, mass distribution campaigns of ITNs, intermittent preventative therapy for pregnant women, and malaria case diagnosis and treatment with artemisinin-based combination therapy. The only mass distribution of ITNs in the district during the study period occurred in April 2016. As part of the MMP, a randomised trial was conducted to assess the effectiveness of additional, community-implemented malaria interventions between May 2016 and May 2018 (McCann et al., 2017a). The trial interventions were implemented at the village level, with villages assigned to one of four groups: a) no additional interventions; b) larval source management; c) house improvement; and d) both larval source management and house improvement (McCann et al., 2017a; van den Berg et al., 2018).
Data
To quantify PfPR and PfEIR over the course of the study, a rolling malaria indicator survey (rMIS) was conducted in conjunction with mosquito sampling (Roca-Feltrer et al., 2012). In the first two rounds of baseline data collection (April through August 2015), an inhibitory geostatistical sampling design (IGSD) was used to select 300 and 270 households, respectively, for the rMIS from an enumeration database of all households in the catchment area (Chipeta et al., 2017). The IGSD helped to ensure that randomly sampled households are relatively uniformly spaced over the study region by requiring each pair of sampled households to be separated by a distance of at least 0.1km, which increases the effciency of hotspot detection (Kabaghe et al., 2017). In the three subsequent rounds of data collection during the baseline, an adaptive geostatistical sampling design (AGSD) was used to select 270 households per round (Chipeta et al., 2016). With AGSD, new households for the current round of rMIS were chosen from regions with high standard errors of estimated prevalence, based on data from all previous rounds. In the baseline period, previously sampled households were not eligible for sampling in subsequent rounds. For the trial period (starting May 2016), IGSD was again used to select households from the enumeration database of all households. All households were eligible for selection in each round of the trial period regardless of whether they were selected in a previous round. At each round of rMIS data collection in the baseline and trial phases, respectively, 75% and 72% of the households chosen at each round of the rMIS were then randomly selected for mosquito sampling.
In each sampled household, children under five (0.5-5 y/o) and women of reproductive age (15-49 y/o) were tested for P. falciparum using an RDT (SD BIOLINE Malaria Ag P.f. HRP-II, Standard Diagnostics, Yongin-si, Republic of Korea).
Mosquitoes were sampled from 5pm to 7am using Suna traps (Biogents AG, Regensburg, Germany) (Hiscox et al., 2014) with MB5 blend plus co2 to mimic human odour (Mburu et al., 2019). For a selected household in a surveillance round, the trap was set for one night indoors and one night outdoors, with the order of indoor/outdoor determined randomly. For households where the residents were sleeping in more than one building, a trap was set at each building. Trapped female anophelines were preserved using a desiccant and identified using standard morphological and molecular techniques (Gillies and Coetzee, 1987; Koekemoer et al., 2002; Scott et al., 1993). Female anophelines were further tested for the presence of P. falciparum in their head and thorax, after removing the abdomen, using quantitative polymerase chain reaction (qPCR) (Bass et al., 2008; Perandin et al., 2004). Specimens with a Ct value below 37.0 were considered positive for P. falciparum.
Environmental and climatic factors
Environmental and climatic factors affect the abundance and suitability of water bodies that support the development of immature mosquitoes (Madder et al., 1983; Loetti et al., 2011), the duration of mosquito development (Ciota et al., 2014; Loetti et al., 2011; Craig et al., 1999), mosquito host-seeking and biting behaviour, and the development rate of malaria parasites in mosquitoes (Rumisha et al., 2014; Amek et al., 2011).
Using hourly measurements of temperature and relative humidity (RH) from a weather station in each focal area, we computed the average temperature and RH for different ranges of days before the day of data collection (Appendix 1).
Spectral indices, namely normalised difference vegetation index (NDVI) and enhanced vegetation index (EVI), were computed using remotely sensed multi-spectral imagery from the Landsat 8 satellite. These data are freely available from the United States Geological Survey (USGS) Earth Explorer (earthexplorer.usgs.gov) as raster files at a spatial resolution of 30 × 30m for every 16 days. For our analysis, we averaged each spectral index over five years, from April 2013 to April 2018, while omitting scenes that were dominated by cloud artefacts.
We extracted raster data of surface elevation from the global digital elevation model (DEM) generated using measurements from the Advanced Space-borne Thermal Emission and Reflection Radiometer (ASTER) (Tachikawa et al., 2011). These data are freely available for download from the USGS Earth Explorer. Using a flow accumulation map derived from the DEM, a river network map was generated and used to calculate and store as raster images the distance to small rivers and large rivers (henceforth, DSR and DLR, respectively).
Geostatistical Analysis
The number of mosquitoes trapped by Suna traps can be used to estimate HBR, as these traps primarily target host-seeking mosquitoes. Hence, we first estimated HBR and the P. falciparum sporozoite rate (PfSR). We then estimated PfEIR as the product of these two quantities.
We carried out separate analyses for A. arabiensis and A. funestus s.s., using explanatory variables and random effects structures that we found to be suitable for each species. Details of the variable selection process and the final sets of explanatory variables for each of the models later described in this section are given in Appendix 1. The correlation structures adopted for the geostatistical models were informed by the variogram-based algorithm described in (Giorgi et al., 2018). The geostatistical models for the HBR and PfPR data described below were fitted us-ing PrevMap (Giorgi and Diggle, 2016), freely available from the Comprehensive R Archive Network (CRAN, www.r-project.org). The PfSR models were fitted using the glmm package, also available on CRAN.
Human biting rate
Let Y (xi, ti), i = 1, …, M, where M = 2432 is the total number of households, denote counts of mosquitoes trapped at location xi in month ti ∈ {1, …, 38}, where ti = 1 denotes April 2015. We modelled the Y (xi, ti) using Poisson mixed models expressed by the following linear predictor where: d(xi, ti) is a vector of spatiotemporal explanatory variables with associated regression coefficients ; the f (ti; α) is a linear combination of several functions of time, including sines, cosines and splines, with an associated vector of regression parameters α, accounting for trends and seasonal patterns; the Zi are independent and identically distributed Gaussian random variables with variance τ2; S(x) is a zero-mean stationary and isotropic Gaussian process with variance σ2 and exponential correlation function ρ(u) = exp(−u/ϕ), where ϕ regulates the pace at which the spatial correlation decays for increasing distance u between any two locations. We allow the explanatory variables d(xi, ti) and f (ti; α) to differ between different mosquito species since different species may respond differently to environmental changes.
Plasmodium falciparum sporozoite rate
Let Y *(xi, ti) be the number of mosquitoes that tested positive for the presence of P. falciparum sporozoites. We assumed that the Y *(xi, ti) follow a Binomial mixed model with number of trials N*(xi, ti), i.e. the total number of successfully tested mosquitoes, and probability of testing positive PfSR (xi, ti). We model the latter as a logit-linear regression given by where each term in Equation 2 has an analogous interpretation to those of Equation 1.
Estimating the Plasmodium falciparum entomological inoculation rate Let PfEIR f (x, t) and PfEIR a(x, t) denote the PfEIR for A. funestus s.s. and A. arabiensis at a given location x and month t. We estimated each of these two as where l(t) is the number of days in month t. Finally, we estimated the overall PfEIR as We then mapped PfEIR as in Equation 3 over a 30 × 30m regular grid covering the whole of the study area for each month across 38 months.
Plasmodium falciparum prevalence
We mapped PfPR in women and in children by fitting a geostatistical model to each group. More specifically, let I(xi, ti) denote the number of RDT positives out of Nit sampled individuals at location xi in month ti. We then assumed that the I(xi, ti) follow a Binomial mixed model with probability of a positive RDT result p(xi, ti), such that where T (xi) is a stationary and isotropic Gaussian process with exponential correlation function and Ui are Gaussian noise, g(ti, ϱ) is a linear combination of splines, and sine and cosine functions of time accounting for trends and seasonality, and φ and ϱ are vectors of regression parameters to be estimated.
Hotspot detection using PfEIR and PfPR
We mapped the respective predictive probabilities that PfEIR and PfPR exceeded predetermined threshold values. We then demarcated hotspots as areas where these probabilities exceeded 0.9. For PfEIR, we chose the threshold of 0.1 ib/person/month. For PfPR, we chose a threshold of 31% for children and 17% for women to correspond to the PfEIR threshold based on the best of six functional relationships between PfEIR and PfPR as described in the next section.
Modelling the relationship between PfEIR and PfPR
In this section, we describe the statistical methods we used to model the relationship between PfEIR and PfPR. Since PfEIR may have a delayed effect on PfPR, possibly due to the time taken for P. falciparum to develop in the human host, we considered that current PfPR may depend on PfEIR l months prior. In particular, we considered l = 0, 1, 2. We then assumed that the number of RDT positive individuals, I(xi, ti), follow independent Binomial distributions such that where h(·) is a function depending on a vector of parameters θ that governs the relationship between PfPR and PfEIR, and PfÊIR (xi, ti − l) is the estimated PfEIR as in Eq (3). We considered six models, each of which provided a different specification for h(·).
We now describe the six models for h(·). Models 1 to 4 make explicit assumptions on the underlying mechanism of transmission, whereas models 5 and 6 describe the functional relationship between PfEIR and PfPR through regression methods.
Model 1: The susceptible-infected-susceptible (SIS) model
Let b be the probability that an infectious mosquito bite results in an infection, referred to as the transmission effciency. Then, infections at (xi, ti − l) are assessed to occur at a rate of b × PfEIR (xi, ti − l). We assumed that each infection cleared independently over a duration 1/r so that the ratio y = b/r is the time taken to clear infection per infectious bite. We assumed that the relationship between PfEIR and PfPR holds throughout the study region. If PfEIR (x, t − l) is constant, the relationship between PfEIR (x, t − l) and PfPR (x, t) is described by the Ross Model (Ross, 1911) We obtained our first model as the non-zero equilibrium solution of Equation 6, given by
Model 2: The SIS model with different infection/recovery rates (D.I/R)
Model 1 assumes that women and children get infected and recover at the same rate. However, the transmission and recovery rates in children may differ from those in women. We, therefore, modified Model 1 by allowing different values of b and r for each category of people. Let ξ1,it and ξ2,it respectively be the proportion of children and women sampled at (xi, ti) and yk = bk/rk, where k = 1 denotes children and k = 2 denotes women. The resulting Model 2 is
Model 3: The SIS model with superinfection (S.I.)
If individuals are super-infected with P. falciparum, then the rate at which infections clear depends on the infection rate, with clearance being faster when infection rate is low, and slower when infection rate is high. To capture this feature, we modelled infection clearance rate as g(ϑ, r) = ϑ/(eϑ/r −1), where ϑ = b × PfEIR (Smith et al., 2005; Walton, 1947; Dletz et al., 1974; Aron and May, 1982). The resulting model for PfPR (x, t) is
Model 4: The SIS model with S.I and D.I/R
Combining the assumptions of heterogeneous infection/recovery rates, as in Model 2 and superinfection, as in Model 3, we obtain Model 4,
Model 5: The Beier model
Beier et al. (1999) assumed that the log of PfEIR is linearly related to PfPR, and fitted the regression model the so called “log-linear model”.
Model 6: The logit-linear model
The Beier model has the limitation that PfPR approaches −∞ as PfEIR goes to 0 and approaches ∞ as PfEIR goes to oo. To constrain PfPR to lie between 0 and 1, we applied the logit-link function to PfPR to give Model 6, We estimated the parameters of each of the six models by maximising the log-likelihood function To fit each model, we first obtained 10,000 bootstrapped data sets of predicted PfEIR as in Equation 3 at the set of all space-time locations sampled for the rMIS. We did this for two reasons: to obtain PfEIR data at locations (xi, ti) that were sampled for rMIS but not for the entomological surveillance; to account for the uncertainty in PfEIR. By fitting each model to each of the 10,000 datasets, we then obtained 10,000 bootstrapped samples for the vector of parameter estimates of each the six candidate models. we then summarised these samples by their mean and central 95% probability interval. We repeated this process for l = 0, 1, 2.
We compared the fit of the six models based on the AIC values and compared their predictive ability by the bias and root-mean-square error when each model is used to predict prevalence at all the observed space-time locations.
Results
rMIS and mosquito sampling
From April 2015 to May 2018, a total of 6870 traps (3439 indoors; 3431 outdoors) were placed at 2432 houses resulting in the collection of 657 female Anopheles mosquitoes (Table 1). Following PCR of the 478 A. gambiae s.l. collected, 92% were identified as A. arabiensis, 2% as A. gambiae s.s., 1% as A. quadriannulatus, and 5% could not be identified further. From the 179 A. funestus s.l. collected, 95% were identified as A. funestus s.s. by PCR, while the remaining 5% could not be identified further. The observed vector composition is therefore 71%, 27% and 2% for A. arabiensis, A. funestus s.s. and A. gambiae s.s., respectively.
Despite the relatively low abundance of A. funestus s.s. compared to A. arabiensis, the higher sporozoite rate of the former made the contribution of A. funestus s.s. to the total PfEIR almost equivalent to that of A. arabiensis (Table 1). The total PfEIR for the 38 months was 8.24 ib/person, equivalent to an average 2.60 ib/person/year.
Over the same 38-month period, 5685 individual P. falciparum RDT tests were conducted across 3096 household visits. Among the 2401 tests conducted on children aged 6 to 59 months, 25.5% were positive, while 14.3% of the 3284 tests conducted on women were positive.
Spatiotemporal patterns of PfEIR and PfPR
We observed clear spatiotemporal heterogeneities in PfEIR, PfPR in children, and PfPR in women when mapped across the study region at a fine spatial resolution (30 x 30 m) and 1-month intervals. For convenient visualisation of the main features of the spatiotemporal maps, we have developed an interactivity web-based application to show the maps at http://chicas.lancaster-university.uk/projects/malaria_in_malawi/pfpr/. Spatially, there were differences both within and between the three focal areas. Focal Area A generally showed the lowest PfEIR and PfPR, while Focal Areas B and C showed similar, higher levels of PfEIR. Within each focal area, the spatial patterns changed from month to month, with hotspots of both PfEIR and PfPR proceeding through seasonal cycles of expansion and retraction over time. Over the 3-year study period, hotspots of PfEIR and PfPR generally disappeared during the low transmission seasons, except for residual hotspots of PfPR that persisted throughout the study period.
When summarised over the whole study region, each of PfPR and PfEIR exhibited seasonal patterns with a single annual peak. The monthly predicted PfEIRs and PfPRs were similar to the observed values (Figure 2). PfEIR increased from November to a peak in May and decreased to a trough in November. PfPR started increasing from December to a peak around July, after which it decreased to a trough between November/December.
Three observations are clear from both the spatiotemporal maps and the monthly summarised data (Figure 2). First, children aged 6 to 59 months consistently had a higher level of PfPR than women throughout the study period. Second, PfPR in both groups generally decreased from the start of the study in April 2015 to December 2016, after which there was a general trend of increasing PfPR in both age groups. Finally, PfEIR was steady in the first two years of the study, followed by a general decrease after May 2016. Strikingly, the observed PfEIR was 0 between June 2017 and the end of the study, while the PfPR increased in both children and women between November 2017 and May 2018.
The relationship between PfEIR and PfPR
Temporally, the seasonal patterns of PfEIR and PfPR within each year were nearly concurrent, with the estimated peak in PfEIR preceding that of PfPR by one month (Figure 2).
Spatially, PfEIR and PfPR showed broadly similar patterns. When comparing the hotspots of PfEIR and PfPR using spatiotemporal maps of exceedance probabilities, the hotspots of PfEIR and PfPR partly overlapped during the high transmission season (http://chicas.lancaster-university.uk/projects/malaria_in_malawi/pfpr/). However, there were hotspots of PfEIR that were not necessarily hotspots of PfPR and vice versa (Figure 3).
Scatter plots of the logit of PfPR against the log of PfEIR show an approximately direct linear relationship (Figure 4).
For each of the six classes of model, the model with a one-month lagged-effect gave a better fit than the corresponding models with lag zero or two (AIC differences 9). For the models with one-month lagged-effect, the empirical models (i.e. logit-linear and Beier) showed lower AIC values (i.e. better model fit, Additional Table 6 in Additional file 1) than the mechanistic models (i.e. SIS 1-4). The logit-linear model was the overall best model in terms of goodness of fit, as measured by AIC, and in terms of predictive performance, as measured by root-mean-square error and bias (Appendix 1 Table 6).
The fitted logit-linear model (Figure 5) shows that PfPR rises quickly with increasing PfEIR at very low PfEIR, followed by a flattening off or saturation. From the estimated relationship for women and children combined (Figure 5 (a)), a decrease in PfEIR from 1 ib/person/month to a very low PfEIR of 0.001 ib/person/month is associated with a reduction in PfPR from 27.1% to 15.8% on average (i.e., a 42.0% decrease in PfPR). Note that even when transmission, as measured by PfEIR, has been driven close to zero, PfPR remains substantial.
An indication of differences in the PfEIR–PfPR relationship between children and women lies in the logit-linear model fitted to children and women separately (Figure 5(b)). The average tra-jectories of PfPR and corresponding 95% confidence intervals with varying PfEIR are distinct for women and children. PfPR in children tends to show a steeper rise with increasing PfEIR than in women. From the estimated relationship for children, a decrease in PfEIR from 1 ib/person/month to 0.001 ib/person/month is associated with a reduction in PfPR from 37.2% to 20.7% on average (i.e., a 44.5% decrease in PfPR). From the estimated relationship for women, the same decrease in PfEIR is associated with a reduction in PfPR from 19.7% to 12.1% (i.e., a 38.3% decrease in PfPR) on average. We make two observations. (1) With decreasing PfEIR, the percentage reduction in PfPR achieved in children tends to be higher than in women. (2) When transmission has been driven almost to zero, PfPR remains consistently high in children.
Discussion
Using data from 38 months of repeated cross-sectional surveys, we have mapped the fine-scale spatiotemporal dynamics of PfEIR and PfPR in a region of Malawi with moderately intense, seasonally variable malaria parasite transmission. We found evident spatial heterogeneity in both PfEIR and PfPR, with areas of higher PfEIR and PfPR expanding and contracting over time. We also found that hotspots of PfEIR and hotspots of PfPR overlapped at times, but the amount of overlap varied over time. Finally, we showed that month-to-month variations in PfEIR over the study period are strongly associated with changes in PfPR. These findings highlight the dynamic nature of malaria parasite transmission and underscore the value of monitoring both PfEIR and PfPR at fine spatial and temporal resolutions.
Previous studies (Beier et al., 1999; Smith et al., 2005) have demonstrated the relationship between PfEIR and PfPR using paired estimates of these metrics from several sites throughout Africa, characterised by a wide range of transmission intensities (PfEIR <1 to >500 ib/person/year). Estimates of PfEIR in our study were lower (2.6 ib/person/year, on average) so that measuring both metrics in the same geographical region, across different transmission seasons, and with a temporal resolution of one month has demonstrated that fluctuations in PfEIR over short periods are associated with predictable changes in PfPR in the same region. More specifically, our data better supported a one-month delayed effect of PfEIR on PfPR than no delayed effect or a two-month delayed effect. The one-month delayed effect is likely due to the incubation period of the parasite (Ruan et al., 2008) and the duration of infections (Felger et al., 2012). For settings with a similar range of parasite transmission intensity, our results imply that PfPR is sensitive to short-term changes in malaria parasite transmission and, therefore, can be useful for monitoring changes in the intensity of parasite transmission linked to either environmental conditions or the effects of malaria interventions. At the same time, this sensitivity to short-term changes in parasite transmission in low to moderate transmission settings suggests that single, annual, cross-sectional surveys intended to monitor inter-annual variation by aiming for a peak in PfPR are more likely to miss the actual peak than in settings with higher parasite transmission intensity (Kang et al., 2018). Our repeated cross-sectional sampling strategy (rolling MIS) (Roca-Feltrer et al., 2012; Kabaghe et al., 2017) ensured that we were able to capture both short-term changes and longer-term trends in both PfEIR and PfPR. Settings where these considerations are applicable have become increasingly common over the last 20 years (Weiss et al., 2019), largely driven by increasing coverage of ITNs (Bhatt et al., 2015b) and ACTs (Bennett et al., 2017). Comparing 2017 with 2010, 122 million fewer people were living in areas with PfPR ≥ 50% (corresponding to PfEIR >15 ib/person/year), and the number of people living in settings with PfPR between 10–50% (i.e. mesoendemic (Hay et al., 2008)) increased to an estimated 600 million in 2017 (Weiss et al., 2019). In settings with higher PfEIR, PfPR likely remains relatively stable, even as PfEIR fluctuates from month to month with weather patterns (Churcher et al., 2015), and therefore the timing of single cross-sectional surveys is less critical.
Whereas within-village and between-village spatial heterogeneities of malaria parasite transmission are well documented across many sites (Greenwood, 1989; Thompson et al., 1997; Amek et al., 2012; Mwandagalirwa et al., 2017), this is the first study of which we are aware to directly compare the fine-scale spatial patterns of PfEIR and PfPR, and these two related but distinct metrics provided a fuller picture of spatial heterogeneity in malaria parasite transmission than could have been provided by monitoring either metric in isolation. As expected, the hotspots of each metric expanded and retracted over time. However, the hotspots of PfEIR and PfPR only partially overlapped, with the most substantial amount of overlap observed during the high transmission seasons. Given the limitations of all currently available metrics of malaria parasite transmission (Tusting et al., 2014), our findings suggest that monitoring two transmission metrics, aligned with widely separated steps of the transmission cycle, may increase our ability to define transmission hotspots accurately. Furthermore, areas with higher transmission risk according to an entomological metric (e.g. PfEIR) than a measure of the potential transmission reservoir (e.g. PfPR) may indicate a need for increased vector control, whereas areas with lower PfEIR and higher PfPR may indicate a need for increased treatment of malaria cases (Cohen et al., 2017); thus, optimising the impact of control activities with minimum resources by targeting different control activities to different types of hotspots.
We found that a logit-linear model explained the PfEIR-PfPR relationship better than any of the other five model classes examined. Our results are similar to the results of Beier et al. (1999), who assumed that the log of EIR is linearly related to PR, although our model differs from that of Beier et al. (1999) in that we account for spatiotemporal heterogeneities. Our model ranking contrasts with Smith et al. (2005), who favoured an SIS model analogous to our Model 4 that assumes both heterogeneous infection rates and superinfection. However, unlike the model of Smith et al. (2005), we did not assume a model for age-related heterogeneities but accounted for these directly since these data were available. These differences in the overall best model between our work and that of Smith et al. (2005) suggest that model performance relative to other models may be context-dependent and cautions against the use of a single model for the whole of Africa. This also highlights the importance of flexible modelling frameworks that allow accounting for spatiotemporal heterogeneity, as is the case with model-based geostatistics (Diggle and Giorgi, 2019).
As shown in previous studies (Beier et al., 1999; Smith et al., 2005), our logit-linear model indicates that PfPR saturates rather than increasing at a constant rate with increasing PfEIR. This saturation in PfPR may be explained by several factors, which are not mutually exclusive. One set of factors relates to people being heterogeneously exposed to vectors (Guelbéogo et al., 2018) because of differences in attractiveness (Knols et al., 1995; Qiu et al., 2006), behaviour Sherrard-Smith et al. (2019); Finda et al. (2019), access to ITNs (Bhatt et al., 2015a), housing design (Tusting et al., 2015, 2017), or the spatial distribution of vector habitat (McCann et al., 2017b), so that as PfEIR increases, it is more likely that infectious vectors are biting already infected individuals (Smith et al., 2007b, 2010). The second set of factors relates to inter-individual variation in acquired immunity, which in some individuals may prevent vector-inoculated sporozoites from progressing to blood-stage in-fection (John et al., 2005; Offeddu et al., 2017), keep blood-stage infections at densities lower than the level of detection (Doolan et al., 2009) (about 50-200 parasites/µl for RDTs as used in our study), or increase the rate at which blood-stage infections are cleared (Hviid et al., 2015). Regardless of the reason, the saturation of PfPR has practical implications for the selection and interpretation of malaria parasite transmission metrics. When PfEIR is high, initial reductions in PfEIR will likely not be met with an immediate appreciable reduction in PfPR. Additionally, the quick rise in PfPR with increasing PfEIR at lower levels of PfEIR suggests two things, (1) that in elimination settings, a little rise in the rate of infectious bites could result in a rapid increase in parasite prevalence, making elimination extra diffcult if extra efforts are not in place to avoid vector-host contacts in elimination settings; (2) that both metrics will reflect short-term changes in transmission as observed in our study.
The monthly PfEIR in our study region was 0 ib/person/month in multiple months. This may indicate that the number of infectious bites received per person during these months was below the level of detection, rather than an actual interruption of transmission during those months, especially in the first two years of the study when these periods only lasted 2-3 months. Our finding that a monthly PfEIR near or equal to zero is associated with substantial PfPR is, therefore, unsurprising given that previous studies have had similar findings when comparing annual PfEIR to PfPR (Kabiru, 1994; Mbogo et al., 1995; Beier et al., 1999; Smith et al., 2005). On the other hand, we observed an increase in PfPR from about November 2017 to May 2018 while PfEIR remained at zero. It remains unclear whether this rise in PfPR was due to new infectious bites that nevertheless remained below the level of detection or to previously infected individuals with parasite densities that increased to detectable levels (Drakeley et al., 2018). Either way, this result shows that a rise in PfPR may be observed even when PfEIR cannot be detected by current methods, and, therefore, both interventions and monitoring need to continue for some time after PfEIR has not been detected. Our results also highlight the importance of monitoring additional metrics of parasite transmission (in addition to PfEIR) when the annual PfEIR is <10 ib/person/year, especially when expecting a reduction in transmission as in the case of testing malaria interventions. Nonetheless, when PfEIR is above the level of detection, it provides information about the vector species involved in transmission, which is critical because different mosquito species may respond differently to vector control interventions (Ferguson et al., 2010; Wilson et al., 2020).
Prior to our study, the most recent assessment of PfEIR in this district of Malawi was from 2002, with an estimated annual PfEIR of 183 ib/person/year (Mzilahowa et al., 2012). The drastic reduction in annual PfEIR since then to an estimated 2.60 ib/person/year in our study is likely due, at least in part, to an increase in the use of ITNs and ACTs. Nationwide, use of ITNs by children under five years old in Malawi has increased from nil in 2000 and 14.8% in 2004 (Mathanga et al., 2012) to 67.8% in 2014 (Malawi National Malaria Control Programme and ICF International, 2014). Treatment for malaria in Malawi switched from sulfadoxine–pyrimethamine to ACT with artemether–lumefantrine in 2007 (Mathanga et al., 2012), and by 2014, 39.3% of children under five reporting a fever had taken ACT (Malawi National Malaria Control Programme and ICF International, 2014). Nationwide malaria interventions also likely impacted malaria parasite transmission over the course of our study. The most recent mass distribution of ITNs in Malawi prior to our study took place in 2012 (World Health Organization, 2013), with a subsequent mass ITN distribution in April 2016 that included our study site. Additionally, randomly selected villages implemented community-led larval source management, house improvement, or both as part of a randomised trial between May 2016 and May 2018 (McCann et al., 2017a; van den Berg et al., 2018). A separate paper assesses the effects of these interventions on PfEIR and PfPR.
We observed a consistently higher PfPR in children 0.5-5 y/o than in women 15-49 y/o throughout the study region and study period, as expected. The extent of difference in PfPR between children and adults for a given region generally increases with parasite transmission intensity. However, even in mesoendemic settings (PfPR between 10–50%), it is common for PfPR in children to be appreciably higher than in adults (Smith et al., 2007a). This pattern is due to increasing acquired immunity with increased exposure to malaria parasites over time (Baird, 1995), which may decrease transmission effciency and time to clear a P. falciparum infection in adults compared to children (see Appendix 1 Table 6 and Smith et al. (2005)). Moreover, the higher PfPR in children than adults, even at the lowest levels of transmission, suggests that children may play a more significant role in transmission, consistent with other studies (Walldorf et al., 2015; Lin Ouédraogo et al., 2015).
One limitation of our study was the use of RDTs to estimate PfPR. RDTs can show false positives after anti-malarial drug treatment due to persistence of the antigens detected by RDTs (Dalrymple et al., 2018). Also, the limit of detection (usually 50-200 parasites/µl) is higher than that of expert microscopy or PCR (Chiodini, 2014). In modelling the relationship between PfEIR and PfPR, we did not account for the sensitivity and specificity of the RDT used to detect P falciparum infection. If the sensitivity αand specificity β were known, we could account for them by setting PfPR (x, t) as used in our analysis to αPfPR (x, t) + (1 − β)(1 − PfPR (x, t)). Thus, strictly, what we have called PfPR should be interpreted as the probability of testing positive for P. falciparum using RDT. However, the use of RDTs as a diagnostic test for the detection of malaria infection provides PfPR estimates that are comparable to national malaria indicator surveys.
PfPR and PfEIR are causally linked by the malaria parasite transmission cycle, which alternates between the human host and the mosquito vector. A higher rate of infectious bites received per person (i.e. EIR) increases the probability of the person becoming infected when bitten. Similarly, a higher rate of parasite infection in people (i.e. PR) increases the probability of a mosquito becoming infected after any given blood meal. Therefore, future modelling efforts may be improved by considering the EIR-PR relationship as cyclic.
Conclusion
Measuring PfEIR and PfPR using the rolling MIS framework allowed us to assess the fine-scale spatial and temporal distributions of malaria parasite transmission over 38 months in a mesoendemic setting. The relationship between PfEIR and PfPR estimated here shows that at low transmission levels, changes in EIR are associated with rapid changes in PR, while at higher transmission levels, changes in EIR are not associated with appreciable changes in PR. Comparing hotspots of PfEIR and PfPR revealed that each metric could identify potential transmission hotspots that the other fails to capture. Our results emphasise that PfEIR and PfPR are essential, complementary metrics for monitoring short term changes in P. falciparum transmission intensity in mesoendemic settings, which have become increasingly common as many regions reduce transmission and shift from the highest malaria endemicity levels. Our study emphasises the need to couple vector control with identifying and treating infected individuals to drive malaria to elimination levels and to monitor both entomological and parasitaemia indices in malaria surveillance.
Acknowledgments
This study was generously supported by Dioraphte Foundation, The Netherlands. RSM received additional support from an NIH-funded postdoctoral fellowship (T32AI007524). The content is solely the responsibility of the authors and does not necessarily represent the offcial views of the funders. We thank African Parks and The Hunger Project for their significant and practical contributions in facilitating the study. We are grateful to the entire Majete Malaria Project team for their tireless efforts in carrying out the study. The population of the study area is thanked for their cooperation with the study. We also thank: Alex Hiscox for advice on mosquito sampling and study design; Jeroen Spitzen for logistical assistance; and Martin Donnelley, Karl Seydel, and their respective laboratory teams for assistance in molecular identification of malaria parasites and anopheline mosquitoes.
Appendix 1
Procedure for building the HBR, PfSR and PfEIR models
Let Avg(Temp(xi, ti), s1, s2) and Avg(RH(xi, ti), s1, s2) respectively denote the average temperature and relative humidity taken over s1 to s2 days prior to the data collection. Appendix 1 Table 1 shows the s1 and s2 values over which average temperature and relative humidity were computed. A set of these variables were selected as the best predictors each of the outcome variables based on the procedure in the next section.
We selected the best combination of fixed and random effects that best explain HBR, PfSR and PfPR using the following procedure.
We first built a generalized linear model in which temperature and RH are considered together with time trends and sine and cosine functions for seasonality. For Avg(Temp(xi, ti), s1, s2), Avg(RH(xi, ti), s1, s2), the choice of s1 and s2, as illustrated by Appendix 1 Table 1, was based on the deviance profile of the variable involved, i.e. either temperature or RH. Piecewise-linear transformations of temperature and RH were considered based on visual inspection and epidemiological knowledge.
Potential confounding between seasonal sinusoids, temperature and RH were checked. Covariates that did not improve the model fit as judged by the AIC were excluded. Sincosine terms were always considered together as if they were one covariate.
With the current model as a basic model we include other available explanatory variables based on forward selection.
When no more explanatory variables significantly improve the model fit, we fit a generalized linear mixed model with a random effect for each unique space-time location.
We then check for the presence of residual spatial, temporal, and spatio-temporal correlations using the algorithm described in (Giorgi et al., 2018), and then include the random effect terms that improve the model fit.
The selected fixed effects for the HBR, PfSR and PfPR models
We specify the set of fixed effects we selected to be in the final model for the A. arabiensis HBR, A. funestus s.s. HBR, PfSR, and the PfPR models. Detailed description of the terms involved in the fixed effects and the estimates of all the parameters of each model are given in S1 Tables 2 to 5.
A. arabiensis human biting rate
A. funestus s.s. human biting rate
View this table:A. arabiensis sporozoite rate
A. funestus s.s. sporozoite rate
P. faciparum prevalence