In Southeast Asia, and particularly the Greater Mekong Sub-region (GMS), Plasmodium falciparum transmission has decreased substantially over the last two decades (World Health Organization, 2011; World Health Organization, 2010b), setting the stage for pre-elimination scenarios, with all GMS countries committing to ambitious elimination timelines (World Health Organization, 2013a). Alignment of global funding bodies’ goodwill with sound national malaria control programmes is crucial for elimination timelines to be met (World Health Organization, 2013c; Alonso and Tanner, 2013), but spreading artemisinin resistance creates a race against time before malaria becomes untreatable with currently available drugs (World Health Organization, 2010a; World Health Organization, 2013b).

Vector control and early diagnosis followed by effective antimalarial treatment have been the mainstay of malaria control programmes, but modelling based projections indicate these approaches alone are unlikely to achieve P. falciparum malaria elimination before failing drug efficacy becomes an issue. Elimination will require more intensive measures to clear the infectious reservoir in asymptomatic populations, especially in the GMS where existing vector bionomics make vector control particularly challenging. The most abundant vector species in the GMS are exophilic (mainly bite outdoors), do not preferentially bite humans, and can bite quite early in the evening (Sinka et al., 2011), rendering typical vector control measures such as insecticide treated nets (ITNs) and indoor residual spraying (IRS) sub-optimal.

Population wide interventions, including mass drug administration (MDA), are under consideration to clear the infectious reservoir in asymptomatic populations and potentially hasten progress toward elimination (Poirot et al., 2013; World Health Organization, 2015a). The proportion of the target population receiving these interventions (‘coverage’) is believed to determine their success (World Health Organization, 2013c; Slater et al., 2015; Okell, 2015; Stuckey et al., 2016). This success can be considered at two spatial levels: global or local. Whilst malaria elimination campaigns have been carried out successfully in some countries or locally in specific regions (Snow et al., 2013; John et al., 2009; World Health Organization, 2015b), reintroductions of malaria from surrounding endemic areas are a constant threat (Cohen et al., 2012; Galappaththy et al., 2013). The importance of mobile populations as a source of malaria transmission in the GMS has been emphasized in recent years (Pindolia et al., 2012; Prosper et al., 2012; Pindolia et al., 2014; Smith and Whittaker, 2014; Edwards et al., 2015; Guyant et al., 2015). Prompt treatment of new clinical cases through village malaria worker (VMW) or village health worker (VHW) networks has proven to be an effective case management strategy (Maude et al., 2014; Rutta et al., 2012) and would be an essential barrier against malaria reintroduction.

We argue that the way in which mass interventions are deployed is what determines their success likelihood. The most efficient and effective roll-outs are laid on a solid community engagement foundation, thus ensuring subsequent adherence and coverage, while preventing malaria reintroduction from adjacent areas. Here, we model target areas as a collection of discrete villages (unit of intervention) and define coverage as the proportion of individuals receiving the intervention within a village and also as proportion of villages receiving the intervention within an area. Critically, we also simulate the minutia of mass intervention roll outs, with all its relevant deployment logistics, thus assigning coverage a temporal dimension which measures the time it takes for all target villages to receive the intervention.

Conducting enough clinical trials to understand the interaction between all variables at play during a mass drug administration, as well as their individual and combined contribution to the expected outcome, is prohibitive. Hence, we turn to computational modelling to explore the relationships between logistical aspects of MDA implementation and demographic aspects such as human population mobility in diverse epidemiological settings (characterized by prevalence, seasonality patterns and heterogeneity in mosquito densities across space). Our focus in on how the predicted impact of mass intervention strategies on malaria transmission changes when these logistical intricacies are taken into consideration, and its implication for the likelihood of P. falciparum elimination. Our research questions are threefold: 1) what is the relevance of logistical implementation details to the outcome of mass interventions? 2) How fast does target coverage need to be reached for the strategy to be successful? 3) What are the key modulators of malaria elimination likelihood in a short timeframe? To offer strategic guidance to national malaria control programmes we also need to understand how the answers to these questions hinge on key features of malaria transmission in specific areas such as artemisinin resistance levels, population mobility networks, transmission heterogeneity over space, and seasonality patterns.

Model description

We developed a modular simulation platform that is customizable to any malaria transmission setting to provide realistic outcome predictions for local and global level interventions. The modules are the building blocks of an individual based, discrete time, spatially explicit, stochastic model, with explicit mosquito population dynamics and human population movements. We thus have villages with different mosquito densities connected by a human flow network, on which different interventions are deployed at different times (Figure 1). One particular innovation compared to previous published work (Gatton and Cheng, 2010; Okell et al., 2011; Maude et al., 2012; Gerardin et al., 2015; Nikolov et al., 2016) is the inclusion of very detailed logistical processes related to intervention deployment in the field.

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Whilst previously published models are extremely good at representing the biological processes underlying malaria transmission, some even making very realistic assumptions on how coverage increases over time (Nikolov et al., 2016), they fail to explicitly model how these interventions are carried out in the field. In practice, teams of workers visit villages sequentially one by one, usually spending 4–7 days to deploy one MDA round in each village, which is quite different from having an unlimited number of teams slowly treating everyone in the target population until a certain coverage is reached. The number of implementation teams is then an input parameter in our simulation platform and each team behaves as an agent. They remain in each village for a fixed period of time (process = 4 days), assumed to be the time needed to complete one round of MDA per village, and move to the next village according to a gravity model. Given a total number of villages V, and a processing time process, the total number of days taken from start of first MDA round in the first village to end of first MDA round in the final village (D) depends on the number of implementing teams (Teams): D = V*process/Teams.

Initially, we simulated thousands of parameter sets that explore how a wide range of key transmission parameters (e.g. mean initial parasite prevalence, proportion of artemisinin resistant parasites) and logistical constraints – Table 1 – modulate the expected outcome of MDA campaigns. Figure 2 illustrates the sensitivity of the predicted proportional decrease in prevalence over 5 years to each parameter. Clearly, the number of MDA campaigns and the initial mean prevalence across all villages are critical covariates when predicting MDA outcome. The distributions characterizing how malaria risk is distributed over space also seem quite important. Artemisinin resistance spread is very sensitive to those same covariates as well as to the number of intervention teams and the intensity of human population mobility (Figure 2—figure supplements 4 and 5).

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We found that there is an intricate relationship between the optimal timing of MDA campaign start, its implementation logistics, and malaria seasonality patterns. Deploying a higher number of MDA teams will yield a higher likelihood of reaching malaria elimination within 2 years, only when population mobility is high – Figure 3. Using a smaller number of intervention teams is predicted to be advantageous in a population of lower mobility, especially when there is only one annual transmission peak and when the MDA start is delayed to day 60 (instead of the default start at the beginning of the calendar year). In settings with 2 malaria seasons per year, the first transmission peak occurs earlier in the year, making the faster 400 team implementation a better option in general. The only exceptions are very static populations in which two MDA campaigns are deployed. We should note that overall, a slower implementation is preferable, especially for the single peak seasonal profiles (Figure 3—figure supplement 1). For the two peak scenarios, a higher number of teams would be beneficial as prevalence increases from 1%. When addressing how to maximize the chances of reaching elimination within a short time span by implementing an MDA strategy, we found that different transmission heterogeneity distributions (depicted in Figure 1D) incur quite different prospects – Figure 4 (Normal), Figure 4—figure supplement 1 (Log-Normal), and Figure 4—figure supplement 2 (Pareto). The likelihood of reaching elimination is strikingly different when comparing the Pareto distribution (most skewed) with the other two (Normal and Log-Normal distributions), except when an extremely efficient vector control program is carried out for a couple of years. Coupling vector control with an MDA campaign vastly improves the chances for elimination across the low prevalence settings explored here, and the longer vector control can be sustained the more likely elimination becomes. Once again, there seems to be a correlation between population mobility and number of MDA teams, with faster MDA implementations being preferred when the human population is more mobile – Figure 4.

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Finally, we explored the value of targeting the top 10 or 20% of villages (sorted by vectorial capacity) and compared its predicted outcome with a full MDA campaign – Figure 5. We confirm that the log-normal and gaussian distributions explored here produce the same elimination likelihood profiles. For very efficacious vector control strategies, the vectorial capacity in the transmission foci will be greatly reduced, causing a greater drop in mean vectorial capacity across all villages in the more skewed distribution (where most villages have negligible numbers or no mosquitoes), compared to the others. This causes the likelihood of elimination in settings with a Pareto distributed risk of infection to be greater on the long-term under those circumstances. Once again, sustaining the vector control for longer, greatly improves the expected outcome (Figure 5—figure supplement 1.

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A series of key interacting features of the transmission-intervention system emerge when intricate logistics are incorporated in spatial-temporal transmission dynamics. Mapping MDA campaign expected outcomes to a specific malaria endemic setting is a complex multivariate problem. Here, we elucidate the way in which the most critical interactions determine MDA success:

• Operational strategy design. Mass intervention strategies rely on a detailed protocol defining the proportion of villages targeted, the target population in each village reached (usually termed target coverage), and the number of intervention teams deployed (determining the speed with which all villages are covered). Unsurprisingly, the chosen number of MDA campaigns is the most significant intervention outcome determinant (Figure 2). This is intuitive in a scenario where treatment failure due to drug resistance is not a serious issue. Assuming 80% of the target population receives each MDA round, and independent coverage between rounds (meaning the likelihood that someone adheres to round 3 for example is independent of their uptake in rounds 1 and 2), by increasing the number of MDA rounds, we are decreasing the proportion of the population not treated with at least one round of ACT. Even if adherence and compliance are correlated, increasing the number of rounds would assure individuals that received treatment would be less likely to become infectious, or be infectious for long, if infected via untreated individuals. Indeed, additional MDA rounds provide a powerful tool to disrupt any resurgence in transmission following the typical 3 round MDA campaigns. The likelihood of elimination being achieved is substantially higher for 2 campaigns of 3 MDA rounds compared to 1 campaign (Figure 3).

• Transmission heterogeneity, described by different mosquito density distributions over space, and initial mean parasite prevalence in the human population also have a clear impact on the predicted reduction in prevalence with MDA (Figure 2—figure supplements 1 and 2). Of note, MDA strategies on their own are not predicted to achieve elimination unless mean malaria prevalence is at very low levels (under 3%) – Figure 2 and Figure 3—figure supplement 1. Coverage speed, increased with a higher number of intervention teams, is programmatically beneficial only when elimination is achievable (prevalence <3%) and in scenarios where MDA is deployed in well-connected populations (consisting of individuals with high mobility) – Figure 3. Counterintuitively, in all other scenarios, a slower MDA implementation is optimal (Figure 2—figure supplement 3, Figure 3—figure supplement 1). When the number of MDA teams is highest, all villages receive the first round within a couple of weeks, meaning a very large proportion of the population will be under treatment simultaneously. Whilst that translates into the largest possible increase in the likelihood of elimination, any resistant infections will have a large selective advantage at that point, causing resistance to spread (Figure 2—figure supplement 5). Interestingly, this effect is less pronounced in populations with high mobility, due to a dilution effect described below. A slower deployment of MDA campaigns is then generally preferable in low mobility populations (here defined as settings where individuals spend on average less than 25 nights per year somewhere other than their home) due to a slower buildup of resistant infections (Figure 4, Figure 2—figure supplement 5).

• Interestingly, prioritizing the very first villages to receive MDA will have very little effect on the MDA campaign’s success (Figure 3—figure supplement 2). This is solely due to the spatial dispersal of transmission foci. In a setting where transmission foci are scattered over space (as simulated here), not much can be gained by prioritizing high incidence villages to receive MDA fist, since once the intervention teams leave those villages, transmission will be re-seeded from lower incidence neighboring villages or forest areas. In fact, if there is only one seasonal peak and only one MDA campaign is carried out, staring in lower incidence villages is predicted to incur a statistically non-significant benefit. Note that in areas where foci are clustered in a small area, a targeted MDA approach would be preferable over a global MDA, with villages outside the foci area not receiving MDA.

• Transmission topology. This is defined by the magnitude of transmission heterogeneity over space combined with the level of mixture between sub-populations through human movement. As mentioned above, spatial transmission heterogeneity has a dramatic effect on predicted outcomes, with more skewed distributions (suggesting most malaria infections occur in a few villages) presenting a challenge for control (Figure 4—figure supplement 2). We should note that P. falciparum transmission in the Greater Mekong Sub-region (GMS) has been reported to be spatially heterogeneous (Gryseels et al., 2015; Cui et al., 2012; Erhart et al., 2005). However, there is very little evidence as to the relative abundance of the main vector species and no quantification of densities exists at a large enough scale, thus we investigated a spectrum of population mobility patterns which at one extreme consists of a set of isolated transmission foci (thus low population movement), where infections in each village are almost exclusively locally acquired (mosquitoes infecting someone will have had acquired that infection from someone else living in the same village). As population mobility increases, these foci become more and more connected, eventually merging with each other in the upper extreme of the spectrum, onto one large homogeneously mixed population (where mosquitoes infecting a person could have acquired that infection from anyone else).

• In low connectivity populations (consisting of individuals with low mobility), the likelihood of resurgence in villages where MDA achieved local elimination is low, since there are only very sporadic introductions of parasites, typically insufficient to reseed endogenous transmission. In these settings, implementation speed should be sacrificed, and a low number of intervention teams deployed, to minimize resistance spread. In populations with high population movement, speed of implementation becomes more important (Figure 3) due to the propensity for recently eliminated intervention units to be reseeded by its neighbors, leading to local resurgences.

• Seasonality. The optimal timing of MDA campaigns relative to malaria seasonal peaks have been theoretically investigated in Brady et al. (2017). Critically, those models do not incorporate implementation logistics in a detailed manner, either simulating instantaneous MDA deployment in all villages, or having a synchronously increasing global coverage until a target coverage is reached. Here, we have explicit intervention teams that deploy sequential MDAs, one village at a time. This is much closer to reality in the field and creates an added dimension when comparing MDA start with malaria seasonal peaks. A very slow implementation that starts 3 months prior to the peak might only have reached a 50% coverage by the time transmission intensity hits the peak, whereas a very fast MDA deployment might start 1 month prior to the peak and end before it.

• When there is only one transmission peak during the year, a slower MDA implementation seems to be preferable (Figure 3), especially if the start of the MDA is set to start one month prior to the peak in vectorial capacity (not to be mistaken with the season malaria incidence peak which occurs later) instead of starting at the beginning of the year. It seems delaying the start of MDA campaigns improves the likelihood of malaria elimination compared to a start at the beginning of the year when a lower number of MDA teams is used (Figure 3—figure supplement 1). This is mostly due to how sensitive near instantaneous MDA campaigns are to the timing of the seasonal peak. In a single annual peak setting, where the incidence peak is at day 140, a near instantaneous MDA would end (all 3 rounds) 70 (for no delay) or 10 (with delay) days prior to the peak. Given the general cosine function simulated here, it seems a longer implementation lasting the whole duration of the high transmission season is optimal. For the two annual peaks scenario, a fast implementation of MDA (covering the whole of the first annual peak) seems preferable.

• Dilution. We uncovered an interesting trade-off between population mobility, transmission heterogeneity and number of MDA teams that results in unexpectedly high predictions for intervention impact in highly mobile populations. This is due to a diluting effect, rooted in the sharing of parasite pools between high transmission foci and very low transmission villages, which is particularly relevant in the post MDA rebound period. Granted high population mobility, after the parasite pool is greatly reduced through MDA, the few infectious mosquitoes in transmission foci are likely to bite migrants, which upon return to low transmission villages, are unlikely to transmit those infections onwards. Increased mobility decreases the proportion of endogenous infections in each village, which consequently increases the radial impact of local interventions, thus also generally contributing to the dilution of artemisinin resistant emerging infections (Figure 2—figure supplement 5). In a scenario where village A with an extremely low vectorial capacity is very close to a high transmission village B and there is intense population movement between villages, it is likely that infections in people living in village A are almost exclusively acquired when they visit village B. Thus, an MDA in village B will have a positive knock-on effect on the incidence of malaria in village A.

• Drug Resistance. We observe that increased transmission heterogeneity is detrimental to intervention success (Figure 4—figure supplement 2), through a mechanism whereby high transmission foci provide a niche for resistance spread which is promoted by drug pressure incurred through multiple MDA rounds (Figure 4, Figure 2—figure supplement 4). Interestingly, this effect is more pronounced for populations with the lowest mobility for all considered spatial heterogeneity distributions. This is due to the dilution effect mentioned above, causing artemisinin resistant parasites expanding in high transmission foci to be diluted across other villages, given a sufficiently high population movement. If the population is very static, however, resistant parasites can gradually outcompete sensitive ones in transmission foci receiving multiple MDA rounds. Drug resistance is also a key driver of why more heterogeneous topologies are predicted to have a lower MDA impact for low mobility populations (red lines in Figure 2—figure supplement 5). Thus, any concerns regarding the enhancement of artemisinin resistance spread with MDA hinge on the transmission heterogeneity of the setting in which MDA is deployed. This entails serious consequences for the likelihood of malaria elimination with an MDA approach in populations where resistance is already established.

Although the elucidation of these intricate relationships is of great scientific interest, National Malaria Control Programmes (NMCPs) might find this exploration to be devoid of applicability, specifically those concerned with drug resistance issues. We have demonstrated that more MDA rounds translate into higher likelihoods of malaria elimination but also show how resistance is very likely to increase dramatically if elimination is not achieved. To explicitly inform policy decisions of NMCPs aiming to eliminate P. falciparum malaria in a short time frame, we provide insights into integrated strategies that combine vector control interventions with a minimal number of MDA rounds:

• Intervention layering and elimination prospects. While MDA strategies consisting of only 3 rounds of ACT are unlikely to interrupt transmission in all but very low prevalence (<2% all-age true prevalence) settings, the village malaria worker (VMW) network providing operation support to MDA campaigns does provide a great foundation for additional interventions to be more easily deployed. Combining a complete VMW network with 3 rounds of MDA at 80% coverage and imperfect vector control strategies, we predict malaria elimination can be reached, provided the initial parasite prevalence is sufficiently low (under ~2%) – Figure 4. Whilst vector control clearly provides a significant increase in the chances of reaching elimination, it would be unlikely to lead to elimination on its own as seen in Figure 4—figure supplement 3. More than a theoretical possibility, elimination, even when in the presence of artemisinin resistance, has been demonstrated to be possible (Lwin et al., 2015). This bistability phenomenon, first proposed for malaria a decade ago (Aguas et al., 2008) and since revisited (Smith et al., 2013), provides the theoretical foundation for the determination of the minimum intervention effort sustained over a defined period of time, after which all intervention measures can be relaxed and elimination is still reached (provided clinical case management remains effective). We thus explored the prospects for elimination with realistic intervention packages coupling vector control with MDAs using our simulation platform – Figure 5. We find that initial mean prevalence is a key determinant of success likelihood and determines the minimum effect size required from the vector control component, for elimination to be reached. We highlight how logistical constraints combine with human movement patterns to modulate the likelihood of an intervention strategy’s success. Clearly, when population mobility is high, elimination becomes likely even with low vector control effect sizes, if MDA is done near instantaneously (400 intervention teams). A much higher vector control effect size would be required if MDA implementation is significantly slower. Conversely, if the human population is static, a slower MDA implementation would increase the likelihood of elimination for the same vector control effect sizes. This illustrates quite well the value of the missing information in simulation models that convert the highly complex logistics of a global MDA administration into an instantaneous process.

• Targeting interventions. Over the last few years, MDA interventions have moved towards a focal approach, where only a proportion of individuals within a village (Eisele et al., 2015), or a proportion of villages in the target area will receive treatment (METF, 2016), to ease drug resistance spread concerns, and to minimize the number of ACT doses given to uninfected individuals. The purpose is to implement MDAs in high transmission foci only, thus bringing mean prevalence across the whole population down very quickly, and then relying on good clinical case management and vector control interventions to eventually reach elimination. The logistical implementation is also simplified, and its associated costs minimized, since only a fraction of MDAs are performed. We explored the likelihood of reaching malaria elimination within 5 years by implementing a targeted elimination program combining 3 rounds of MDA with different vector control intensities and found that the duration and effect size of the vector control component greatly influences the prospects for elimination. Interestingly, increasing the target size (number of villages receiving the intervention), minimizes the differences across transmission heterogeneities. In fact, the most skewed distribution offers better elimination prospects for higher prevalence settings where intense vector control measures (VC efficacy = 0.9) are put in place. The nature of the distribution provides the basis for this effect. Given that most villages have a negligible vectorial capacity, transmission is sustained by a few high transmission foci. If those are targeted efficiently, you can expect to have a disproportionately higher disruption of transmission compared to settings where the distribution of mosquitoes over space is more homogeneous.

We have refrained from doing a cost-effectiveness analysis, since we do not have enough information on most unit costs, which are currently being assessed in different settings, and are likely to be quite variable across countries in the GMS. Any recommendation and cost-effectiveness analysis would have to be tailored to each specific country/area. We also have not extensively addressed synchronous migration patterns but have included long term and seasonal migration events in the simulation platform. The sensitivity of the model’s predictions to these types of migration is much lower than to the general population’s short-term mobility actions explored to great lengths throughout. This is, in all likelihood, a result of the low proportion of seasonal or long-term migrants in the overall population. In settings where migrants constitute a more considerable (>20%) fraction of the population, the predicted impact might vary. We also considered an uncorrelated uptake of ACT rounds during MDA, meaning there is no relationship between the likelihood of receiving a future ACT round and having received a previous one. This can be an issue in areas where religious and/or cultural beliefs cause individuals to refuse any and all drug treatments, but if that is the case, then it would manifest itself at the time of the prevalence survey, when blood would have to be drawn. In practice, we concede that we may be unable to deploy MDA in whole villages due to these constraints, but in the absence of data we refrain from making any assumptions. For simplicity, we have assumed that asymptomatic and clinical infections are equally infective to mosquitoes throughout. In reality, further empirical studies are greatly needed to better characterise this controversial quantity that bears critical consequences for malaria elimination prospects (Aguas et al., 2018). In Figure 3—figure supplement 3 we demonstrate this critical nature, with malaria elimination becoming more amenable if asymptomatic infections are less infectious. To keep the mosquito population comparable to that in all other simulations shown here, we leverage the biting rate in simulations with lower infectivity of asymptomatic infection to obtain comparable prevalence levels. That means that for a given prevalence value, we took the mosquito density in previous simulations and calibrate the biting rate (proxy for effective number of human/mosquito contacts) needed to obtain the same prevalence at equilibrium when infectivity is lowered. Since the overall infectiousness of asymptomatic infections is decreased, the biting rate will have to increase to reach the same level of prevalence. Therefore, the infection pool will be sustained in a smaller population of mosquitoes which bite humans more frequently to make up for the decrease in human to mosquito infection efficiency. We can then conclude that the true catalyst of malaria elimination is the crash of the infectious population of mosquitoes after MDA, rather than a complete elimination of infections in the human population.

Here, we present a theoretical exploration of the potential impact of MDA strategies in different settings of the GMS, with special emphasis on the sensitivity of the predicted impact to logistical constraints, and transmission or population topologies. The ranges of parameters and distributions explored are meant to represent the current malaria situation in the GMS but need to be adjusted for application to specific areas/countries. In conclusion, we propose that mass drug interventions can be an invaluable tool towards malaria elimination in the right context. The model presented here predicts that an MDA’s success likelihood is bounded by the initial malaria prevalence and we elucidate how those chances can be improved through tailoring of implementation logistics. Although MDA is being revisited by the global community, very little attention has been paid to implementation logistics, and there seems to be no protocol adjustment across settings with completely different seasonality and human mobility patters, thus risking a sub-optimal MDA outcome.

We developed an individual based, discrete time, spatially explicit, stochastic model, with mosquito population dynamics and human population movement. The flow diagram in Figure 1A describes the natural history of malaria infection in the human population. Details of how the dynamics of malaria transmission, human mobility and interventions are simulated are provided in the simulation protocol section below. All model parameters are presented in Table 2 along with their respective references when applicable. The simulated synthetic population mimics the demographics of a set of 1000 villages in SE Asia, with the distribution of villages over space, village sizes and age distribution of people likely not applicable to African settings. They should be generic enough to give a fair representation of rural settings in SE Asia. The parameter exploration presented here provides the limits of plausibility in terms of how people are expected to move, the levels of drug resistance and malaria prevalence, and how spatially heterogeneous transmission is.

Spatial demographics for both mosquitoes and humans are implemented at the village level, that is, humans can only move between villages and transmission within each village follows a pseudo-homogenous process where each mosquito is equally likely to bite a given individual. We assume villages are transmission units that encapsulate the village itself and the surrounding farms/forest areas. Whilst clearly a simplification of reality, we know that mosquitoes can easily cover the distance between village and proximal farms over the course of a single day, and most SE-Asian vector species engage in late afternoon biting (some even having a near flat biting rate throughout the day). Given that people tend to move freely within their village during those hours we can reasonably assume that all humans in one village can potentially be bitten by any one mosquito in that village. Having villages as both the transmission and intervention units is obviously computationally convenient, since all model processes related to transmission and intervention can then be evaluated at the same scale.

Malaria transmission in the Greater Mekong Sub-region (GMS) has been reported to be spatially heterogeneous (Gryseels et al., 2015; Cui et al., 2012; Erhart et al., 2005). However, there is very little evidence as to the relative abundance of the main vector species and no quantification of densities exists at a large enough scale. Given the lack of data to inform the discrepancies in mosquito densities across different villages, we chose to explore three mosquito density distributions (Mn, Ml, and Mp). Two of those distributions represent extreme scenarios: one in which all villages have approximately the same biting rate (Gaussian distribution); another where the vast majority has very low biting rates with a few hotspots (Pareto). The third distribution illustrates a scenario possibly more applicable to most areas in which some villages have a quite high transmission intensity, but where most have low mosquito abundance. These distributions were chosen arbitrarily and are parameterised as follows:

We take these distributions of mosquito density across villages as reference ($M(t=0)$) and impose some seasonal variation to reflect the observed malaria incidence seasonal patterns. Mosquito density at time t in village j, for all mosquito density distributions is then given by:

where amp reflects the amplitude of the seasonal fluctuation.

Transmission in a given simulation is characterised by a single extra parameter, the mosquito biting rate, which determines the vectorial capacity and is adjusted to reach a specific baseline malaria prevalence in the human population. The mosquito biting rate calibration was performed for each combination of transmission heterogeneity distribution, population mobility intensity and malaria mean prevalence. Thus, for each population mobility and mosquito density distribution, hundreds of model runs were performed until the desired mean malaria prevalence was reached with a specific mosquito biting rate within the first 5 years of simulation.

Population movement patterns and their importance for infectious disease transmission and emergence has recently garnered a lot of increased scientific interest, with new tools and analysis frameworks being developed for mobility inference (Tatem et al., 2014; Tatem et al., 2009). Whilst census data and mobile phone data can help in proposing a connectivity network for a given region, the lack of general precision in questionnaires and the relative difficulty in capturing a lot of outside home overnight stays in mobile phone records, begs for a new source of data to resolve transmission relevant mobility patterns. Spatially explicit malaria models have in so far used gravity models to describe population movement, which is supported by some data (notably, daytime travel data). Whilst we agree that a gravity model can be the most appropriate to describe some seasonal and long-term migration patterns, we argue that overnight stays a very short distance from your home are generally unlikely. It is more likely for someone to return home for the night if they are within a certain critical distance threshold (crit) in km, instead of staying overnight somewhere else. We thus consider that daily population flow (FL_short) between villages i and j is best characterised by a modified gravity model given by:

where FL_ij refers to the daily population flow of a standard gravity model

where pop refers to village population size, and dist to the Euclidean distance (in km) between villages i and j.

The frequency of general population’s short-term movements (very small number of nights spent somewhere other than their own village at a time) is given by the overall population mobility parameter – mobility – which is explored at length in the main text and assumes 2 extreme values (5 and 250 nights spent somewhere other than the home village, per year). The population is further partitioned into temporary (seasonal) or long-term migrant groups. Seasonal migration can only occur during a 3 month period. This roughly corresponds to the duration of crop seasons, at which time people typically go back to their village of origin to help their families harvest crops or for other economic/personal reasons. After 3 months they return to larger villages or surrounding cities following FL_ij. Long-term migrants only move between a priori defined (at random) economic hubs, comprising 2% of the target villages, spending an average of 6 months in each before moving to the next. For simplicity, we only explore the effects of short-term movements throughout this paper, excluding seasonal and long-term migration events from the simulations presented here. We should note that the sensitivity of the model’s predictions to seasonal and long-term migration is much lower than to the general population short-term movements explored to great lengths throughout this paper. We simulate malaria elimination strategies composed of MDA, a village malaria worker (VMW) network for improved case management, and an annual bed net distribution program. Villages are given an MDA of one full course (3 monthly rounds) of artemisinin combination therapy (ACT) plus one dose of primaquine, irrespective of their illness or infection status. Logistically, intervention teams sweep through all villages and give out ACTs without any prior screening, staying for a given number of days and then moving on to the next village. The details of how implementation logistics were incorporated into the simulation protocol can be found in the Simulation Protocol below.

When exploring the factors driving MDA outcome prediction, we explored all possible combinations of parameter values presented in Table 1, comprising 3888 sets of parameters. The model was run 100 times for each parameter set.

We also explored the layering of further intervention efforts on top of a global MDA initiative (with 3 ACT rounds), such as the implementation of indoor residual spraying (IRS) or larvicidal deployment, for example. Vector control effect size can be modelled as a reduction in vectorial capacity or EIR, as a direct consequence of a decrease in life expectancy, increase in sporogony cycle length and/or decreased biting rate on humans. Depending on what vector control measure one considers and how the mosquito life cycle is modelled, there might be interest in detailing the impact of a vector control intervention on a particular aspect of the mosquito life cycle. That is beyond the scope of what is intended in this paper, and we present vector control effect size as a measure of how much vectorial capacity is decreased when vector control interventions are in place. Thus, a transmission reduction efficacy of 0.10 means that the implemented vector control strategy reduces the number of infectious bites per person per year by 10%. Whilst MDA is programmatically well defined, with a specific number of ACT rounds being deployed, it is less clear how vector control strategies are sustained over time. Thus, we ran simulations for a range of vector control efficacy/duration of intervention pairs and evaluated the proportion of simulations in which elimination is reached.

The study presented here is purely theoretical and no data has been used apart from previously (and publicly) available data.

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Author details

1. Bo Gao

   Centre for Tropical Medicine and Global Health, Nuffield Department of Medicine, University of Oxford, Oxford, United Kingdom

   Contribution

   Software, Formal analysis, Methodology

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-7405-7507

2. Sompob Saralamba

   Mahidol-Oxford Tropical Medicine Research Unit, Faculty of Tropical Medicine, Mahidol University, Bangkok, Thailand

   Contribution

   Software, Methodology

   Competing interests

   No competing interests declared

3. Yoel Lubell

   1. Centre for Tropical Medicine and Global Health, Nuffield Department of Medicine, University of Oxford, Oxford, United Kingdom
   2. Mahidol-Oxford Tropical Medicine Research Unit, Faculty of Tropical Medicine, Mahidol University, Bangkok, Thailand

   Contribution

   Conceptualization, Writing - review and editing

   Competing interests

   No competing interests declared

4. Lisa J White

   1. Centre for Tropical Medicine and Global Health, Nuffield Department of Medicine, University of Oxford, Oxford, United Kingdom
   2. Mahidol-Oxford Tropical Medicine Research Unit, Faculty of Tropical Medicine, Mahidol University, Bangkok, Thailand

   Contribution

   Conceptualization, Supervision

   Competing interests

   No competing interests declared

5. Arjen M Dondorp

   1. Centre for Tropical Medicine and Global Health, Nuffield Department of Medicine, University of Oxford, Oxford, United Kingdom
   2. Mahidol-Oxford Tropical Medicine Research Unit, Faculty of Tropical Medicine, Mahidol University, Bangkok, Thailand

   Contribution

   Conceptualization, Supervision

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-5190-2395

6. Ricardo Aguas

   1. Centre for Tropical Medicine and Global Health, Nuffield Department of Medicine, University of Oxford, Oxford, United Kingdom
   2. Mahidol-Oxford Tropical Medicine Research Unit, Faculty of Tropical Medicine, Mahidol University, Bangkok, Thailand

   Contribution

   Conceptualization, Software, Formal analysis, Methodology

   For correspondence

   ricardo@tropmedres.ac

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-6507-6597

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