Examining the impact of larval source management and insecticide-treated nets using a spatial agent-based model of Anopheles gambiae and a landscape generator tool

In the spatial ABM, movement of female mosquitoes is restricted: they move only when in Blood Meal Seeking or Gravid states (marked in red in Figure 1) to seek for resources. The resource-seeking process is modelled with random, non-directional flights with limited flight ability and perceptual ranges until they can perceive resources at close proximity, at which point, the flight becomes directional. At any point in the resource-seeking process, a mosquito’s neighbourhood is modelled as an eight-directional Moore neighbourhood (in cellular automata, a Moore neighbourhood comprises the eight cells surrounding a central cell on a two-dimensional square grid, or lattice). If the current cell and its neighbourhood do not contain any resource, the mosquito starts a random flight and moves randomly into one of the adjacent eight cells (like [10], the probability of moving into a diagonally-adjacent cell is set as half that of moving into a horizontally- or vertically-adjacent cell). If, on the other hand, it perceives a resource in the neighbourhood, it flies directly to the cell containing the resource.

In the Blood Meal Seeking state, the mosquito looks for human houses, and the search continues until it successfully finds a house. In the Gravid state, the mosquito looks for an aquatic habitat, and once found, lays its eggs. The number of eggs it can lay is governed by the density-dependent oviposition rules (see [18, 19] for details). If all of the eggs are laid, it goes to the Blood Meal Seeking state again, initiating a new gonotrophic cycle. Otherwise, it either remains in the same aquatic habitat or searches for another one to lay the remaining eggs, and this process continues until all the eggs are laid. The movement activities for both states are depicted as logical flowcharts in Figure 2.

The current work is theoretical. The presence of only one vector, An. Gambiae, is assumed. The vector life cycle dynamics is emphasized, and the parasite life cycle and the malaria transmission cycle are not yet included. Mosquitoes senesce, and their probability of death increases with age. The human population is modelled as static, i.e., humans do not move in space. All humans are assumed to be identical. For host-seeking, alternative hosts for blood-feeding (e.g., cattle) are not modelled, and the only blood meal-sources are humans in the houses. Daily temperature, variations in which can affect the model’s output (see [18, 19] for details), is fixed at 25°C for this study. Seasonality and other weather/climate parameters are not included. Each aquatic habitat is set with a carrying capacity (CC) of 1,000 (see [18, 20] for details). Time is modelled with hourly (instead of daily) time-steps, since this approach provides much more flexibility in modelling certain agent behaviours (e.g., host-seeking to start at a particular hour at night). For the grid-based landscapes, the size of each cell is set as 50 m, reflecting the limited perceptual range of An. gambiae[10]. For LSM, all aquatic habitats are treated indifferently, i.e., with no inherent differences in their attractiveness and productivity. For ITNs, the transient effects such as the decay of insecticide effectiveness of the bed nets are ignored. Complete usage (adherence) is assumed, i.e., humans provided with a bed net are always assumed to sleep under it during night. All ITN parameters (coverage, repellence and insecticidal effect) are assumed to be invariant over time, and any possible development of insecticide resistance in the mosquitoes is ignored.

Female adult mosquito abundance is treated as the primary output of the model. The associated CC of each aquatic habitat serves two purposes: 1) it limits the number of eggs a female mosquito may oviposit in an aquatic habitat (thus determining soft limits on larval density of the habitat); and 2) is used to model the Gravid female’s inclination to avoid less suitable (e.g., over-crowded) habitats. Unlike other studies [10, 11], CC is not treated as a hard limit. When no intervention is in action, the mosquito population is governed by the combined carrying capacities of all aquatic habitats, and the density-dependent oviposition mechanism, which limits the potential number of eggs that a female mosquito may preferentially lay in an aquatic habitat, considering both the associated CC and the biomass already present in the habitat (for details, see [18, 19]).

All simulations are started with 20,000 Gravid mosquitoes seeking human blood meals, which are initially placed at randomly selected houses. Each simulation is run 50 times and average results of all 50 runs are reported. Each simulation is run for at least one year. Intervention(s) are applied on day 100 and continued up to the end of the simulation. Thus, it is ensured that a long enough warm-up period has passed to reach a steady state (which, without any intervention, occurs around day 50), and that the results are reported after the simulation reaches equilibrium. Where applicable, percent reduction (PR) values in mosquito abundance are calculated by averaging 30-day abundances (after the population reaches steady state) from two intervals: before and after applying the intervention(s) to the base mosquito population. All simulations are submitted using the Sun Grid Engine (SGE) job scheduler, and run as single-threaded programs, in single-process per core mode in computing clusters with multiple cores.

To explore the impact of LSM in isolation (i.e., without any other intervention) and to replicate the results of GN-LSM, the 40 × 40 grid-based landscapes used in GN-LSM [10] are discretized and digitized. In the digitization process, the original tiny landscapes (from [10]) are enlarged, and gridlines are added to aid in measuring the objects’ coordinates. The coordinates are then measured by inspection. To locate the center of each object (an aquatic habitat or a house), distances (in both x- and y- axes) from the nearest gridlines are used. Whenever multiple objects overlap and appear to be rendered on top of one another, the center coordinates are inferred as best guesses (for example, in the original tiny landscapes (from [10]), if two objects seem to possess the same center coordinates, they are assigned to same or different cells in the digitized landscapes, depending on their distances from the nearest gridlines in the enlarged versions). The landscapes are then generated by using the landscape generator tool VectorLand. Each of the 18 landscapes, depicted in Additional file 5, contains 70 aquatic habitats (blue circles) and three different arrangements of 20 houses (black house icons): diagonal, horizontal and vertical (for details on these landscape patterns, see [10] and Additional file 5). For each arrangement, different LSM scenarios (targeted and non-targeted) are also constructed, as was done by [10]. The three targeted interventions (targeted removal of larval habitats) T1, T2 and T3 refer to the removal of aquatic habitats within 100, 200 and 300 m of surrounding houses, accounting for 4, 17 and 28 of 70 habitats, respectively. C1, C2 and C3 refer to non-targeted, random removal of the same numbers of aquatic habitats as the corresponding targeted interventions. Removal of an aquatic habitat makes it completely inaccessible to Gravid mosquitoes, and no eggs can be laid in it during oviposition. In practice, this is usually done by habitat modification (a category of LSM), which results in permanent change of land and water, and is performed by means that include landscaping, drainage of surface water, land reclamation and filling, coverage of large water storage containers, wells and other potential breeding sites, etc. [25]. Increasing LSM coverage, although affecting the larval population (by killing the biomass in the corresponding aquatic habitats), does not increase the mortality of adult mosquitoes; it just decreases the probability of successfully finding an aquatic habitat (and hence delaying the process) by adult females trying to oviposit. Note that the digitization of these landscapes from GN-LSM [10] (and later from GN-ITN [11]) is conducted primarily for validation, comparison and replication purposes. It is much easier and less time-consuming to generate new landscapes with any desired spatial distribution and parameter combinations using VectorLand (as shown later for applying LSM and ITNs in combination). However, to be able to directly compare the results with GN-LSM, and to adhere to the requirements of a standard replication process, the digitization of the original landscapes is necessary.

To compare the impact of LSM using the above landscapes, a fixed daily mortality rate (DMR) of 0.2 is used for the absorbing boundary in order to match the DMR of the GN-LSM study [10]. However, the original model uses age-dependent DMRs for some states in the life cycle of mosquito agents (age-dependent DMRs for all Adult states and the Larva state, and fixed DMRs of 0.1 for Egg and Pupa states) [18‐20]. Hence, in simulations that use a non-absorbing boundary, age-dependent DMRs are used for all Adult states and the Larva state.

Response of host-seeking mosquitoes to ITNs is modelled as a series of three ITN parameters: coverage C, repellence R and mortality M (note that the term mortality is used to refer to the insecticidal effect of the bed nets, i.e., the mortality concurred by ITNs). When a female mosquito (being in the Blood Meal Seeking state) finds a house, coverage is checked first to ensure whether the house is ITN-covered. If it is covered, repellence comes into action: the mosquito may be repelled by ITN and thus forced to search for another house. If it can avoid repellence, a random host is picked in the house. If the host sleeps under bed net, mortality comes into action: it may be killed due to mortality. If it survives the exposure to an ITN, depending on the ITN coverage scheme (see below), it either picks another random host in the same house or must search for another house. If, on the other hand, the host does not sleep under bed net, feeding is assumed to be always successful.

As stated before, simulating the three different definitions (schemes) of ITN coverage is important because although different studies used different schemes [2, 8, 11, 12, 30], none (including ABMs and mathematical models of malaria) actually compared their relative impacts side-by-side. Without a precise definition of the scheme used in a particular model, the task of replication becomes much harder. Hence, the comparison of results from using the three schemes may guide future modellers to decide and choose from which one to use in their models. These three schemes of ITN coverage differ by the number of persons actually covered by bed nets in a house that is under ITN coverage. Note that the same household-level coverage in different schemes may yield different population-level coverage, as shown in Table 2. These three schemes are depicted as logical flowcharts in Figure 3. Household-level coverage and population-level coverage are defined as:

The distinction between partial and complete schemes becomes apparent when the respective numbers for varying levels of ITN coverage are compared. As shown in Table 2, for any ITN coverage level (column 1), the complete coverage scheme has almost twice the number of bed net users (compare columns 2 and 5) and the population-level coverage (compare columns 4 and 7) than those in the partial coverage scheme.

In household-level partial coverage with single chance for host-seeking, each house with ITN coverage is assigned a single bed net, and two randomly selected persons are protected by the bed net (irrespective of the total number of persons in the house). Once a host-seeking mosquito enters a ITN-covered house, and is not deterred by the repellence, it gets a single chance of obtaining a blood meal by picking a random host in the house. Since at most two persons can sleep under the bed net, the probability of a random host sleeping under the bed net is 2/n, where n is the number of persons in the house. Thus, the probability to obtain a blood meal from a non-protected host in the house is 1 - 2/n. If the host is protected (sleeps under the bed net), the mosquito cannot get a blood meal but still runs the risk of being killed by the ITN mortality (insecticidal effect of the bed nets). If it can survive, it must start searching for another house. Otherwise (i.e., if the host is unprotected), the mosquito gets a blood meal.

The second scheme, household-level partial coverage with multiple chances for host-seeking, works similarly as the first one, except for the fact that a host-seeking mosquito gets n chances in the same house (where n is the number of persons in the house). If it cannot get a blood meal within n chances and still survives the ITN mortality, it must start searching for another house. Note that with this scheme, even though the mosquito gets multiple chances for host-seeking, it also encounters the risk of being exposed to the ITN mortality each time (if the randomly selected host sleeps under bed net). With both these schemes, even when all houses are ITN-covered (i.e., 100% household-level coverage), a portion of the human population may still remain unprotected, and thus, the vector population may not be completely suppressed. With the last scheme, household-level complete coverage, if a house is ITN-covered, all persons in the house are protected by bed nets (and hence the term complete is used). This can simulate, for example, an ITN study over a region where there are enough bed nets to protect every person in a ITN-covered house. In this scheme, when a host-seeking mosquito enters a ITN-covered house and is not deterred by the repellence, it cannot get a blood meal (because all persons are covered), and must search for another house. Thus, it incurs additional delays and risks for the mosquito to be eventually successful in obtaining a blood meal.

To evaluate the impact of ITNs, the settings used in the GN-ITN study [11] are replicated. Using VectorLand, the single 40 × 40 grid-based landscape used in GN-ITN is digitized by the same procedure as described before (to digitize the 18 landscapes from GN-LSM). The landscape, depicted in Additional file 6, contains 90 aquatic habitats (blue circles) that are randomly distributed, and 50 houses (black squares) that are arranged diagonally. To run the simulations, representative sample values are used from the parameter space for the three ITN parameters (coverage, repellence and mortality). The parameter values used are shown in Table 3. Combining these values yields 60 distinct parameter combinations. For each combination, 50 replicated simulations are run for each of the three coverage schemes (see description above and Figure 3), and the average results are reported. A non-absorbing boundary is used for all cases.

The 50 houses in the landscape used in the GN-ITN study [11] accommodate a total human population of 185, with the average of household residents being 3.7 (with standard deviation of 1.2). The same distribution is used to generate the population profiles, ensuring that the total human population is 185, with each house having at least two residents.

To evaluate the impact of applying LSM and ITNs in combination, three 40 × 40 landscapes are created (using VectorLand), with varying densities of houses (blood meal locations), density _houses , where the density refers to the number of houses: Low (20), Medium (70) and High (200). For each density _houses , a corresponding human population density (total human population) is also set: Low (100), Medium (350) and High (1,000). Sample landscapes with the three density _houses levels are shown in Figure 4. Parameter values used to run simulations with these three landscapes are shown in Table 4. For each of the 240 distinct parameter combinations, 50 replicated simulations are run, yielding a total of 12,000 simulations. For all cases, the household-level complete coverage scheme is used for ITNs, and ITN repellence (R) is ignored (i.e., R is set to 0.0). Initially, aquatic habitat density is fixed at 50 per km² (in 40 × 40 landscapes, since each cell represents 50 m × 50 m, the 200 aquatic habitats are scattered across an area of 4,000,000 m², or 4 km²), and later reduced as LSM coverage is increased.

Impact of applying LSM in isolation on mosquito abundance is shown in Figures 5 and 6, using absorbing and non-absorbing boundaries, respectively (the reproduced landscapes used for LSM application are shown in Additional file 5). For brevity, the 150 days results (day 100 - day 249) are shown, with LSM being applied on day 100; the full one-year results are shown in Additional files 7 and 8. To compare the results with GN-LSM [10], the PR values in abundances are calculated, which are shown in Table 5.

Although the two models (i.e., the GN-ABM [10] and the ABM used in this study) differ in several assumptions, in most cases, general agreement in changes in PRs (i.e., an increase or decrease) is observed for the different landscapes, as shown in Figures 5, 6 and Table 5. For all landscape types (Diagonal, Horizontal and Vertical), in the model, the absorbing boundary almost always (in 17 out of 18 scenarios, i.e., 94% cases) yields larger PR than that of the non-absorbing case within the same scenario. While this trend is generally expected due to the additional (but unrealistic) killing effect of the absorbing boundary, this indicates the validity of results obtained from comparing the models using different boundary types.

It is interesting to observe that in Figures 5 and 6, except for scenario T1, abundances in all other scenarios for the Horizontal landscape are greater than those for the Diagonal and Vertical landscapes. This is because the average distance between aquatic habitats and blood meal locations (when both of these resource types are ranked according to distances from one another) for the Horizontal landscape is less than those for the Diagonal and Vertical landscapes. As a result, female mosquitoes need to travel shorter average distances in the Horizontal case in order to find resources, and thus completing their gonotrophic cycles. For scenario T1 (which is obtained by removing four aquatic habitats from the baseline landscapes), however, abundance for the Diagonal landscape is greater than that for the Horizontal landscape. To explore why, the effective shortest distances (ESDs) between each of the four removed aquatic habitats, and to their seven nearest blood meal locations, are measured. ESD measures the shortest distance, in units of number of cells, between the source and the destination cells (recall that each cell in the landscape is 50 m × 50 m; thus, x ESD means x × 50 m), and includes diagonal paths wherever necessary, since mosquitoes are allowed to move diagonally in the ABM. It turns out that ESD _Diagonal = 143 and ESD _Horizontal = 197, i.e., ESD _Diagonal < ESD _Horizontal (see Additional file 5 for the specific landscapes). This suggests that removal of these four aquatic habitats in scenario T1 has less impact for the Diagonal landscape than for the Horizontal landscape - female mosquitoes can find blood meals more easily by travelling less distances in the former (Diagonal) case, resulting greater abundances.

As explained before, different simulation runs (with identical parameter settings) can produce significantly different results due to the stochasticity involved while generating random draws from the probability distributions. The importance of multiple simulation runs, instead of a single run, is depicted in Figure 7, where the maximum, minimum and average abundance values, obtained in each time-step across 50 replicated runs from four sample scenarios, are derived. As evident from Figure 7, the average plot lies within a band (envelope) defined by the maximum and minimum plots. If replication is not done (by performing multiple simulation runs), the results could have potentially taken any trajectory bounded within the band, and thus would have been less reliable. Also, note that the average plot is much smoother than the other two, suggesting much less abrupt changes (caused by the random events). All simulation results reported in this work represent the same replication mechanism of multiple runs.

As stated above, in 94% cases, use of an absorbing boundary yields less abundance than that with a non-absorbing boundary. Also, with an absorbing boundary, even before applying LSM (i.e., before day 100), abundances with all landscapes are too low when compared to those with a non-absorbing boundary (see Additional files 7 and 8 for the full one-year results). Since at the beginning of all simulations, female mosquitoes start their activities from randomly selected houses, a good portion of them aggregate around these clumped houses. In many cases, these clumped houses have comparatively far smaller average distance to their nearest edges in the landscape (see Additional file 5 for the landscapes). As a result, female mosquitoes that start moving around from these houses find an edge much quicker (and thus being killed) than those which start from other houses. Thus, just due to using an absorbing boundary, more mosquitoes die out due to the additional unrealistic killing effect imposed by the absorbing boundary. This suggests the importance of using a non-absorbing boundary in the ABM to avoid the potential bias created by a specific boundary type.

Impact of ITNs in isolation on mosquito abundance is shown in Figures 8 and 9, using household-level partial coverage (with multiple chances for host-seeking) and complete coverage, respectively (the reproduced landscape from GN-ITN [11] used for ITN application is shown in Additional file 6). For brevity, the 100 days results (day 100 - day 199), involving a subset of the parameters (from Table 3) are shown, with ITNs being applied on day 100. The full one-year results for the entire parameter space are shown in Additional files 9, 10 and 11. Figure 10 and Additional file 12 show PR values in abundance obtained by applying ITNs for household-level partial coverage (with multiple chances) and complete coverage for host-seeking.

The two partial coverage schemes with single or multiple chances produce little difference when compared (see Additional files 9 and 10). Searching for a host within the same house for n times does not give much leverage to the mosquito, because each time, if the randomly-picked host is protected by a bed net, the risk of being exposed to the insecticidal effect of ITNs (and thus getting killed) still exists. Since GN-ITN [11] is based on partial coverage, their abundance results are compared with Figure 8 (which shows household-level partial coverage with multiple chances for host-seeking). As coverage C increases, abundance is eventually reduced from 4,000 to ≈ 2,000, as shown in Figure 8. This seems more plausible as opposed to achieving a 100% reduction in abundance as was shown by GN-ITN [11], because with the partial coverage scheme, since only 54% of the human population are protected by bed nets, a portion of the mosquitoes can still find enough blood meals, and hence a complete suppression of the mosquito population cannot be expected.

As shown in Figure 9 and Additional files 11 and 12, with household-level complete coverage scheme, abundance is reduced from 4,000 to ≈ 1,000 when coverage is in the range 60% < C ≤ 80% and repellence R is not too high (see subfigure 1 in Figure 9). As C approaches 100% (i.e., all humans are protected by bed nets), irrespective of repellence, abundance can be completely suppressed, as seen in subfigures 3 and 4 in Figure 9. However, too high repellence (e.g., 0.5% ≤ R ≤ 0.9), though unlikely to be present in commonly used insecticides in real-world scenarios, can have a detrimental effect on vector control (by increasing abundance) with the same levels of coverage and mortality, but the degree of this negative impact is reduced as coverage increases (see subfigure 2 in Figure 9, subfigure 4 in Figure 10, and subfigures 7-8 in Additional file 12). As seen in subfigures 5-7 in Additional file 12, when R ≤ 0.5, around 60% PR can be achieved with coverage and mortality being as low as ≈ 60% and ≈ 30%, respectively. However, when 0.5 < R ≤ 0.9, to achieve the same PR, the coverage needs to be as high as ≈ 85%. Also, R = 0.9 means 90% of the host-seeking mosquitoes are driven away from the house before the ITN mortality can play any role (see the complete coverage flowchart in Figure 3c). This is why mortality seems to have less impact in subfigure 4 than in subfigure 3 in Figure 10.

Interestingly, with the complete coverage scheme, even with no ITN mortality, very high PR (around 80%) can be achieved with high coverage (≈ 90%), irrespective of repellence (see subfigures 3-4 in Figure 10). With 90% coverage, around 90% of the population sleeps under bed nets. Since the ABM assumes complete usage of bed nets, and the An. gambiae mosquitoes are almost exclusively anthropophilic and highly endophagic, no blood meal can be obtained from sources other than humans, or during daytime. Thus, though no mosquitoes are killed due to ITN mortality, they cannot complete their gonotrophic cycles (because ≈ 90% of the host-seeking attempts fail), and eventually, the mosquito population dies out.

To evaluate the impact of applying LSM and ITNs in combination, three 40 × 40 landscapes are used with varying density _houses (see Methods). The results, depicted as PR values in mosquito abundance, are shown in Figure 11 and Additional file 13 (PRs are calculated as described before). Figure 11 depicts selected results that involve a subset of the parameters from Table 4; Additional file 13 depicts results that involve the entire parameter space. In these figures, each subfigure represents a filled contour plot where the isolines are labelled with specific PRs, whose magnitudes are shown in the colourbar on the right. Each row represents a specific mortality (M) value for ITNs (e.g., M = 0.2), as marked on the left. Each column represents a specific density _houses , as marked on the top.

Figure 11 indicates some interesting observations. First, impact of ITN mortality (M) becomes increasingly important as the density _houses increases. Comparing the subfigures column-wise, increasing ITN mortality (M) has less impact on the landscape with Low density _houses than with Medium or High cases. With Low density _houses , number of available human hosts is also low, making the number of host-seeking events much lower than the other two cases. Less host-seeking events in turn mean reduced possibility of a mosquito being in contact with an ITN, and as a result, increasing ITN mortality (M) cannot affect PR values as greatly as it can with the other two cases. In general, as ITN mortality and density _houses increase, more successes with the combined interventions are observed, indicating the importance of at least some ITN mortality being there when ITN is applied.

Increase in ITN mortality (M) also influences the general shape of the PR isolines. With High density _houses (column 3), as M increases, the combined interventions become more effective, as seen by the increases of higher PR values: for PR > 40%, the corresponding area increases from 70.83% (for M = 0.2) to 83.33% (for M = 0.8). This trend is also seen for Low and Medium densities (columns 1 and 2), with the Low density column having the least impact.

Next, considering the impact of each intervention in isolation (i.e., looking exactly at both the x-axis and y-axis PR values with y = 0 and x = 0, respectively) in Figure 11, on a per-row or per-column basis, the rate of changes in PR is similar across all subfigures. For example, with Low density _houses at subfigures 1 and 4 (column 1), looking at the y-axis (i.e., at x = 0, meaning when ITN is ignored, and LSM coverage is gradually increased), the isolines of PR values intersect the y-axes at approximately similar intervals (e.g., PR ₁₀ with LSM coverage ≈ 0.18, PR ₂₀ with LSM coverage ≈ 0.63, etc.). Similar trends are observed for columns 2 and 3, and also across the x-axis (i.e., at y = 0, meaning when LSM is ignored, and ITN coverage is gradually increased). This ensures that without the presence of the other intervention, both LSM and ITNs, with their respective parameters varied, yield significant impact on abundance, and confirms the first notion discussed before (ensuring the individual efficacy of each intervention).

Next, when ITN Mortality (M) is non-zero (i.e., the bed nets are at least partially lethal to mosquitoes), increasing ITN Coverage is more effective in reducing mosquito abundance (i.e., increasing PR) than increasing LSM Coverage, which is observed by the more pronounced increase in PR across the x-axis than up the y-axis. This observation is in agreement with similar results obtained in reducing the basic reproductive number of malaria (R ₀ ) by Yakob and Yan [2]. However, as seen in row 1 of Additional file 13, with non-lethal ITNs (M = 0), the efficacies of both interventions approach more equivalency as the density _houses approaches from Low to High. Also, comparing the subfigures column-wise in Figure 11, integrating both interventions yield more synergistic effect as the density _houses approaches from Low to High. Again, this trend agrees with similar results obtained in reducing R ₀ in [2].

Not surprisingly, the increases in PR values indicate more synergistic patterns when all parameters are in effect (i.e., have non-zero values). For example, looking at subfigures 2, 3, 5 and 6, where the density _houses is Medium to High, and M is in the range 0.2-0.8, increasing coverages of both interventions yield more synergistic benefits, as indicated by the more convexity of the PR isolines in general. In these cases, with sufficient number of host-seeking events, and ITNs in action with some mortality (insecticidal effect), both interventions play more effective roles in reducing abundances, and thus increasing PRs.