Malaria transmission model

We used an established model of malaria transmission to predict the impact of combining SMC with seasonal deployment of a novel therapeutic. This individual-based model, called OpenMalaria (https://github.com/SwissTPH/openmalaria/wiki), has been fully described previously [21]. OpenMalaria combines multiple, smaller models that each represent a component in the malaria transmission lifecycle. Model components simulate the dynamics of mosquito populations, malaria parasitaemia in the course of an infection, onward transmission, and the processes leading to clinical illness, severe disease, and death (Table A in S1 Text). This model has been validated to historical data on a range of epidemiological outcomes, including patterns of age-specific prevalence and incidence, and age-specific rates for malaria mortality and hospitalisation [21].

Importantly for this study, OpenMalaria includes detailed within-host models that represent parasite dynamics across multiple stages of the Plasmodium falciparum life cycle. The model simulates the probability of liver stage infection following an infectious mosquito bite, the resulting blood stage parasite density, and the probability of onward transmission. Therapeutics can target each of these stages independently. As a result, synergistic effects of combining interventions on population-level outcomes, such as those observed in the clinical trial of RTS,S/AS01 and SMC [7–9], can arise from the underlying model mechanisms, rather than being imposed at an individual level through assumed interaction terms or fixed efficacy profiles. This allows interactions between therapeutics, including vaccines and drugs, to emerge at the population level as a consequence of their combined effects on parasite development and host immunity.

Finally, OpenMalaria’s model components capture the dynamics of acquired immunity to the asexual blood stages of Plasmodium falciparum infection. Acquired immunity is represented as a function of an individual’s cumulative density of asexual parasitaemia since birth, including maternal immunity, and their total number of prior infections. Infection densities are drawn from parasitaemia records of malaria-naive patients infected with Plasmodium falciparum for treatment of neurosyphilis [22–24]. The number of prior infections influences pre-erythrocytic immunity, and both prior infections and cumulative asexual parasitaemia influence blood stage immunity. Immunity acts by reducing an infected host’s parasite densities and affecting the probability that parasitaemia will reach the specific parasite densities, or pyrogenic thresholds, that trigger symptoms of uncomplicated and severe malaria [23,24].

Intervention dynamics and deployment

To model SMC with SP-AQ, we represented the drug combination with both preventative and curative effects. SP-AQ was assumed to prevent new infections by blocking liver-stage parasite emergence and to cure existing infections by clearing blood and liver-stage parasites at the time of administration. These assumptions followed our review of the mechanisms of action of SP-AQ for malaria prevention [25]. Efficacy decay for the preventative action was calculated with a Weibull function:, where E(0) was the initial probability of preventing infection at the time of administration, L the scale parameter was the number of days until this probability reached half of its initial value, and k the shape parameter influenced the rate of efficacy decay.

To model novel malaria prevention therapeutics, we simulated a range of malaria vaccine, monoclonal antibody, and long-acting injectable drug candidates by combining modelling their activity against different stages of the Plasmodium falciparum parasite life cycle. Pre-liver stage therapeutics were assumed to reduce the probability of infection following exposure, while blood stage therapeutics killed circulating parasites. Multi-stage therapeutics were modelled by combining both components. As for SP-AQ, the efficacy of each component was represented with a Weibull function of time following administration. These model parameters are illustrated in Fig A in S1 Text.

For each therapeutic (SP-AQ, pre-liver stage, blood stage, and multi-stage profiles), Table 1 outlines the modelled range of parameters used. For SMC, model parameter values were previously calibrated to data from a randomised non-inferiority trial of SMC with SP-AQ [26,27]. For novel therapeutics, we sampled 500 sets of parameter values using Latin hypercube sampling with a uniform probability distribution. Parameter ranges were chosen to represent the broadest possible range of therapeutic profiles, from a highly efficacious, long-acting vaccine (initial efficacy 100%, protection half-life 500 days, exponential decay shape of one) to a low-efficacy, short-acting drug (30% initial efficacy, 30 day protection half-life, rapid decay shape of nine). By simulating outcomes for this broad parameter space of protective properties, we were able to explore the impact of combining SMC with a full spectrum of possible therapeutics. This space aimed to encompass the properties of future novel vaccines, monoclonal antibodies, and long-acting injectable drugs.

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Table 1. Model assumptions for dynamics of therapeutic efficacy and decay.

https://doi.org/10.1371/journal.pcbi.1014021.t001

We then used our individual-based model of malaria transmission to simulate the deployment of SMC with SP-AQ, both alone and in combination with novel malaria prevention therapeutics. The novel therapeutic (pre-liver stage, blood stage, multi-stage) was deployed together with the distribution of SP-AQ in the first cycle of SMC, representing a scenario where a child receives a vaccine, monoclonal antibody or long-acting injectable in combination with receipt of SP-AQ. All interventions were deployed to children aged between three and 59 months of age. Importantly, as described above, we did not make any assumptions about drug-drug or vaccine-vaccine interactions, synergies or antagonisms between the two components of multi-stage therapeutics; any synergistic effects on clinical outcomes at population-level emerged from the underlying within-host intervention dynamics of OpenMalaria.

Intervention model validation

In a previous study, we validated our model’s ability to accurately represent the effectiveness of SMC in combination with a pre-liver stage vaccine [28]. We used OpenMalaria to replicate outcomes from the only available clinical trial evaluating this combination: the individually randomised trial of RTS,S with or without SMC conducted in Mali and Burkina Faso [7,8]. Using data from the first two years of the trial, we calibrated vaccine booster efficacy and the therapeutic properties of SP-AQ to match observed clinical incidence in all three trial arms: SMC alone, RTS,S alone, and the combination. This was done with a Bayesian optimisation framework within OpenMalaria, taking initial efficacy estimates for RTS,S after the three-dose primary series (91.1%) and a half-life of 7.3 months from previous modelling studies and clinical trial data [29]. These values were used as inputs, and boosting efficacies were estimated by optimising model predictions against trial data.

In this previous study, OpenMalaria successfully reproduced monthly clinical incidence and hazard ratios for all arms of the trial in both countries. For RTS,S booster doses, the model estimated that a 12-month post-primary booster restored efficacy to 78.96% (95% CI 70.74 – 87.18%) in the vaccine-only arm and 77.45% (95% CI 68.26 – 86.62%) in the combination arm. A second booster restored maximum efficacy to 57.31% (95% CI 44.05 – 70.56%) and 48.76% (95% CI 34.57 – 62.95%), in the vaccine only and combination arms respectively. These values matched closely with observed outcomes, and our model captured both temporal trends and relative effectiveness across trial arms.

Outcome measures

Our primary outcome measures captured reductions in the cumulative incidence of uncomplicated and severe malaria throughout childhood. We followed children born in the first year of intervention delivery and evaluated cumulative incidence at five (as the intervention ends) and ten years old (five years after interventions have ended). As illustrated in Fig 1, we then calculated the reductions in the cumulative incidence of uncomplicated and severe malaria attributed to the combination of SMC with SP-AQ and the novel therapeutic. Reductions were evaluated relative to two counterfactual scenarios: regular deployment of SMC alone, and seasonal deployment of a novel therapeutic alone (Section 1 in S1 Text). We report these reductions as the percentage of burden averted by the combination relative to a standard of care; we do not compare to a no-intervention scenario.

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Fig 1. Illustration of seasonality profiles, intervention timing, and primary outcome measures.

Panel A illustrates the two seasonal profiles modelled, where 70% of malaria cases occur within a four- or six-month period and where the y-axis represents the average annual entomological inoculation rate (EIR). Panel B illustrates interventions deployed according to four seasonal deployment scenarios. Scenario 1. Perfect deployment: All children aged between three and 59 months had perfect compliance to five yearly SMC cycles. Scenario 2. Imperfect seasonal coverage: All children aged three to 59 months had perfect compliance to four yearly SMC cycles but missed the final cycle. Scenario 3. Imperfect deployment: All children aged three to 59 months had perfect compliance to yearly SMC cycles one, three, and five. Scenario 4. Random allocation: 30% to 100% of children were randomly selected to receive each of five yearly SMC cycles. Panel C illustrates the evaluation of our primary outcome measures. We tracked a cohort of children born in the first year of intervention deployment, and evaluated cumulative incidence when children were five and ten years old. We then calculated the reductions in the cumulative incidence of uncomplicated and severe malaria attributed to the combination of SMC and the novel therapeutic. Reductions were evaluated relative to two counterfactual scenarios: regular deployment of SMC alone, and seasonal deployment of a novel therapeutic alone. Shaded regions indicate the minimum and maximum cumulative cases per person observed across ten stochastic replicates of simulations from the individual-based malaria transmission model.

https://doi.org/10.1371/journal.pcbi.1014021.g001

Simulation and model scenarios

The malaria transmission model was used to simulate cumulative case outcomes for a range of transmission and health system scenarios. Each model scenario captured a unique combination of the following characteristics: a low (10%) or high (50%) probability of seeking first-line treatment for clinical malaria over 14 days post-infection; 70% of malaria cases occurring within a four- or six-month transmission season (Fig 1); six levels of transmission intensity ranging from low-moderate to very high baseline annual prevalence. Annual prevalence was measured as the prevalence rate of Plasmodium falciparum infections detectable by rapid diagnostic test in children aged two to ten years old (PfPR_2–10) when no intervention was deployed. Since PfPR_2–10 is calculated from simulated outcomes, it varies with both model scenario and stochasticity.

We also modelled four different deployment scenarios for SMC, as illustrated in Fig 1. In the perfect deployment scenario, all children aged between three and 59 months had perfect compliance to five yearly SMC cycles. This scenario represented an ideal clinical trial where every child is perfectly adherent to the SP-AQ chemoprevention regimen. In the imperfect seasonal coverage scenario, all children aged three to 59 months had perfect compliance to four yearly SMC cycles but missed the final cycle. This scenario represented a setting where the number of SMC cycles may not provide protection for the full transmission season. In the imperfect deployment scenario, all children aged three to 59 months had perfect compliance to yearly SMC cycles one, three, and five. This scenario represented a setting where children systematically miss out on multiple SMC cycles. In the random allocation scenario, 30% to 100% of children were randomly selected to receive each of five yearly SMC cycles. This scenario represented a setting where children randomly miss out on one or more SMC cycles. In all four deployment scenarios, the novel prevention intervention was co-deployed seasonally together with the first cycle of SMC. By varying deployment, we were able to quantify differences in the novel intervention’s benefit when children are more or less covered by SMC.

Statistical analysis

We followed an existing mathematical framework for defining essential therapeutic characteristics for malaria prevention interventions [30]. This framework has previously been used to explore determinants of malaria intervention impact for long-acting injectable drugs [26] and for novel seasonal malaria chemoprevention therapeutics [31].

In brief, following our methodology (Section 1 and Fig B in S1 Text), we first generated a Latin hypercube sample of 500 values for the novel intervention’s parameters: therapeutic initial efficacy, protection half-life, and decay shape. For each sample, we used our individual-based malaria transmission model to simulate outcomes with ten stochastic replicates. Heteroskedastic Gaussian process regression models [32] were then fitted to predict primary outcome measures (reductions in cumulative uncomplicated and severe cases at five and ten years old) as a function of intervention inputs (initial efficacy, protection half-life, and decay shape). These models were used to emulate the relationship between therapeutic properties and our primary outcome measures without additional simulation from the individual-based model, which would have required intensive computation. Emulator performance was evaluated against a 10% hold-out set. Finally, for each model scenario, we quantified the impact of a small change in each key therapeutic property on variation in our primary outcome measures by performing a non-parametric sensitivity analysis using the Sobol-Jansen method [33,34]. Sobol total-order indices were computed for two Latin hypercube samples of 50 000 intervention parameters. All analyses were conducted in R [35].

Combining SMC with seasonal deployment of a pre-liver stage therapeutic

We first simulated cumulative case outcomes among children for exemplar malaria therapeutic profiles: one pre-liver stage therapeutic with long duration and high efficacy (protection half-life 354 days, 90% initial efficacy) and a second with shorter duration and partial efficacy (protection half-life 120 days, 50% initial efficacy). This allowed us to explore the therapeutic properties needed for a pre-liver stage therapeutic to add benefit to SMC with SP-AQ. Fig 2 depicts the cumulative incidence curves predicted by our model for two hypothetical pre-liver stage therapeutics. First, we saw that both therapeutics contributed to reductions in cumulative uncomplicated and severe cases by the time children were five years old (reductions >10%). This result confirmed the positive effects observed in the randomised control trial of seasonal vaccination with RTS,S in combination with SMC, [8,9] and the R21 phase three clinical trial. [10]

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Fig 2. Predicted cumulative case curves when seasonal deployment of two exemplar pre-liver stage therapeutics are combined with SMC.

The median number of cumulative cases per year of age were calculated when children aged three to 59 months received one of the following interventions: no intervention, three SMC cycles (imperfect deployment scenario), seasonal deployment of a pre-liver stage therapeutic, or the combination of three SMC cycles and the pre-liver stage therapeutic. Top panels include deployment of a pre-liver stage therapeutic with a protection half-life of 354 days, 90% initial efficacy, and decay shape parameter of 1. Bottom panels include a pre-liver stage therapeutic with a protection half-life of 120 days, 50% initial efficacy, and decay shape parameter of 1. The pink shaded regions indicate age-eligibility for SMC and the novel therapeutic. Shaded regions indicate the minimum and maximum cumulative cases per person observed across stochastic replicates of simulations from the individual-based malaria transmission model. Model results are shown for a scenario with transmission intensity corresponding to 32% PfPR_2-10, where 75% of malaria cases occur within six months of the year and the probability of seeking first-line treatment for clinical malaria over 14 days is low (10%).

https://doi.org/10.1371/journal.pcbi.1014021.g002

However, we saw that pre-liver stage therapeutics needed to have a long duration and high efficacy to maintain their benefits in comparison to SMC as children aged. The exemplar therapeutic with shorter duration and partial efficacy (Fig 2) led to no observable difference in cumulative uncomplicated cases by the time children were eight years old. Furthermore, we observed that the combination of SMC with SP-AQ and the pre-liver stage therapeutic was more beneficial than the pre-liver stage therapeutic alone throughout childhood. Similar patterns were observed for other SMC deployment scenarios (Fig C, D in S1 Text) and across the full range of pre-liver stage therapeutic properties (Fig E in S1 Text). Together, these findings indicate that pre-liver stage therapeutics may need a long duration to limit the potential for delayed malaria when added to SMC and may not fully replace SMC’s benefits.

In addition to a long duration, we found that pre-liver stage therapeutics needed a long tail of protection to maintain reductions in cumulative burden as children aged. Higher reductions in cumulative cases by ten years of age were observed for pre-liver stage therapeutics with a long tail of protection, encompassing exponential and biphasic decay profiles (decay shape <1, Fig 3), in comparison to sigmoidal decay (decay shape >1). For example, in Fig 3, deploying a pre-liver stage therapeutic with a decay shape parameter between 0.6 and 0.8 was associated with a 9.9% median reduction (interquartile range 5.5-16.0% across the parameter range for protection half-life and initial efficacy) in cumulative uncomplicated cases by the time children were ten years old, evaluated relative to SMC alone. In contrast, deploying a therapeutic with a decay shape between 4.0 and 4.2 led to a lower median reduction of 5.3% (interquartile range 1.8-10.0%). Similar findings were observed across deployment scenarios (Fig F, G, H in S1 Text).

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Fig 3. Gaussian Process regression emulator predictions for the relationship between pre-liver stage therapeutic properties and reductions in cumulative uncomplicated and severe cases relative to SMC alone.

Results show the imperfect deployment scenario, where children aged three to 59 months received three SMC cycles. Transmission is high (32% PfPR_2-10), 75% of malaria cases occur within six months of the year, and the probability of seeking first-line treatment for clinical malaria over 14 days is low (10%). Each panel shows the median reduction in cumulative uncomplicated (solid lines) or severe cases (dashed lines) achieved by combining seasonal deployment of a pre-liver stage therapeutic with SMC, relative to cumulative cases when SMC is deployed alone. Median reductions are calculated by dividing the parameter range for the therapeutic property shown on the x-axis (protection half-life, initial efficacy, decay shape) into 51 segments, and calculating the median outcome for each given segment across all other parameter values. Shaded regions represent the 25th and 75th percentiles of the corresponding reductions. Predictions are shown separately for cumulative case outcomes at five (top panels) and ten years old (bottom panels). SMC = seasonal malaria chemoprevention.

https://doi.org/10.1371/journal.pcbi.1014021.g003

Our results showed that co-deploying SMC with a pre-liver stage therapeutic is likely to have the most impact in settings where SMC does not fully protect children. For example, for a pre-liver stage therapeutic with 50% initial efficacy and a long tail of protection (biphasic decay shape 0.7) deployed as in our imperfect SMC deployment scenario, with three yearly cycles of SMC, a target 5% reduction in cumulative severe cases by ten years old required a protection half-life of at least 237 days (Fig 4). For the same therapeutic profile, a protection half-life of at least 237 days corresponded to a reduction in severe cases by five years old of more than 23%. When the same therapeutic was combined with five SMC cycles, as in our perfect SMC deployment scenario, however, a 5% reduction required a protection half-life of at least 340 days. Results also indicated that higher initial efficacy could be traded for shorter duration requirements; in Fig 4, the target 5% reduction in cumulative severe cases by ten years old could be achieved with a protection half-life of 153 days if pre-liver stage initial efficacy was 70%. Similar dynamics were observed across seasonal transmission settings and levels of access to care, although with higher impact observed when the season was longer (six month vs. four month seasonal profile) and when access to care was higher (50% vs. 10% access to care). (Fig I in S1 Text)

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Fig 4. Predicted relationships between pre-liver stage therapeutic properties and reductions in cumulative severe cases relative to SMC alone, compared across SMC deployment scenarios.

Grid squares indicate the predicted reduction if a pre-liver stage therapeutic with the given protection half-life (x-axis) and initial efficacy (y-axis) were deployed in addition to SMC, assuming a long tail of protection (decay shape parameter 0.7). Reductions are rounded to the nearest 5%. Results show a scenario where transmission is high (32% PfPR_2-10), 75% of malaria cases occur within six months of the year, and the probability of seeking first-line treatment for clinical malaria over 14 days is low (10%). Panels depict predicted relationships for four different SMC deployment scenarios. In deployment scenario 4, SMC coverage is fixed at 70%. SMC = seasonal malaria chemoprevention, PfPR_2-10 = Annual Plasmodium falciparum parasite prevalence in children aged between 2 and 10 years old.

https://doi.org/10.1371/journal.pcbi.1014021.g004

Combining SMC with seasonal deployment of a blood stage therapeutic

Our results indicate that combining a blood stage therapeutic with SMC is likely to reduce the occurrence of severe malaria but may not reduce uncomplicated cases. When a blood stage therapeutic was combined with SMC, increasing a therapeutic’s initial efficacy or protection half-life led to limited change in reductions in uncomplicated malaria. As shown in Fig 5, a near-perfect initial blood stage efficacy of 95.8% was required to achieve a positive median reduction in cumulative uncomplicated cases by ten years old. In contrast, a 10% reduction in cumulative severe cases could be achieved with an initial blood stage efficacy of 86%. Similar trends were observed across SMC deployment scenarios (Figs K, L, M in S1 Text).

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Fig 5. Gaussian Process regression emulator predictions for the relationship between blood stage therapeutic properties and expected reductions in cumulative uncomplicated and severe cases relative to SMC alone.

Results show the imperfect deployment scenario, where children aged three to 59 months received three SMC cycles. Transmission is high (32% PfPR_2-10), 75% of malaria cases occur within six months of the year, and the probability of seeking first-line treatment for clinical malaria over 14 days is low (10%). Each panel shows the median reduction in cumulative uncomplicated (solid lines) or severe cases (dashed lines) achieved by combining seasonal deployment of a blood stage therapeutic with SMC, relative to cumulative cases when SMC is deployed alone. Median reductions are calculated by dividing the parameter range for the therapeutic property shown on the x-axis (protection half-life, initial efficacy, decay shape) into 51 segments, and calculating the median outcome for each given segment across all other parameter values. Shaded regions represent the 25th and 75%th percentiles of the corresponding reductions. Emulator predictions are shown separately for cumulative case outcomes at five (panels A) and ten years old (panels B). SMC = seasonal malaria chemoprevention, PfPR_2-10 = Annual Plasmodium falciparum parasite prevalence in children aged between 2 and 10 years old.

https://doi.org/10.1371/journal.pcbi.1014021.g005

Combining SMC with seasonal deployment of a multi-stage therapeutic

Finally, results suggest that multi-stage therapeutics with both pre-liver and blood stage activity may be preferred for interventions that aim to reduce the burden of severe malaria in children. When three SMC cycles were deployed with a multi-stage therapeutic with both pre-liver and blood stage activity, we found that pre-liver stage activity was the primary driver of impact on cumulative uncomplicated cases. More than 88% of variation in uncomplicated cases measured by five years old was attributed to the combined impact of the pre-liver stage component’s initial efficacy and protection half-life (Fig 6, panel A), and more than 75% of variation in cumulative uncomplicated cases measured by ten years old. However, blood stage activity was crucial for impact on cumulative severe cases by the time children were ten years old; up to 89% of variation in the reduction in cumulative severe cases at ten years could be attributed to the blood stage component’s initial efficacy and protection half-life (Fig 6, panel A).

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Fig 6. Impact of combining a therapeutic with both pre-liver stage and blood stage activity with three yearly cycles of SMC on cumulative uncomplicated and severe cases, compared with SMC deployed alone.

Panel A shows the drivers of impact on all cumulative case outcomes for a therapeutic with both pre-liver stage and blood stage activity deployed together with three yearly cycles of SMC, compared with SMC deployed alone. Bars show the total Sobol effect indices for intervention model parameters. Total Sobol effect indices can be interpreted as the proportion of variation in the cumulative case outcome that can be attributed to a small change in each model parameter and its interactions with other parameters. Indices are shown across levels of transmission intensity (x-axis) for a scenario where three yearly cycles of SMC are deployed (imperfect coverage scenario) in a setting where 75% of malaria cases occur within six months of the year and the probability of seeking first-line treatment for clinical malaria over 14 days is low (10%). Panel B shows differences in the median impact on cumulative case outcomes for therapeutics with pre-liver stage activity alone, blood stage activity alone, and multi-stage pre-liver stage and blood stage activity. Results are shown for the same scenario as in panel A. Points in each panel show the median expected reduction in cumulative cases achieved by combining seasonal deployment of a pre-liver stage, blood stage, or multi-stage therapeutic with SMC, relative to cumulative cases when SMC is deployed alone. Median reductions are evaluated across all possible combinations of therapeutic initial efficacy, protection half-life, and decay shape. Bars indicate the 25th and 75th percentiles of the corresponding reductions. SMC = seasonal malaria chemoprevention, PfPR_2-10 = Annual Plasmodium falciparum parasite prevalence in children aged between 2 and 10 years old.

https://doi.org/10.1371/journal.pcbi.1014021.g006

Across different transmission intensities, we found that the main trends remained consistent: pre-liver stage properties drove most of the effect on uncomplicated cases, and blood stage properties were important for impact on severe cases, particularly by ten years of age. However, there were some differences at moderate transmission levels. For example, at 33% PfPR_2–10, 19% of the variation in reductions in uncomplicated cases by ten years old was explained by the decay shape of the pre-liver stage component, compared with 10% or less at higher transmission levels (Fig 6, panel A). Similarly, blood stage properties contributed less to reductions in cumulative severe cases by ten years old when transmission was 33% PfPR_2–10 or lower, than they did in very high transmission settings. These patterns were consistent across different assumptions about access to care and seasonality (Fig N in S1 Text).

Importantly, model results indicated that deploying a therapeutic with combined pre-liver stage and blood stage activity could lead to greater impact than either therapeutic component alone. When children received three SMC cycles, the expected gain in median outcome between therapeutics with pre-liver stage activity alone and both pre-liver stage and blood stage activity was up to 22.5% across levels of transmission intensity for reductions by five years old, and up to 9.4% for reductions by ten years old (Fig 6, panel B). This trend occurred across SMC deployment scenarios (Fig O, P, Q in S1 Text). This result suggests that multi-stage therapeutics layered with SMC may offer substantial additional benefit for malaria outcomes in comparison to a single-stage therapeutic.

Interestingly, the added benefit of combining pre-liver and blood stage activity remained stable, or declined slightly, as transmission increased when considering outcomes at five years old (Fig 6, panel B). In contrast, we saw the opposite pattern for outcomes at ten years old: the benefit of including blood stage activity, either alone or as part of a multi-stage therapeutic, was greater in very high transmission settings than in moderate ones.