Since the failed campaign to eradicate malaria in the middle of the last century 1, control of malaria infection has been targeted at reduction in morbidity and mortality while protecting the longevity of chemotherapy from drug resistance. Anti-malarial drug resistance occurs when spontaneously arising mutants with reduced drug susceptibility are provided with a survival advantage by the use of the anti-malarial. The sparing use of new anti-malarial drugs has been recommended to minimize the selective pressure on the parasite 23. This is a reasonable argument if the aim is to accept the continued presence of malaria and control its most deleterious effects. However, recent initiatives stating elimination and eventually eradication as the new aim of malaria control require a sea change in strategy 4. Strategies designed to extend the lifespan of chemotherapies conflict with those likely to be required to successfully and rapidly eliminate the disease 5. Elimination strategies require that transmission rather than disease is targeted. In this situation, where data are often sparse 6 and the cumulative effect of multiple control methods is complex and dependent on transmission intensity and many other factors, mathematical modelling plays an important role in informing decisions 7.

The phases of eradication of an infectious disease as defined by Molyneux et al 8, are as follows:

• Control: Reduction of disease incidence, prevalence, morbidity or mortality to a locally acceptable level as a result of deliberate efforts. Continued intervention measures are required to maintain the reduction.

• Elimination of disease: Reduction to zero of the incidence of a specified disease in a defined geographical area as a result of deliberate efforts. Continued intervention measures are required.

• Elimination of infection: Reduction to zero of the incidence of infection caused by a specified agent in a defined geographical area as a result of deliberate efforts. Continued measures to prevent re-establishment of transmission are required.

• Eradication: Permanent reduction to zero of the worldwide incidence of infection caused by a specific agent as a result of deliberate efforts. Intervention measures are no longer needed.

• Extinction: The specific infectious agent no longer exists in nature or the laboratory

A simple mathematical structure is used to consider the 'elimination of infection' phase. The potential of combining multiple strategies that applied singly would not necessarily result in elimination, but applied in combination have the potential to achieve this aim within the timelines predicted by other more complex modelling exercises 9 is demonstrated. It is predicted that non-treatment control measures (such as deployment of an effective vaccine or insecticide-treated bed nets (ITNs)) could prevent the spread of drug resistance (as suggested in 3) in a similar way to drug combination therapy, but at the population rather than individual level (as with multiple first-line therapies 10). It is predicted that in many scenarios even a failure to eliminate the disease would result in a lower cumulative morbidity and mortality than if the attempt were never made. The key exception to this result is the scenario where drug resistance is spreading. Then if the same drugs are used in an elimination strategy, an acceleration of the spread of resistance is predicted, in some cases resulting in higher morbidity following failed elimination attempts.

Eradication of any disease is an ambitious aim that to date has only been achieved for smallpox. There are only a few WHO sanctioned disease targets for eradication or elimination and malaria is not listed among them. Therefore, considering the potential outcomes of failures to eliminate is an important role for mathematical modelling.

As Figure 1 illustrates, in the absence of drug resistance, for low transmission intensities (up to about 20% parasite prevalence) it is predicted that presumptive treatment of clinical cases with a sufficiently high coverage (60%) is adequate for elimination. For intermediate transmission intensities (from 20% to 50% parasite prevalence), the model predicts that the introduction of any one of MSAT, ITN or annual vaccination, at the levels described earlier, would be adequate to eliminate malaria infection. For intermediate to high transmission intensities (from 50% to 75% parasite prevalence), any two combined interventions at least would be required for elimination of malaria infection. For very high levels of transmission (parasite prevalence from 75% to 85%) three combined interventions are predicted to be required to eliminate malaria infection. Resistance spreading at a given speed is predicted to have the effect of decreasing the prevalence thresholds for elimination for each strategy, rendering some strategies ineffective in any setting.

For a high transmission setting (75% parasite prevalence with 10% of infections being clinically apparent, Figure 1) into which a single intervention (red solid), pairs of interventions (blue dashed), or a combination of all three (green solid) are introduced, only a combination of all three interventions was sufficient to reduce the predicted reproduction number below unity, thus predicting that elimination would be possible.

With the proliferation of partially effective interventions proposed for the elimination of malaria, informed choices are needed now on how they should be used. Simple compartmental modelling allows the effects of large number of possible combinations of controls and administration methods to be predicted across a range of transmission settings. The model presented here is deliberately simple in nature. It is for the purposes of understanding the more general behaviour of malaria transmission specifically during elimination and could be used as a first step by policy makers for strategy planning for a few years ahead. The benefit of a simple model is that it requires very little data input and can be run quickly for a range of scenarios. For longer term planning, more complex models are required. The benefit of such models is that they are likely to predict accurately for a longer time period, but only if they are correctly parameterized with large and multiple datasets for the specific country. If these data are not available an alternative approach is to use simple models initially and then upgrade them with increasing complexity as more data are collected during the elimination process. This approach has been applied successfully for other diseases in the UK by the Health Protection Agency 19.

A simple mathematical model is used here to demonstrate the interrelationships between different interventions and the potential for elimination when they are combined. The qualitative behaviour corresponds well to that of three more complex models that consider different aspects of malaria transmission in far more detail. Comprehensive models that consider every aspect of malaria transmission and infection are highly computer intensive, often sensitive to poorly characterized input parameters, and the time required to run all combinations of potential interventions could be longer than the time available to contribute to elimination policies within a realistic timeframe. The number of combinations of interventions is large. Simple models that can consider many scenarios in a short length of time are useful in reducing the number of runs required for the more complex but computer intensive models tailored to specific regions. The ability of this simple model to reproduce the main trends predicted by its more complex counterparts is demonstrated indicating its value as a precursor to more complex models to allow predominant trends and behaviours to be explored very quickly before quantitative predictions and recommendations are retrieved.

The model includes one interaction between interventions as an example, namely that when MSAT is active we assume that presumptive treatment does not occur. Other interactions that may negatively affect elimination (such as the possibility that individuals who experience high biting rates also experience a lower coverage from vaccination) have not been considered. By definition, a simple model does not include everything. However the simple model structure could easily be extended to include such an effect if it were considered significant for a particular setting. For this example, individuals not covered by vaccination could be given a higher transmission coefficient during the intervention.

If resistance is not spreading, predictions for impact on clinical infection are positive even when elimination fails. This is because, in the absence of an elimination strategy, transmission and clinical infection will continue at the same level, resulting in an accumulation of cases of clinical infection. An elimination strategy is likely to involve aggressive treatment of infected individuals regardless of their clinical signs. Early cessation of an aggressive elimination strategy in a high transmission setting and the resulting rebound in clinical infection (due to increased transmission in a population with reduced immunity) was considered. This is predicted to have a deleterious effect only in the presence of the spread of resistance. Even some successful elimination strategies will result in higher selective pressure than control. However, in combination with other interventions, such as vector control or vaccination, the deleterious effects can be abated and in some cases removed completely. This analysis provides evidence for the argument that attempting malaria elimination using a suitable strategy is low risk in terms of the burden of clinical disease and the spread of drug resistance.

The model presented here can also be used for the initial stages of target product profiling in terms of the target efficacy levels and durations required for a given product applied in combination with of a range of interventions for a range of transmission settings. The model can be used to propose suitable delivery strategies of new and existing products and to assess the most likely relative efficacy of such products.

In conclusion, the modelling exercise demonstrates that combining interventions with suitable delivery strategies can protect drugs from selective pressure through indirect effects on the transmission dynamics. Also, single interventions that have previously been assessed as weak can be combined to make a seemingly unhopeful strategy more likely to succeed due to the herd effect of combining strategies. This is a conclusion that reiterates the results of previous modelling work 202122. Furthermore, in the current climate of increased commitment to the eradication of malaria, the model results indicate that even in a high transmission setting a suitable combination of interventions could achieve elimination through a sustained aggressive integrated control strategy without significantly increasing selective pressure against anti-malarial drugs.

ITN: insecticide-treated bed net; WHO: World Health Organization; MAST: mass screen and treat; ACT: artemisinin combination therapy.

TE is an employee of GlaxoSmithKline Biologicals.

LW developed the model structures (based on previous work by RA, LW et al.) and performed the mathematical analysis. RM, WP, SS, TE, and RA participated in developing the initial concept of the study, review of the mathematical analysis and manuscript revision. RM, ND and NW provided the clinical context of the study and participated in manuscript revision. All authors read and approved the final manuscript.