A mathematical model of the impact of present and future malaria vaccines

HM, Brady OJ, Guerra CA, García GA, Carter AR, Ferguson HM, Afolabi BE, Hay SI, Reiner RC, Kiware S, Smith DL. Spatial dynamics of malaria transmission

The Ross-Macdonald model has exerted enormous influence over the study of malaria transmission dynamics and control, but it lacked features to describe parasite dispersal, travel, and other important aspects of heterogeneous transmission. Here, we present a patch-based differential equation modeling framework that extends the Ross-Macdonald model with sufficient skill and complexity to support planning, monitoring and evaluation for Plasmodium falciparum malaria control. We designed a generic interface for building structured, spatial models of malaria transmission based on a new algorithm for mosquito blood feeding. We developed new algorithms to simulate adult mosquito demography, dispersal, and egg laying in response to resource availability. The core dynamical components describing mosquito ecology and malaria transmission were decomposed, redesigned and reassembled into a modular framework. Structural elements in the framework-human population strata, patches, and aquatic habitats-interact through a flexible design that facilitates construction of ensembles of models with scalable complexity to support robust analytics for malaria policy and adaptive malaria control. We propose updated definitions for the human biting rate and entomological inoculation rates. We present new formulas to describe parasite dispersal and spatial dynamics under steady state conditions, including the human biting rates, parasite dispersal, the "vectorial capacity matrix," a human transmitting capacity distribution matrix, and threshold conditions. An [Formula: see text] package that implements the framework, solves the differential equations, and computes spatial metrics for models developed in this framework has been developed. Development of the model and metrics have focused on malaria, but since the framework is modular, the same ideas and software can be applied to other mosquito-borne pathogen systems.

Insights from modelling malaria vaccines for policy decisions: the focus on RTS,S

Mathematical models are increasingly used to inform decisions throughout product development pathways from pre-clinical studies to country implementation of novel health interventions. This review illustrates the utility of simulation approaches by reviewing the literature on malaria vaccine modelling, with a focus on its link to the development of policy guidance for the first licensed product, RTS,S/AS01. The main contributions of modelling studies have been in inferring the mechanism of action and efficacy profile of RTS,S; to predicting the public health impact; and economic modelling mainly comprising cost-effectiveness analysis. The value of both product-specific and generic modelling of vaccines is highlighted.

Cost-effectiveness and public health impact of RTS,S/AS01 E malaria vaccine in Malawi, using a Markov static model

Background: The RTS,S/AS01 _E malaria vaccine is being assessed in Malawi, Ghana and Kenya as part of a large-scale pilot implementation programme. Even if impactful, its incorporation into immunisation programmes will depend on demonstrating cost-effectiveness. We analysed the cost-effectiveness and public health impact of the RTS,S/AS01 _E malaria vaccine use in Malawi.

Methods: We calculated the Incremental Cost Effectiveness Ratio (ICER) per disability-adjusted life year (DALY) averted by vaccination and compared it to Malawi’s mean per capita Gross Domestic Product. We used a previously validated Markov model, which simulated malaria progression in a 2017 Malawian birth cohort for 15 years. We used a 46% vaccine efficacy, 75% vaccine coverage, USD5 estimated cost per vaccine dose, published local treatment costs for clinical malaria and Malawi specific malaria indicators for interventions such as bed net and antimalarial use. We took a healthcare provider, household and societal perspective. Costs were discounted at 3% per year, no discounting was applied to DALYs. For public health impact, we calculated the DALYs, and malaria events averted.

Results: The ICER/DALY averted was USD115 and USD109 for the health system perspective and societal perspective respectively, lower than GDP per capita of USD398.6 for Malawi. Sensitivity analyses exploring the impact of variation in vaccine costs, vaccine coverage rate and coverage of four doses showed vaccine implementation would be cost-effective across a wide range of different outcomes. RTS,S/AS01 was predicted to avert a median of 93,940 (range 20,490–126,540) clinical cases and 394 (127–708) deaths for the three-dose schedule, or 116,480 (31,450–160,410) clinical cases and 484 (189–859) deaths for the four-dose schedule, per 100 000 fully vaccinated children.

Conclusions: We predict the introduction of the RTS,S/AS01 vaccine in the Malawian expanded programme of immunisation (EPI) likely to be highly cost effective.

Assessing the impact of low-technology emanators alongside long-lasting insecticidal nets to control malaria

Malaria control in sub-Saharan Africa relies on the widespread use of long-lasting insecticidal nets (LLINs) or the indoor residual spraying of insecticide. Disease transmission may be maintained even when these indoor interventions are universally used as some mosquitoes will bite in the early morning and evening when people are outside. As countries seek to eliminate malaria, they can target outdoor biting using new vector control tools such as spatial repellent emanators, which emit airborne insecticide to form a protective area around the user. Field data are used to incorporate a low-technology emanator into a mathematical model of malaria transmission to predict its public health impact across a range of scenarios. Targeting outdoor biting by repeatedly distributing emanators alongside LLINs increases the chance of elimination, but the additional benefit depends on the level of anthropophagy in the local mosquito population, emanator effectiveness and the pre-intervention proportion of mosquitoes biting outdoors. High proportions of pyrethroid-resistant mosquitoes diminish LLIN impact because of reduced mosquito mortality. When mosquitoes are highly anthropophagic, this reduced mortality leads to more outdoor biting and a reduced additional benefit of emanators, even if emanators are assumed to retain their effectiveness in the presence of pyrethroid resistance. Different target product profiles are examined, which show the extra epidemiological benefits of spatial repellents that induce mosquito mortality. This article is part of the theme issue 'Novel control strategies for mosquito-borne diseases'.

Cost-effectiveness and public health impact of RTS,S/AS01E malaria vaccine in Malawi, using a Markov static model

Background: The RTS,S/AS01E malaria vaccine is being assessed in Malawi, Ghana and Kenya as part of a large-scale pilot implementation programme. Even if impactful, its incorporation into immunisation programmes will depend on demonstrating cost-effectiveness. We analysed the cost-effectiveness and public health impact of the RTS,S/AS01E malaria vaccine use in Malawi. Methods: We calculated the Incremental Cost Effectiveness Ratio (ICER) per disability-adjusted life year (DALY) averted by vaccination and compared it to Malawi’s mean per capita Gross Domestic Product. We used a previously validated Markov model, which simulated malaria progression in a 2017 Malawian birth cohort for 15 years. We used a 46% vaccine efficacy, 75% vaccine coverage, USD5 estimated cost per vaccine dose, published local treatment costs for clinical malaria and Malawi specific malaria indicators for interventions such as bed net and antimalarial use. We took a healthcare provider, household and societal perspective. Costs were discounted at 3% per year, no discounting was applied to DALYs. For public health impact, we calculated the DALYs, and malaria events averted. Results: The ICER/DALY averted was USD115 and USD109 for the health system perspective and societal perspective respectively, lower than GDP per capita of USD398.6 for Malawi. Sensitivity analyses exploring the impact of variation in vaccine costs, vaccine coverage rate and coverage of four doses showed vaccine implementation would be cost-effective across a wide range of different outcomes. RTS,S/AS01 was predicted to avert a median of 93,940 (range 20,490–126,540) clinical cases and 394 (127–708) deaths for the three-dose schedule, or 116,480 (31,450–160,410) clinical cases and 484 (189–859) deaths for the four-dose schedule, per 100 000 fully vaccinated children. Conclusions: We predict the introduction of the RTS,S/AS01 vaccine in the Malawian expanded programme of immunisation (EPI) likely to be highly cost effective.

Agent-based models of malaria transmission: a systematic review

BACKGROUND

Much of the extensive research regarding transmission of malaria is underpinned by mathematical modelling. Compartmental models, which focus on interactions and transitions between population strata, have been a mainstay of such modelling for more than a century. However, modellers are increasingly adopting agent-based approaches, which model hosts, vectors and/or their interactions on an individual level. One reason for the increasing popularity of such models is their potential to provide enhanced realism by allowing system-level behaviours to emerge as a consequence of accumulated individual-level interactions, as occurs in real populations.

METHODS

A systematic review of 90 articles published between 1998 and May 2018 was performed, characterizing agent-based models (ABMs) relevant to malaria transmission. The review provides an overview of approaches used to date, determines the advantages of these approaches, and proposes ideas for progressing the field.

RESULTS

The rationale for ABM use over other modelling approaches centres around three points: the need to accurately represent increased stochasticity in low-transmission settings; the benefits of high-resolution spatial simulations; and heterogeneities in drug and vaccine efficacies due to individual patient characteristics. The success of these approaches provides avenues for further exploration of agent-based techniques for modelling malaria transmission. Potential extensions include varying elimination strategies across spatial landscapes, extending the size of spatial models, incorporating human movement dynamics, and developing increasingly comprehensive parameter estimation and optimization techniques.

CONCLUSION

Collectively, the literature covers an extensive array of topics, including the full spectrum of transmission and intervention regimes. Bringing these elements together under a common framework may enhance knowledge of, and guide policies towards, malaria elimination. However, because of the diversity of available models, endorsing a standardized approach to ABM implementation may not be possible. Instead it is recommended that model frameworks be contextually appropriate and sufficiently described. One key recommendation is to develop enhanced parameter estimation and optimization techniques. Extensions of current techniques will provide the robust results required to enhance current elimination efforts.

malERA: An updated research agenda for combination interventions and modelling in malaria elimination and eradication

This paper summarises key advances and priorities since the 2011 presentation of the Malaria Eradication Research Agenda (malERA), with a focus on the combinations of intervention tools and strategies for elimination and their evaluation using modelling approaches. With an increasing number of countries embarking on malaria elimination programmes, national and local decisions to select combinations of tools and deployment strategies directed at malaria elimination must address rapidly changing transmission patterns across diverse geographic areas. However, not all of these approaches can be systematically evaluated in the field. Thus, there is potential for modelling to investigate appropriate 'packages' of combined interventions that include various forms of vector control, case management, surveillance, and population-based approaches for different settings, particularly at lower transmission levels. Modelling can help prioritise which intervention packages should be tested in field studies, suggest which intervention package should be used at a particular level or stratum of transmission intensity, estimate the risk of resurgence when scaling down specific interventions after local transmission is interrupted, and evaluate the risk and impact of parasite drug resistance and vector insecticide resistance. However, modelling intervention package deployment against a heterogeneous transmission background is a challenge. Further validation of malaria models should be pursued through an iterative process, whereby field data collected with the deployment of intervention packages is used to refine models and make them progressively more relevant for assessing and predicting elimination outcomes.

Role of mass drug administration in elimination of Plasmodium falciparum malaria: a consensus modelling study

Background

Mass drug administration for elimination of Plasmodium falciparum malaria is recommended by WHO in some settings. We used consensus modelling to understand how to optimise the effects of mass drug administration in areas with low malaria transmission.

Methods

We collaborated with researchers doing field trials to establish a standard intervention scenario and standard transmission setting, and we input these parameters into four previously published models. We then varied the number of rounds of mass drug administration, coverage, duration, timing, importation of infection, and pre-administration transmission levels. The outcome of interest was the percentage reduction in annual mean prevalence of P falciparum parasite rate as measured by PCR in the third year after the final round of mass drug administration.

Findings

The models predicted differing magnitude of the effects of mass drug administration, but consensus answers were reached for several factors. Mass drug administration was predicted to reduce transmission over a longer timescale than accounted for by the prophylactic effect alone. Percentage reduction in transmission was predicted to be higher and last longer at lower baseline transmission levels. Reduction in transmission resulting from mass drug administration was predicted to be temporary, and in the absence of scale-up of other interventions, such as vector control, transmission would return to pre-administration levels. The proportion of the population treated in a year was a key determinant of simulated effectiveness, irrespective of whether people are treated through high coverage in a single round or new individuals are reached by implementation of several rounds. Mass drug administration was predicted to be more effective if continued over 2 years rather than 1 year, and if done at the time of year when transmission is lowest.

Interpretation

Mass drug administration has the potential to reduce transmission for a limited time, but is not an effective replacement for existing vector control. Unless elimination is achieved, mass drug administration has to be repeated regularly for sustained effect.

Funding

Bill & Melinda Gates Foundation.

Advancing digital methods in the fight against communicable diseases

Important advances are being made in the fight against communicable diseases by using new digital tools. While they can be a challenge to deploy at-scale, GPS-enabled smartphones, electronic dashboards and computer models have multiple benefits. They can facilitate program operations, lead to new insights about the disease transmission and support strategic planning. Today, tools such as these are used to vaccinate more children against polio in Nigeria, reduce the malaria burden in Zambia and help predict the spread of the Ebola epidemic in West Africa.

The time-course of protection of the RTS,S vaccine against malaria infections and clinical disease

Background

Recent publications have reported follow-up of the RTS,S/AS01 malaria vaccine candidate Phase III trials at 11 African sites for 32 months (or longer). This includes site- and time-specific estimates of incidence and efficacy against clinical disease with four different vaccination schedules. These data allow estimation of the time-course of protection against infection associated with two different ages of vaccination, both with and without a booster dose.

Methods

Using an ensemble of individual-based stochastic models, each trial cohort in the Phase III trial was simulated assuming many different hypothetical profiles for the vaccine efficacy against infection in time, for both the primary course and boosting dose and including the potential for either exponential or non-exponential decay. The underlying profile of protection was determined by Bayesian fitting of these model predictions to the site- and time-specific incidence of clinical malaria over 32 months (or longer) of follow-up. Using the same stochastic models, projections of clinical efficacy in each of the sites were modelled and compared to available observed trial data.

Results

The initial protection of RTS,S immediately following three doses is estimated as providing an efficacy against infection of 65 % (when immunizing infants aged 6–12 weeks old) and 91 % (immunizing children aged 5–17 months old at first vaccination). This protection decays relatively rapidly, with an approximately exponential decay for the 6–12 weeks old cohort (with a half-life of 7.2 months); for the 5–17 months old cohort a biphasic decay with a similar half-life is predicted, with an initial rapid decay followed by a slower decay. The boosting dose was estimated to return protection to an efficacy against infection of 50–55 % for both cohorts. Estimates of clinical efficacy by trial site are consistent with those reported in the trial for all cohorts.

Conclusions

The site- and time-specific clinical observations from the RTS,S/AS01 trial data allowed a reasonably precise estimation of the underlying vaccine protection against infection which is consistent with common underlying efficacy and decay rates across the trial sites. This calibration suggests that the decay in efficacy against clinical disease is more rapid than that against infection because of age-shifts in the incidence of disease. The dynamical models predict that clinical effectiveness will continue to decay and that likely effects beyond the time-scale of the trial will be small.

Electronic supplementary material

The online version of this article (doi:10.1186/s12936-015-0969-8) contains supplementary material, which is available to authorized users.

Vaccine approaches to malaria control and elimination: Insights from mathematical models

A licensed malaria vaccine would provide a valuable new tool for malaria control and elimination efforts. Several candidate vaccines targeting different stages of the malaria parasite's lifecycle are currently under development, with one candidate, RTS,S/AS01 for the prevention of Plasmodium falciparum infection, having recently completed Phase III trials. Predicting the public health impact of a candidate malaria vaccine requires using clinical trial data to estimate the vaccine's efficacy profile--the initial efficacy following vaccination and the pattern of waning of efficacy over time. With an estimated vaccine efficacy profile, the effects of vaccination on malaria transmission can be simulated with the aid of mathematical models. Here, we provide an overview of methods for estimating the vaccine efficacy profiles of pre-erythrocytic vaccines and transmission-blocking vaccines from clinical trial data. In the case of RTS,S/AS01, model estimates from Phase II clinical trial data indicate a bi-phasic exponential profile of efficacy against infection, with efficacy waning rapidly in the first 6 months after vaccination followed by a slower rate of waning over the next 4 years. Transmission-blocking vaccines have yet to be tested in large-scale Phase II or Phase III clinical trials so we review ongoing work investigating how a clinical trial might be designed to ensure that vaccine efficacy can be estimated with sufficient statistical power. Finally, we demonstrate how parameters estimated from clinical trials can be used to predict the impact of vaccination campaigns on malaria using a mathematical model of malaria transmission.

The effect of malaria control on Plasmodium falciparum in Africa between 2000 and 2015

Since the year 2000, a concerted campaign against malaria has led to unprecedented levels of intervention coverage across sub-Saharan Africa. Understanding the effect of this control effort is vital to inform future control planning. However, the effect of malaria interventions across the varied epidemiological settings of Africa remains poorly understood owing to the absence of reliable surveillance data and the simplistic approaches underlying current disease estimates. Here we link a large database of malaria field surveys with detailed reconstructions of changing intervention coverage to directly evaluate trends from 2000 to 2015, and quantify the attributable effect of malaria disease control efforts. We found that Plasmodium falciparum infection prevalence in endemic Africa halved and the incidence of clinical disease fell by 40% between 2000 and 2015. We estimate that interventions have averted 663 (542-753 credible interval) million clinical cases since 2000. Insecticide-treated nets, the most widespread intervention, were by far the largest contributor (68% of cases averted). Although still below target levels, current malaria interventions have substantially reduced malaria disease incidence across the continent. Increasing access to these interventions, and maintaining their effectiveness in the face of insecticide and drug resistance, should form a cornerstone of post-2015 control strategies.

Defining the relationship between infection prevalence and clinical incidence of Plasmodium falciparum malaria

In many countries health system data remain too weak to accurately enumerate Plasmodium falciparum malaria cases. In response, cartographic approaches have been developed that link maps of infection prevalence with mathematical relationships to predict the incidence rate of clinical malaria. Microsimulation (or ‘agent-based') models represent a powerful new paradigm for defining such relationships; however, differences in model structure and calibration data mean that no consensus yet exists on the optimal form for use in disease-burden estimation. Here we develop a Bayesian statistical procedure combining functional regression-based model emulation with Markov Chain Monte Carlo sampling to calibrate three selected microsimulation models against a purpose-built data set of age-structured prevalence and incidence counts. This allows the generation of ensemble forecasts of the prevalence–incidence relationship stratified by age, transmission seasonality, treatment level and exposure history, from which we predict accelerating returns on investments in large-scale intervention campaigns as transmission and prevalence are progressively reduced.

Mathematical models are used to predict malaria burden to inform disease control efforts. Here, Cameron et al. use Bayesian statistics to calibrate previous models against a data set of age-structured prevalence and incidence, generating stratified forecasts of the prevalence–incidence relationship.

The public health impact of malaria vaccine RTS,S in malaria endemic Africa: country-specific predictions using 18 month follow-up Phase III data and simulation models

BACKGROUND

The RTS,S/AS01 malaria vaccine candidate recently completed Phase III trials in 11 African sites. Recommendations for its deployment will partly depend on predictions of public health impact in endemic countries. Previous predictions of these used only limited information on underlying vaccine properties and have not considered country-specific contextual data.

METHODS

Each Phase III trial cohort was simulated explicitly using an ensemble of individual-based stochastic models, and many hypothetical vaccine profiles. The true profile was estimated by Bayesian fitting of these models to the site- and time-specific incidence of clinical malaria in both trial arms over 18 months of follow-up. Health impacts of implementation via two vaccine schedules in 43 endemic sub-Saharan African countries, using country-specific prevalence, access to care, immunisation coverage and demography data, were predicted via weighted averaging over many simulations.

RESULTS

The efficacy against infection of three doses of vaccine was initially approximately 65 % (when immunising 6-12 week old infants) and 80 % (children 5-17 months old), with a 1 year half-life (exponential decay). Either schedule will avert substantial disease, but predicted impact strongly depends on the decay rate of vaccine effects and average transmission intensity.

CONCLUSIONS

For the first time Phase III site- and time-specific data were available to estimate both the underlying profile of RTS,S/AS01 and likely country-specific health impacts. Initial efficacy will probably be high, but decay rapidly. Adding RTS,S to existing control programs, assuming continuation of current levels of malaria exposure and of health system performance, will potentially avert 100-580 malaria deaths and 45,000 to 80,000 clinical episodes per 100,000 fully vaccinated children over an initial 10-year phase.

Development of malaria transmission-blocking vaccines: from concept to product

Despite decades of effort battling against malaria, the disease is still a major cause of morbidity and mortality. Transmission-blocking vaccines (TBVs) that target sexual stage parasite development could be an integral part of measures for malaria elimination. In the 1950s, Huff et al. first demonstrated the induction of transmission-blocking immunity in chickens by repeated immunizations with Plasmodium gallinaceum-infected red blood cells. Since then, significant progress has been made in identification of parasite antigens responsible for transmission-blocking activity. Recombinant technologies accelerated evaluation of these antigens as vaccine candidates, and it is possible to induce effective transmission-blocking immunity in humans both by natural infection and now by immunization with recombinant vaccines. This chapter reviews the efforts to produce TBVs, summarizes the current status and advances and discusses the remaining challenges and approaches.

Calibration of an intrahost malaria model and parameter ensemble evaluation of a pre-erythrocytic vaccine

Background

A pre-erythrocytic vaccine could provide a useful tool for burden reduction and eventual eradication of malaria. Mathematical malaria models provide a mechanism for evaluating the effective burden reduction across a range of transmission conditions where such a vaccine might be deployed.

Methods

The EMOD model is an individual-based model of malaria transmission dynamics, including vector lifecycles and species-specific behaviour, coupled to a mechanistic intrahost model of malaria parasite and host immune system dynamics. The present work describes the extension of the EMOD model to include diagnoses of severe malaria and iterative calibration of the immune system parameters and parasite antigenic variation to age-stratified prevalence, incidence and severe disease incidence data obtained from multiple regions with broadly varying transmission conditions in Africa. An ensemble of calibrated model parameter sets is then employed to evaluate the potential impact of routine immunization with a pre-erythrocytic vaccine.

Results

The reduction in severe malaria burden exhibits a broad peak at moderate transmission conditions. Under sufficiently intense transmission, a vaccine that reduces but does not eliminate the probability of acquisition from a single challenge bite may delay infections but produces minimal or no net reduction. Conversely, under sufficiently weak transmission conditions, a vaccine can provide a high fractional reduction but avert a relatively low absolute number of cases due to low baseline burden.

Conclusions

Roll-out of routine immunization with pre-erythrocytic malaria vaccines can provide substantial burden reduction across a range of transmission conditions typical to many regions in Africa.

Electronic supplementary material

The online version of this article (doi:10.1186/1475-2875-14-6) contains supplementary material, which is available to authorized users.

Fun with maths: exploring implications of mathematical models for malaria eradication

Mathematical analyses and modelling have an important role informing malaria eradication strategies. Simple mathematical approaches can answer many questions, but it is important to investigate their assumptions and to test whether simple assumptions affect the results. In this note, four examples demonstrate both the effects of model structures and assumptions and also the benefits of using a diversity of model approaches. These examples include the time to eradication, the impact of vaccine efficacy and coverage, drug programs and the effects of duration of infections and delays to treatment, and the influence of seasonality and migration coupling on disease fadeout. An excessively simple structure can miss key results, but simple mathematical approaches can still achieve key results for eradication strategy and define areas for investigation by more complex models.

How effective is integrated vector management against malaria and lymphatic filariasis where the diseases are transmitted by the same vector?

BACKGROUND

The opportunity to integrate vector management across multiple vector-borne diseases is particularly plausible for malaria and lymphatic filariasis (LF) control where both diseases are transmitted by the same vector. To date most examples of integrated control targeting these diseases have been unanticipated consequences of malaria vector control, rather than planned strategies that aim to maximize the efficacy and take the complex ecological and biological interactions between the two diseases into account.

METHODOLOGY/PRINCIPAL FINDINGS

We developed a general model of malaria and LF transmission and derived expressions for the basic reproductive number (R0) for each disease. Transmission of both diseases was most sensitive to vector mortality and biting rate. Simulating different levels of coverage of long lasting-insecticidal nets (LLINs) and larval control confirms the effectiveness of these interventions for the control of both diseases. When LF was maintained near the critical density of mosquitoes, minor levels of vector control (8% coverage of LLINs or treatment of 20% of larval sites) were sufficient to eliminate the disease. Malaria had a far greater R0 and required a 90% population coverage of LLINs in order to eliminate it. When the mosquito density was doubled, 36% and 58% coverage of LLINs and larval control, respectively, were required for LF elimination; and malaria elimination was possible with a combined coverage of 78% of LLINs and larval control.

CONCLUSIONS/SIGNIFICANCE

Despite the low level of vector control required to eliminate LF, simulations suggest that prevalence of LF will decrease at a slower rate than malaria, even at high levels of coverage. If representative of field situations, integrated management should take into account not only how malaria control can facilitate filariasis elimination, but strike a balance between the high levels of coverage of (multiple) interventions required for malaria with the long duration predicted to be required for filariasis elimination.

Comparative assessment of diverse strategies for malaria vector population control based on measured rates at which mosquitoes utilize targeted resource subsets

Background

Eliminating malaria requires vector control interventions that dramatically reduce adult mosquito population densities and survival rates. Indoor applications of insecticidal nets and sprays are effective against an important minority of mosquito species that rely heavily upon human blood and habitations for survival. However, complementary approaches are needed to tackle a broader diversity of less human-specialized vectors by killing them at other resource targets.

Methods

Impacts of strategies that target insecticides to humans or animals can be rationalized in terms of biological coverage of blood resources, quantified as proportional coverage of all blood resources mosquito vectors utilize. Here, this concept is adapted to enable impact prediction for diverse vector control strategies based on measurements of utilization rates for any definable, targetable resource subset, even if that overall resource is not quantifiable.

Results

The usefulness of this approach is illustrated by deriving utilization rate estimates for various blood, resting site, and sugar resource subsets from existing entomological survey data. Reported impacts of insecticidal nets upon human-feeding vectors, and insecticide-treated livestock upon animal-feeding vectors, are approximately consistent with model predictions based on measured utilization rates for those human and animal blood resource subsets. Utilization rates for artificial sugar baits compare well with blood resources, and are consistent with observed impact when insecticide is added. While existing data was used to indirectly measure utilization rates for a variety of resting site subsets, by comparison with measured rates of blood resource utilization in the same settings, current techniques for capturing resting mosquitoes underestimate this quantity, and reliance upon complex models with numerous input parameters may limit the applicability of this approach.

Conclusions

While blood and sugar consumption can be readily quantified using existing methods for detecting natural markers or artificial tracers, improved techniques for labelling mosquitoes, or other arthropod pathogen vectors, will be required to assess vector control measures which target them when they utilize non-nutritional resources such as resting, oviposition, and mating sites.

Electronic supplementary material

The online version of this article (doi:10.1186/1475-2875-13-338) contains supplementary material, which is available to authorized users.

The Separatrix Algorithm for synthesis and analysis of stochastic simulations with applications in disease modeling

Decision makers in epidemiology and other disciplines are faced with the daunting challenge of designing interventions that will be successful with high probability and robust against a multitude of uncertainties. To facilitate the decision making process in the context of a goal-oriented objective (e.g., eradicate polio by [Formula: see text]), stochastic models can be used to map the probability of achieving the goal as a function of parameters. Each run of a stochastic model can be viewed as a Bernoulli trial in which "success" is returned if and only if the goal is achieved in simulation. However, each run can take a significant amount of time to complete, and many replicates are required to characterize each point in parameter space, so specialized algorithms are required to locate desirable interventions. To address this need, we present the Separatrix Algorithm, which strategically locates parameter combinations that are expected to achieve the goal with a user-specified probability of success (e.g. 95%). Technically, the algorithm iteratively combines density-corrected binary kernel regression with a novel information-gathering experiment design to produce results that are asymptotically correct and work well in practice. The Separatrix Algorithm is demonstrated on several test problems, and on a detailed individual-based simulation of malaria.

Made-to-measure malaria vector control strategies: rational design based on insecticide properties and coverage of blood resources for mosquitoes

Eliminating malaria from highly endemic settings will require unprecedented levels of vector control. To suppress mosquito populations, vector control products targeting their blood hosts must attain high biological coverage of all available sources, rather than merely high demographic coverage of a targeted resource subset, such as humans while asleep indoors. Beyond defining biological coverage in a measurable way, the proportion of blood meals obtained from humans and the proportion of bites upon unprotected humans occurring indoors also suggest optimal target product profiles for delivering insecticides to humans or livestock. For vectors that feed only occasionally upon humans, preferred animal hosts may be optimal targets for mosquito-toxic insecticides, and vapour-phase insecticides optimized to maximize repellency, rather than toxicity, may be ideal for directly protecting people against indoor and outdoor exposure. However, for vectors that primarily feed upon people, repellent vapour-phase insecticides may be inferior to toxic ones and may undermine the impact of contact insecticides applied to human sleeping spaces, houses or clothing if combined in the same time and place. These concepts are also applicable to other mosquito-borne anthroponoses so that diverse target species could be simultaneously controlled with integrated vector management programmes. Measurements of these two crucial mosquito behavioural parameters should now be integrated into programmatically funded, longitudinal, national-scale entomological monitoring systems to inform selection of available technologies and investment in developing new ones.