Accelerating Progress Towards the 2030 Neglected Tropical Diseases Targets: How Can Quantitative Modeling Support Programmatic Decisions?

Over the past decade, considerable progress has been made in the control, elimination, and eradication of neglected tropical diseases (NTDs). Despite these advances, most NTD programs have recently experienced important setbacks; for example, NTD interventions were some of the most frequently and severely impacted by service disruptions due to the coronavirus disease 2019 (COVID-19) pandemic. Mathematical modeling can help inform selection of interventions to meet the targets set out in the NTD road map 2021-2030, and such studies should prioritize questions that are relevant for decision-makers, especially those designing, implementing, and evaluating national and subnational programs. In September 2022, the World Health Organization hosted a stakeholder meeting to identify such priority modeling questions across a range of NTDs and to consider how modeling could inform local decision making. Here, we summarize the outputs of the meeting, highlight common themes in the questions being asked, and discuss how quantitative modeling can support programmatic decisions that may accelerate progress towards the 2030 targets.

Testing and treatment for malaria elimination: a systematic review.

BACKGROUND: Global interest in malaria elimination has prompted research on active test and treat (TaT) strategies. METHODS: A systematic review and meta-analysis were conducted to assess the effectiveness of TaT strategies to reduce malaria transmission. RESULTS: A total of 72 empirical research and 24 modelling studies were identified, mainly focused on proactive mass TaT (MTaT) and reactive case detection (RACD) in higher and lower transmission settings, respectively. Ten intervention studies compared MTaT to no MTaT and the evidence for impact on malaria incidence was weak. No intervention studies compared RACD to no RACD. Compared to passive case detection (PCD) alone, PCD + RACD using standard diagnostics increased infection detection 52.7% and 11.3% in low and very low transmission settings, respectively. Using molecular methods increased this detection of infections by 1.4- and 1.1-fold, respectively. CONCLUSION: Results suggest MTaT is not effective for reducing transmission. By increasing case detection, surveillance data provided by RACD may indirectly reduce transmission by informing coordinated responses of intervention targeting.

Repurposing Know-how for Drug Development: Case Studies from the Swiss Tropical and Public Health Institute.

In pursuing novel therapeutic solutions, drug discovery and development rely on efficiently utilising existing knowledge and resources. Repurposing know-how, a strategy that capitalises on previously acquired information and expertise, has emerged as a powerful approach to accelerate drug discovery and development processes, often at a fraction of the costs of de novo developments. For 80 years, collaborating within a network of partnerships, the Swiss Tropical and Public Health Institute (Swiss TPH) has been working along a value chain from innovation to validation and application to combat poverty-related diseases. This article presents an overview of selected know-how repurposing initiatives conducted at Swiss TPH with a particular emphasis on the exploration of drug development pathways in the context of neglected tropical diseases and other infectious diseases of poverty, such as schistosomiasis, malaria and human African trypanosomiasis.

Modelling to Quantify the Likelihood that Local Elimination of Transmission has Occurred Using Routine Gambiense Human African Trypanosomiasis Surveillance Data.

BACKGROUND: The gambiense human African trypanosomiasis (gHAT) elimination programme in the Democratic Republic of Congo (DRC) routinely collects case data through passive surveillance and active screening, with several regions reporting no cases for several years, despite being endemic in the early 2000s. METHODS: We use mathematical models fitted to longitudinal data to estimate the probability that selected administrative regions have already achieved elimination of transmission (EOT) of gHAT. We examine the impact of active screening coverage on the certainty of model estimates for transmission and therefore the role of screening in the measurement of EOT. RESULTS: In 3 example health zones of Sud-Ubangi province, we find there is a moderate (>40%) probability that EOT has been achieved by 2018, based on 2000-2016 data. Budjala and Mbaya reported zero cases during 2017-18, and this further increases our respective estimates to 99.9% and 99.6% (model S) and to 87.3% and 92.1% (model W). Bominenge had recent case reporting, however, that if zero cases were found in 2021, it would substantially raise our certainty that EOT has been met there (99.0% for model S and 88.5% for model W); this could be higher with 50% coverage screening that year (99.1% for model S and 94.0% for model W). CONCLUSIONS: We demonstrate how routine surveillance data coupled with mechanistic modeling can estimate the likelihood that EOT has already been achieved. Such quantitative assessment will become increasingly important for measuring local achievement of EOT as 2030 approaches.

Predicted Impact of COVID-19 on Neglected Tropical Disease Programs and the Opportunity for Innovation.

Due to the COVID-19 pandemic, many key neglected tropical disease (NTD) activities have been postponed. This hindrance comes at a time when the NTDs are progressing towards their ambitious goals for 2030. Mathematical modelling on several NTDs, namely gambiense sleeping sickness, lymphatic filariasis, onchocerciasis, schistosomiasis, soil-transmitted helminthiases (STH), trachoma, and visceral leishmaniasis, shows that the impact of this disruption will vary across the diseases. Programs face a risk of resurgence, which will be fastest in high-transmission areas. Furthermore, of the mass drug administration diseases, schistosomiasis, STH, and trachoma are likely to encounter faster resurgence. The case-finding diseases (gambiense sleeping sickness and visceral leishmaniasis) are likely to have fewer cases being detected but may face an increasing underlying rate of new infections. However, once programs are able to resume, there are ways to mitigate the impact and accelerate progress towards the 2030 goals.

Evaluation of different deployment strategies for larviciding to control malaria: a simulation study.

BACKGROUND: Larviciding against malaria vectors in Africa has been limited to indoor residual spraying and insecticide-treated nets, but is increasingly being considered by some countries as a complementary strategy. However, despite progress towards improved larvicides and new tools for mapping or treating mosquito-breeding sites, little is known about the optimal deployment strategies for larviciding in different transmission and seasonality settings. METHODS: A malaria transmission model, OpenMalaria, was used to simulate varying larviciding strategies and their impact on host-seeking mosquito densities, entomological inoculation rate (EIR) and malaria prevalence. Variations in coverage, duration, frequency, and timing of larviciding were simulated for three transmission intensities and four transmission seasonality profiles. Malaria transmission was assumed to follow rainfall with a lag of one month. Theoretical sub-Saharan African settings with Anopheles gambiae as the dominant vector were chosen to explore impact. Relative reduction compared to no larviciding was predicted for each indicator during the simulated larviciding period. RESULTS: Larviciding immediately reduced the predicted host-seeking mosquito densities and EIRs to a maximum that approached or exceeded the simulated coverage. Reduction in prevalence was delayed by approximately one month. The relative reduction in prevalence was up to four times higher at low than high transmission. Reducing larviciding frequency (i.e., from every 5 to 10 days) resulted in substantial loss in effectiveness (54, 45 and 53% loss of impact for host-seeking mosquito densities, EIR and prevalence, respectively). In seasonal settings the most effective timing of larviciding was during or at the beginning of the rainy season and least impactful during the dry season, assuming larviciding deployment for four months. CONCLUSION: The results highlight the critical role of deployment strategies on the impact of larviciding. Overall, larviciding would be more effective in settings with low and seasonal transmission, and at the beginning and during the peak densities of the target species populations. For maximum impact, implementers should consider the practical ranges of coverage, duration, frequency, and timing of larviciding in their respective contexts. More operational data and improved calibration would enable models to become a practical tool to support malaria control programmes in developing larviciding strategies that account for the diversity of contexts.

Incidence and consequences of damage to insecticide-treated mosquito nets in Kenya.

BACKGROUND: Efforts to improve the impact of long-lasting insecticidal nets (LLINs) should be informed by understanding of the causes of decay in effect. Holes in LLINs have been estimated to account for 7-11% of loss in effect on vectorial capacity for Plasmodium falciparum malaria in an analysis of repeated cross-sectional surveys of LLINs in Kenya. This does not account for the effect of holes as a cause of net attrition or non-use, which cannot be measured using only cross-sectional data. There is a need for estimates of how much these indirect effects of physical damage on use and attrition contribute to decay in effectiveness of LLINs. METHODS: Use, physical integrity, and survival were assessed in a cohort of 4514 LLINs followed for up to 4 years in Kenya. Flow diagrams were used to illustrate how the status of nets, in terms of categories of use, physical integrity, and attrition, changed between surveys carried out at 6-month intervals. A compartment model defined in terms of ordinary differential equations (ODEs) was used to estimate the transition rates between the categories. Effects of physical damage to LLINs on use and attrition were quantified by simulating counterfactuals in which there was no damage. RESULTS: Allowing for the direct effect of holes, the effect on use, and the effect on attrition, 18% of the impact on vectorial capacity was estimated to be lost because of damage. The estimated median lifetime of the LLINs was 2.9 years, but this was extended to 5.7 years in the counterfactual without physical damage. Nets that were in use were more likely to be in a damaged state than unused nets but use made little direct difference to LLIN lifetimes. Damage was reported as the reason for attrition for almost half of attrited nets, but the model estimated that almost all attrited nets had suffered some damage before attrition. CONCLUSIONS: Full quantification of the effects of damage will require measurement of the supply of new nets and of household stocks of unused nets, and also of their impacts on both net use and retention. The timing of mass distribution campaigns is less important than ensuring sufficient supply. In the Kenyan setting, nets acquired damage rapidly once use began and the damage led to rapid attrition. Increasing the robustness of nets could substantially increase their lifetime and impact but the impact of LLIN programmes on malaria transmission is ultimately limited by levels of use. Longitudinal analyses of net integrity data from different settings are needed to determine the importance of physical damage to nets as a driver of attrition and non-use, and the importance of frequent use as a cause of physical damage in different contexts.

Screening Strategies for a Sustainable Endpoint for Gambiense Sleeping Sickness.

BACKGROUND: Gambiense human African trypanosomiasis ([gHAT] sleeping sickness) is a vector-borne disease that is typically fatal without treatment. Intensified, mainly medical-based, interventions in endemic areas have reduced the occurrence of gHAT to historically low levels. However, persistent regions, primarily in the Democratic Republic of Congo (DRC), remain a challenge to achieving the World Health Organization's goal of global elimination of transmission (EOT). METHODS: We used stochastic models of gHAT transmission fitted to DRC case data and explored patterns of regional reporting and extinction. The time to EOT at a health zone scale (~100 000 people) and how an absence of reported cases informs about EOT was quantified. RESULTS: Regional epidemiology and level of active screening (AS) both influenced the predicted time to EOT. Different AS cessation criteria had similar expected infection dynamics, and recrudescence of infection was unlikely. However, whether EOT has been achieved when AS ends is critically dependent on the stopping criteria. Two or three consecutive years of no detected cases provided greater confidence of EOT compared with a single year (~66%-75% and ~82%-84% probability of EOT, respectively, compared with 31%-51%). CONCLUSIONS: Multiple years of AS without case detections is a valuable measure to assess the likelihood that the EOT target has been met locally.

A metapopulation model of dog rabies transmission in N'Djamena, Chad.

Rabies transmission was interrupted for several months in N'Djamena, the capital city of Chad, after two mass vaccination campaigns of dogs. However, there was a resurgence in cases, which was not predicted by previous models of rabies transmission. We developed a deterministic metapopulation model with importation of latent dogs, calibrated to four years of weekly incidence data from passive surveillance, to investigate possible causes for the early resurgence. Our results indicate that importation of latently infective dogs better explains the data than heterogeneity or underreporting. Stochastic implementations of the model suggest that the two vaccination campaigns averted approximately 67 cases of dog rabies (out of an estimated 74 cases without vaccination) and 124 human exposures (out of an estimated 148 human exposures without vaccination) over two years. Dog rabies vaccination is therefore an effective way of preventing rabies in the dog population and to subsequently reduce human exposure. However, vaccination campaigns have to be repeated to maintain the effect or reintroduction through importation has to be prevented.

Modelling reactive case detection strategies for interrupting transmission of Plasmodium falciparum malaria.

BACKGROUND: As areas move closer to malaria elimination, a combination of limited resources and increasing heterogeneity in case distribution and transmission favour a shift to targeted reactive interventions. Reactive case detection (RCD), the following up of additional individuals surrounding an index case, has the potential to target transmission pockets and identify asymptomatic cases in them. Current RCD implementation strategies vary, and it is unclear which are most effective in achieving elimination. METHODS: OpenMalaria, an established individual-based stochastic model, was used to simulate RCD in a Zambia-like setting. The capacity to follow up index cases, the search radius, the initial transmission and the case management coverage were varied. Suitable settings were identified and probabilities of elimination and time to elimination estimated. The value of routinely collected prevalence and incidence data for predicting the success of RCD was assessed. RESULTS: The results indicate that RCD with the aim of transmission interruption is only appropriate in settings where initial transmission is very low (annual entomological inoculation rate (EIR) 1-2 or prevalence approx. < 7-19% depending on case management levels). Every index case needs to be followed up, up to a maximum case-incidence threshold which defines the suitability threshold of settings for elimination using RCD. Increasing the search radius around index cases is always beneficial. CONCLUSIONS: RCD is highly resource intensive, requiring testing and treating of 400-500 people every week for 5-10 years for a reasonable chance of elimination in a Zambia-like setting.

Resurgence of malaria infection after mass treatment: a simulation study.

BACKGROUND: Field studies are evaluating if mass drug administration (MDA) might shorten the time to elimination of Plasmodium falciparum malaria, when vector control measures and reactive surveillance strategies are scaled-up. A concern with this strategy is that there may be resurgence of transmission following MDA. METHODS: A conceptual model was developed to classify possible outcomes of an initial period of MDA, followed by continuously implementing other interventions. The classification considered whether elimination or a new endemic stable state is achieved, and whether changes are rapid, transient, or gradual. These categories were informed by stability analyses of simple models of vector control, case management, and test-and-treat interventions. Individual-based stochastic models of malaria transmission (OpenMalaria) were then used to estimate the probability and likely rates of resurgence in realistic settings. Effects of concurrent interventions, including routine case management and test-and-treat strategies were investigated. RESULTS: Analysis of the conceptual models suggest resurgence will occur after MDA unless transmission potential is very low, or the post-MDA prevalence falls below a threshold, which depends on both transmission potential and on the induction of bistability. Importation rates are important only when this threshold is very low. In most OpenMalaria simulations the approximately stable state achieved at the end of the simulations was independent of inclusion of MDA and the final state was unaffected by importation of infections at plausible rates. Elimination occurred only with high effective coverage of case management, low initial prevalence, and high intensity test-and-treat. High coverage of case management but not by test-and-treat induced bistability. Where resurgence occurred, its rate depended mainly on transmission potential (not treatment rates). CONCLUSIONS: A short burst of high impact MDA is likely to be followed by resurgence. To avert resurgence, concomitant interventions need either to substantially reduce average transmission potential or to be differentially effective in averting or clearing infections at low prevalence. Case management at high effective coverage has this differential effect, and should suffice to avert resurgence caused by imported cases at plausible rates of importation. Once resurgence occurs, its rate depends mainly on transmission potential, not on treatment strategies.

The development and evaluation of a self-marking unit to estimate malaria vector survival and dispersal distance.

BACKGROUND: A clear understanding of mosquito biology is fundamental to the control efforts of mosquito-borne diseases such as malaria. Mosquito mark-release-recapture (MMRR) experiments are a popular method of measuring the survival and dispersal of disease vectors; however, examples with African malaria vectors are limited. Ethical and technical difficulties involved in carrying out MMRR studies may have held back research in this area and, therefore, a device that marks mosquitoes as they emerge from breeding sites was developed and evaluated to overcome the problems of MMRR. METHODS: A modified self-marking unit that marks mosquitoes with fluorescent pigment as they emerge from their breeding site was developed based on a previous design for Culex mosquitoes. The self-marking unit was first evaluated under semi-field conditions with laboratory-reared Anopheles arabiensis to determine the marking success and impact on mosquito survival. Subsequently, a field evaluation of MMRR was conducted in Yombo village, Tanzania, to examine the feasibility of the system. RESULTS: During the semi-field evaluation the self-marking units successfully marked 86% of emerging mosquitoes and there was no effect of fluorescent marker on mosquito survival. The unit successfully marked wild male and female Anopheles gambiae sensu lato (s.l.) in sufficiently large numbers to justify its use in MMRR studies. The estimated daily survival probability of An. gambiae s.l. was 0.87 (95% CI 0.69-1.10) and mean dispersal distance was 579 m (95% CI 521-636 m). CONCLUSIONS: This study demonstrates the successful use of a self-marking device in an MMRR study with African malaria vectors. This method may be useful in investigating population structure and dispersal of mosquitoes for deployment and evaluation of future vector control tools, such as gene drive, and to better parameterize mathematical models.

Models of effectiveness of interventions against malaria transmitted by Anopheles albimanus.

BACKGROUND: Most impact prediction of malaria vector control interventions has been based on African vectors. Anopheles albimanus, the main vector in Central America and the Caribbean, has higher intrinsic mortality, is more zoophilic and less likely to rest indoors. Therefore, relative impact among interventions may be different. Prioritizing interventions, in particular for eliminating Plasmodium falciparum from Haiti, should consider local vector characteristics. METHODS: Field bionomics data of An. albimanus from Hispaniola and intervention effect data from southern Mexico were used to parameterize mathematical malaria models. Indoor residual spraying (IRS), insecticide-treated nets (ITNs), and house-screening were analysed by inferring their impact on the vectorial capacity in a difference-equation model. Impact of larval source management (LSM) was assumed linear with coverage. Case management, mass drug administration and vaccination were evaluated by estimating their effects on transmission in a susceptible-infected-susceptible model. Analogous analyses were done for Anopheles gambiae parameterized with data from Tanzania, Benin and Nigeria. RESULTS: While LSM was equally effective against both vectors, impact of ITNs on transmission by An. albimanus was much lower than for An. gambiae. Assuming that people are outside until bedtime, this was similar for the impact of IRS with dichlorodiphenyltrichloroethane (DDT) or bendiocarb, and impact of IRS was less than that of ITNs. However, assuming people go inside when biting starts, IRS had more impact on An. albimanus than ITNs. While house-screening had less impact than ITNs or IRS on An. gambiae, it had more impact on An. albimanus than ITNs or IRS. The impacts of chemoprevention and chemotherapy were comparable in magnitude to those of strategies against An. albimanus. Chemo-prevention impact increased steeply as coverage approached 100%, whilst clinical-case management impact saturated because of remaining asymptomatic infections. CONCLUSIONS: House-screening and repellent IRS are potentially highly effective against An. albimanus if people are indoors during the evening. This is consistent with historical impacts of IRS with DDT, which can be largely attributed to excito-repellency. It also supports the idea that housing improvements have played a critical role in malaria control in North America. For elimination planning, impact estimates need to be combined with feasibility and cost-analysis.

Theory of reactive interventions in the elimination and control of malaria.

BACKGROUND: Reactive case detection (RCD) is an integral part of many malaria control and elimination programmes and can be conceived of as a way of gradually decreasing transmission. However, it is unclear under what circumstances RCD may have a substantial impact on prevalence, how likely it is to lead to local elimination, or how effective it needs to be to prevent reintroduction after transmission has been interrupted. METHODS: Analyses and simulations of a discrete time compartmental susceptible-infectious-susceptible (SIS) model were used to understand the mechanisms of how RCD changes transmission dynamics and estimate the impact of RCD programmes in a range of settings with varying patterns of transmission potential and programme characteristics. Prevalence survey data from recent studies in Zambia were used to capture the effects of spatial clustering of patent infections. RESULTS: RCD proved most effective at low prevalence. Increasing the number of index cases followed was more important than increasing the number of neighbours tested per index case. Elimination was achieved only in simulations of situations with very low transmission intensity and following many index cases. However, RCD appears to be helpful in maintaining the disease-free state after achieving malaria elimination (through other interventions). CONCLUSION: RCD alone can eliminate malaria in only a very limited range of settings, where transmission potential is very low, and improving the coverage of RCD has little effect on this range. In other settings, it is likely to reduce disease burden. RCD may also help maintain the disease-free state in the face of imported infections. Prevalence survey data can be used to estimate a targeting ratio (the ratio of prevalence found through RCD to that in the general population) which is an important determinant of the effect of RCD.

Assessing Strategies Against Gambiense Sleeping Sickness Through Mathematical Modeling.

Background: Control of gambiense sleeping sickness relies predominantly on passive and active screening of people, followed by treatment. Methods: Mathematical modeling explores the potential of 3 complementary interventions in high- and low-transmission settings. Results: Intervention strategies that included vector control are predicted to halt transmission most quickly. Targeted active screening, with better and more focused coverage, and enhanced passive surveillance, with improved access to diagnosis and treatment, are both estimated to avert many new infections but, when used alone, are unlikely to halt transmission before 2030 in high-risk settings. Conclusions: There was general model consensus in the ranking of the 3 complementary interventions studied, although with discrepancies between the quantitative predictions due to differing epidemiological assumptions within the models. While these predictions provide generic insights into improving control, the most effective strategy in any situation depends on the specific epidemiology in the region and the associated costs.

Mathematical analysis of the transmission dynamics of the liver fluke, Opisthorchis viverrini.

We develop and analyse two population-based models of the transmission dynamics of the worm parasite Opisthorchis viverrini. The life cycle of O. viverrini includes humans, cats and dogs as definitive hosts; and snails and fish as intermediate hosts. The first model has only one definitive host (humans) while the second model has two additional hosts: the reservoir hosts, cats and dogs. We define reproduction numbers and endemic equilibrium points for the two models. We use prevalence data for the five hosts from two islands in Lao People's Democratic Republic to estimate distributions of parameter values. We use these distributions to compute the sensitivity index and the partial rank correlation coefficient of the basic reproduction number and the endemic equilibrium point to the parameters. We calculate distributions of the host-specific type-reproduction number to show that humans are necessary to maintain transmission and can sustain transmission without additional reservoir hosts. Therefore interventions targeting humans could be sufficient to interrupt transmission of O. viverrini.

Mathematical analysis to prioritise strategies for malaria elimination.

Malaria and some other tropical diseases are currently targeted for elimination and eventually eradication. Since resources are limited, prioritisation of countries or areas for elimination is often necessary. However, this prioritisation is frequently conducted in an ad hoc manner. Lower transmission areas are usually targeted for elimination first, but for some areas this necessitates long and potentially expensive surveillance programs while transmission is eliminated from neighbouring higher transmission areas. We use a mathematical model to compare the implications of prioritisation choices in reducing overall burden and costs. We show that when the duration of the elimination program is independent of the transmission potential, burden is always reduced most by targeting high transmission areas first, but to reduce costs the optimal ordering depends on the actual transmission levels. In general, when overall transmission potential is low and the surveillance cost per secondary case compared to the cost per imported case is low, targeting the higher transmission area for elimination first is favoured.

Modelling the implications of stopping vector control for malaria control and elimination.

BACKGROUND: Increasing coverage of malaria vector control interventions globally has led to significant reductions in disease burden. However due to its high recurrent cost, there is a need to determine if and when vector control can be safely scaled back after transmission has been reduced. METHODS AND FINDINGS: A mathematical model of Plasmodium falciparum malaria epidemiology was simulated to determine the impact of scaling back vector control on transmission and disease. A regression analysis of simulation results was conducted to derive predicted probabilities of resurgence, severity of resurgence and time to resurgence under various settings. Results indicate that, in the absence of secular changes in transmission, there are few scenarios where vector control can be removed without high expectation of resurgence. These, potentially safe, scenarios are characterized by low historic entomological inoculation rates, successful vector control programmes that achieve elimination or near elimination, and effective surveillance systems with high coverage and effective treatment of malaria cases. CONCLUSIONS: Programmes and funding agencies considering scaling back or withdrawing vector control from previously malaria endemic areas need to first carefully consider current receptivity and other available interventions in a risk assessment. Surveillance for resurgence needs to be continuously conducted over a long period of time in order to ensure a rapid response should vector control be withdrawn.

A stochastic model for the probability of malaria extinction by mass drug administration.

BACKGROUND: Mass drug administration (MDA) has been proposed as an intervention to achieve local extinction of malaria. Although its effect on the reproduction number is short lived, extinction may subsequently occur in a small population due to stochastic fluctuations. This paper examines how the probability of stochastic extinction depends on population size, MDA coverage and the reproduction number under control, R c . A simple compartmental model is developed which is used to compute the probability of extinction using probability generating functions. The expected time to extinction in small populations after MDA for various scenarios in this model is calculated analytically. RESULTS: The results indicate that mass drug administration (Firstly, R c must be sustained at R c  < 1.2 to avoid the rapid re-establishment of infections in the population. Secondly, the MDA must produce effective cure rates of >95% to have a non-negligible probability of successful elimination. Stochastic fluctuations only significantly affect the probability of extinction in populations of about 1000 individuals or less. The expected time to extinction via stochastic fluctuation is less than 10 years only in populations less than about 150 individuals. Clustering of secondary infections and of MDA distribution both contribute positively to the potential probability of success, indicating that MDA would most effectively be administered at the household level. CONCLUSIONS: There are very limited circumstances in which MDA will lead to local malaria elimination with a substantial probability.