A periodically-forced mathematical model for the seasonal dynamics of malaria in mosquitoes

A mathematical interpretation for outbreaks of bacterial meningitis under the effect of time-dependent transmission parameters

We consider a SIR-type compartmental model divided into two age classes to explain the seasonal exacerbations of bacterial meningitis, especially among children outside of the meningitis belt. We describe the seasonal forcing through time-dependent transmission parameters that may represent the outbreak of the meningitis cases after the annual pilgrimage period (Hajj) or uncontrolled inflows of irregular immigrants. We present and analyse a mathematical model with time-dependent transmission. We consider not only periodic functions in the analysis but also general non-periodic transmission processes. We show that the long-time average values of transmission functions can be used as a stability marker of the equilibrium. Furthermore, we interpret the basic reproduction number in case of time-dependent transmission functions. Numerical simulations support and help visualize the theoretical results.

The influence of biological, epidemiological, and treatment factors on the establishment and spread of drug-resistant Plasmodium falciparum

The effectiveness of artemisinin-based combination therapies (ACTs) to treat Plasmodium falciparum malaria is threatened by resistance. The complex interplay between sources of selective pressure-treatment properties, biological factors, transmission intensity, and access to treatment-obscures understanding how, when, and why resistance establishes and spreads across different locations. We developed a disease modelling approach with emulator-based global sensitivity analysis to systematically quantify which of these factors drive establishment and spread of drug resistance. Drug resistance was more likely to evolve in low transmission settings due to the lower levels of (i) immunity and (ii) within-host competition between genotypes. Spread of parasites resistant to artemisinin partner drugs depended on the period of low drug concentration (known as the selection window). Spread of partial artemisinin resistance was slowed with prolonged parasite exposure to artemisinin derivatives and accelerated when the parasite was also resistant to the partner drug. Thus, to slow the spread of partial artemisinin resistance, molecular surveillance should be supported to detect resistance to partner drugs and to change ACTs accordingly. Furthermore, implementing more sustainable artemisinin-based therapies will require extending parasite exposure to artemisinin derivatives, and mitigating the selection windows of partner drugs, which could be achieved by including an additional long-acting drug.

Sub-national tailoring of malaria interventions in Mainland Tanzania: simulation of the impact of strata-specific intervention combinations using modelling

Background

To accelerate progress against malaria in high burden countries, a strategic reorientation of resources at the sub-national level is needed. This paper describes how mathematical modelling was used in mainland Tanzania to support the strategic revision that followed the mid-term review of the 2015–2020 national malaria strategic plan (NMSP) and the epidemiological risk stratification at the council level in 2018.

Methods

Intervention mixes, selected by the National Malaria Control Programme, were simulated for each malaria risk strata per council. Intervention mixes included combinations of insecticide-treated bed nets (ITN), indoor residual spraying, larval source management, and intermittent preventive therapies for school children (IPTsc). Effective case management was either based on estimates from the malaria indicator survey in 2016 or set to a hypothetical target of 85%. A previously calibrated mathematical model in OpenMalaria was used to compare intervention impact predictions for prevalence and incidence between 2016 and 2020, or 2022.

Results

For each malaria risk stratum four to ten intervention mixes were explored. In the low-risk and urban strata, the scenario without a ITN mass campaign in 2019, predicted high increase in prevalence by 2020 and 2022, while in the very-low strata the target prevalence of less than 1% was maintained at low pre-intervention transmission intensity and high case management. In the moderate and high strata, IPTsc in addition to existing vector control was predicted to reduce the incidence by an additional 15% and prevalence by 22%. In the high-risk strata, all interventions together reached a maximum reduction of 76%, with around 70% of that reduction attributable to high case management and ITNs. Overall, the simulated revised NMSP was predicted to achieve a slightly lower prevalence in 2020 compared to the 2015–2020 NMSP (5.3% vs 6.3%).

Conclusion

Modelling supported the choice of intervention per malaria risk strata by providing impact comparisons of various alternative intervention mixes to address specific questions relevant to the country. The use of a council-calibrated model, that reproduces local malaria trends, represents a useful tool for compiling available evidence into a single analytical platform, that complement other evidence, to aid national programmes with decision-making processes.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12936-022-04099-5.

Target Product Profiles for Mosquito Gene Drives: Incorporating Insights From Mathematical Models

Mosquito-borne diseases such as malaria continue to pose a major global health burden, and the impact of currently-available interventions is stagnating. Consequently, there is interest in novel tools to control these diseases, including gene drive-modified mosquitoes. As these tools continue to be refined, decisions on whether to implement them in the field depend on their alignment with target product profiles (TPPs) that define product characteristics required to achieve desired entomological and epidemiological outcomes. TPPs are increasingly being used for malaria and vector control interventions, such as attractive targeted sugar baits and long-acting injectable drugs, as they progress through the development pipeline. For mosquito gene drive products, reliable predictions from mathematical models are an essential part of these analyses, as field releases could potentially be irreversible. Here, we review the prior use of mathematical models in developing TPPs for malaria and vector control tools and discuss lessons from these analyses that may apply to mosquito gene drives. We recommend that, as gene drive technology gets closer to field release, discussions regarding target outcomes engage a wide range of stakeholders and account for settings of interest and vector species present. Given the relatively large number of parameters that describe gene drive products, machine learning approaches may be useful to explore parameter space, and an emphasis on conservative fitness estimates is advisable, given the difficulty of accurately measuring these parameters prior to field studies. Modeling may also help to inform the risk, remediation and cost dimensions of mosquito gene drive TPPs.

Model-informed target product profiles of long-acting-injectables for use as seasonal malaria prevention

Seasonal malaria chemoprevention (SMC) has proven highly efficacious in reducing malaria incidence. However, the continued success of SMC is threatened by the spread of resistance against one of its main preventive ingredients, Sulfadoxine-Pyrimethamine (SP), operational challenges in delivery, and incomplete adherence to the regimens. Via a simulation study with an individual-based model of malaria dynamics, we provide quantitative evidence to assess long-acting injectables (LAIs) as potential alternatives to SMC. We explored the predicted impact of a range of novel preventive LAIs as a seasonal prevention tool in children aged three months to five years old during late-stage clinical trials and at implementation. LAIs were co-administered with a blood-stage clearing drug once at the beginning of the transmission season. We found the establishment of non-inferiority of LAIs to standard 3 or 4 rounds of SMC with SP-amodiaquine was challenging in clinical trial stages due to high intervention deployment coverage. However, our analysis of implementation settings where the achievable SMC coverage was much lower, show LAIs with fewer visits per season are potential suitable replacements to SMC. Suitability as a replacement with higher impact is possible if the duration of protection of LAIs covered the duration of the transmission season. Furthermore, optimising LAIs coverage and protective efficacy half-life via simulation analysis in settings with an SMC coverage of 60% revealed important trade-offs between protective efficacy decay and deployment coverage. Our analysis additionally highlights that for seasonal deployment for LAIs, it will be necessary to investigate the protective efficacy decay as early as possible during clinical development to ensure a well-informed candidate selection process.

Emulator-based Bayesian optimization for efficient multi-objective calibration of an individual-based model of malaria

Individual-based models have become important tools in the global battle against infectious diseases, yet model complexity can make calibration to biological and epidemiological data challenging. We propose using a Bayesian optimization framework employing Gaussian process or machine learning emulator functions to calibrate a complex malaria transmission simulator. We demonstrate our approach by optimizing over a high-dimensional parameter space with respect to a portfolio of multiple fitting objectives built from datasets capturing the natural history of malaria transmission and disease progression. Our approach quickly outperforms previous calibrations, yielding an improved final goodness of fit. Per-objective parameter importance and sensitivity diagnostics provided by our approach offer epidemiological insights and enhance trust in predictions through greater interpretability.

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.

Overview of the modeling of complex biological systems and its role in neurosurgery

Biological systems are complex with distinct characteristics such as nonlinearity, adaptability, and self-organization. Biomedical research has helped in advancing our understanding of certain components the human biology but failed to illustrate the behavior of the biological systems within. This failure can be attributed to the use of the linear approach, which reduces the system to its components then study each component in isolation. This approach assumes that the behavior of complex systems is the result of the sum of the function of its components. The complex systems approach requires the identification of the components of the system and their interactions with each other and with the environment. Within neurosurgery, this approach has the potential to advance our understanding of the human nervous system and its subsystems.

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.

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.

Simulating the council-specific impact of anti-malaria interventions: A tool to support malaria strategic planning in Tanzania

INTRODUCTION

The decision-making process for malaria control and elimination strategies has become more challenging. Interventions need to be targeted at council level to allow for changing malaria epidemiology and an increase in the number of possible interventions. Models of malaria dynamics can support this process by simulating potential impacts of multiple interventions in different settings and determining appropriate packages of interventions for meeting specific expected targets.

METHODS

The OpenMalaria model of malaria dynamics was calibrated for all 184 councils in mainland Tanzania using data from malaria indicator surveys, school parasitaemia surveys, entomological surveillance, and vector control deployment data. The simulations were run for different transmission intensities per region and five interventions, currently or potentially included in the National Malaria Strategic Plan, individually and in combination. The simulated prevalences were fitted to council specific prevalences derived from geostatistical models to obtain council specific predictions of the prevalence and number of cases between 2017 and 2020. The predictions were used to evaluate in silico the feasibility of the national target of reaching a prevalence of below 1% by 2020, and to suggest alternative intervention stratifications for the country.

RESULTS

The historical prevalence trend was fitted for each council with an agreement of 87% in 2016 (95%CI: 0.84-0.90) and an agreement of 90% for the historical trend (2003-2016) (95%CI: 0.87-0.93) The current national malaria strategy was expected to reduce the malaria prevalence between 2016 and 2020 on average by 23.8% (95% CI: 19.7%-27.9%) if current case management levels were maintained, and by 52.1% (95% CI: 48.8%-55.3%) if the case management were improved. Insecticide treated nets and case management were the most cost-effective interventions, expected to reduce the prevalence by 25.0% (95% CI: 19.7%-30.2) and to avert 37 million cases between 2017 and 2020. Mass drug administration was included in most councils in the stratification selected for meeting the national target at minimal costs, expected to reduce the prevalence by 77.5% (95%CI: 70.5%-84.5%) and to avert 102 million cases, with almost twice higher costs than those of the current national strategy. In summary, the model suggested that current interventions are not sufficient to reach the national aim of a prevalence of less than 1% by 2020 and a revised strategic plan needs to consider additional, more effective interventions, especially in high transmission areas and that the targets need to be revisited.

CONCLUSION

The methodology reported here is based on intensive interactions with the NMCP and provides a helpful tool for assessing the feasibility of country specific targets and for determining which intervention stratifications at sub-national level will have most impact. This country-led application could support strategic planning of malaria control in many other malaria endemic countries.

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.

Mass campaigns combining antimalarial drugs and anti-infective vaccines as seasonal interventions for malaria control, elimination and prevention of resurgence: a modelling study

Background

The only licensed malaria vaccine, RTS,S/AS01, has been developed for morbidity-control in young children. The potential impact on transmission of deploying such anti-infective vaccines to wider age ranges, possibly with co-administration of antimalarial treatment, is unknown. Combinations of existing malaria interventions is becoming increasingly important as evidence mounts that progress on reducing malaria incidence is stalling and threatened by resistance.

Methods

Malaria transmission and intervention dynamics were simulated using OpenMalaria, an individual-based simulation model of malaria transmission, by considering a seasonal transmission setting and by varying epidemiological and setting parameters such as transmission intensity, case management, intervention types and intervention coverages. Chemopreventive drugs and anti-infective vaccine efficacy profiles were based on previous studies in which model parameters were fitted to clinical trial data. These intervention properties were used to evaluate the potential of seasonal mass applications of preventative anti-infective malaria vaccines, alone or in combination with chemoprevention, to reduce malaria transmission, prevent resurgence, and/or reach transmission interruption.

Results

Deploying a vaccine to all ages on its own is a less effective intervention strategy compared to chemoprevention alone. However, vaccines combined with drugs are likely to achieve dramatic prevalence reductions and in few settings, transmission interruption. The combined mass intervention will result in lower prevalence following the intervention compared to chemoprevention alone and will increase chances of interruption of transmission resulting from a synergistic effect between both interventions. The combination of vaccine and drug increases the time before transmission resurges after mass interventions cease compared to mass treatment alone. Deploying vaccines and drugs together requires fewer rounds of mass intervention and fewer years of intervention to achieve the same public health impact as chemoprevention alone.

Conclusions

Through simulations we identified a previously unidentified value of deploying vaccines with drugs, namely the greatest benefit will be in preventing and delaying transmission resurgence for longer periods than with other human targeted interventions. This is suggesting a potential role for deploying vaccines alongside drugs in transmission foci as part of surveillance-response strategies.

Transition from endemic behavior to eradication of malaria due to combined drug therapies: An agent-model approach

We introduce an agent-based model describing a susceptible-infectious-susceptible (SIS) system of humans and mosquitoes to predict malaria epidemiological scenarios in realistic biological conditions. Emphasis is given to the transition from endemic behavior to eradication of malaria transmission induced by combined drug therapies acting on both the gametocytemia reduction and on the selective mosquito mortality during parasite development in the mosquito. Our mathematical framework enables to uncover the critical values of the parameters characterizing the effect of each drug therapy. Moreover, our results provide quantitative evidence of what was up to now only partially assumed with empirical support: interventions combining gametocytemia reduction through the use of gametocidal drugs, with the selective action of ivermectin during parasite development in the mosquito, may actively promote disease eradication in the long run. In the agent model, the main properties of human-mosquito interactions are implemented as parameters and the model is validated by comparing simulations with real data of malaria incidence collected in the endemic malaria region of Chimoio in Mozambique. Finally, we discuss our findings in light of current drug administration strategies for malaria prevention, which may interfere with human-to-mosquito transmission process.

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.

Synergy and timing: a concurrent mass medical campaign predicted to augment indoor residual spraying for malaria

Background

Control programmes for high burden countries are tasked with charting effective multi-year strategies for malaria control within significant resource constraints. Synergies between different control tools, in which more than additive benefit accrues from interventions used together, are of interest because they may be used to obtain savings or to maximize health impact per expenditure. One commonly used intervention in sub-Saharan Africa is indoor residual spraying (IRS), typically deployed through a mass campaign. While possible synergies between IRS and long-lasting insecticide-treated nets (LLINs) have been investigated in multiple transmission settings, coordinated synergy between IRS and other mass medical distribution campaigns have not attracted much attention. Recently, a strong timing-dependent synergy between an IRS campaign and a mass drug administration (MDA) was theoretically quantified. These synergistic benefits likely differ across settings depending on transmission intensity and its overall seasonal pattern.

Methods

High coverage interventions are modelled in different transmission environments using two methods: a Ross–Macdonald model variant and openmalaria simulations. The impact of each intervention strategy was measured through its ability to prevent host infections over time, and the effects were compared to the baseline case of deploying interventions in isolation.

Results

By modelling IRS and MDA together and varying their deployment times, a strong synergy was found when the administered interventions overlapped. The added benefit of co-timed interventions was robust to differences in the models. In the Ross–Macdonald model, the impact compared was roughly double the sequential interventions in most transmission settings. Openmalaria simulations of this medical control augmentation of an IRS campaign show an even stronger response with the same timing relationship.

Conclusions

The strong synergies found for these control tools between the complementary interventions demonstrate a general feature of effective concurrent campaign-style vector and medical interventions. A mass treatment campaign is normally short-lived, especially in higher transmission settings. When co-timed, the rapid clearing of the host parasite reservoir via chemotherapy is protected from resurgence by the longer duration of the vector control. An effective synchronous treatment campaign has the potential to greatly augment the impact of indoor residual spraying. Mass screening and treatment (MSAT) with highly sensitive rapid diagnostic tests may demonstrate a comparable trend while mass LLIN campaigns may similarly coordinate with MDA/MSAT.

Modelling the transmission dynamics of Campylobacter in Ontario, Canada, assuming house flies, Musca domestica, are a mechanical vector of disease transmission

Campylobacter's complicated dynamics and multiple transmission routes have made it difficult to describe using a mathematical framework. Vector-borne disease transmission has been proposed as a potential transmission route of Campylobacter with house flies acting as a mechanical vector. This study aimed to (i) determine if a basic SIR compartment model that included flies as a mechanical vector and incorporated a seasonally forced environment compartment could be used to capture the observed disease dynamics in Ontario, Canada, and (ii) use this model to determine potential changes to campylobacteriosis incidence using predicted changes to fly population size and fly activity under multiple climate change scenarios. The model was fit to 1 year of data and validated against 8 and 12 years of data. It accurately captured the observed incidence. We then explored changes in human disease incidence under multiple climate change scenarios. When fly activity levels were at a 25% increase, our model predicted a 28.15% increase in incidence by 2050 using the medium-low emissions scenario and 30.20% increase using the high emissions scenario. This model demonstrates that the dynamics of Campylobacter transmission can be captured by a model that assumes that the primary transmission of the pathogen occurs via insect vectors.

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.

Medical and entomological malarial interventions, a comparison and synergy of two control measures using a Ross/Macdonald model variant and openmalaria simulation

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An adaptation of the classical Ross–Macdonald model for vector disease transmission to incorporate time-dependent medical and entomological control measures.

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Modeling both mass drug administration and indoor residual spraying campaigns, the synchronous deployment of both yields a synergy where the impact of a joint intervention exceeds that of isolated campaigns.

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Openmalaria simulations, separately run, indicate comparable intervention impacts to the Ross/Macdonald model variant.

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The vector reservoir of parasitemia is found to be labile, and this dictates the impacts of the medical and entomological interventions.

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A scaling-law level of analysis is performed that estimates the rebound of infections in a community after interventions expire, and not only do higher transmission environments bounce back to prevalent infections faster, communities with stronger interventions are shown to have a slower relapse to parasitemia.

Using an established Ross/Macdonald model variant for mosquito-born parasite transmission, we extend the formalism to simply incorporate time-dependent control measures. In particular, two interventions are considered, mass drug administration (MDA) and indoor residual spraying (IRS), whose individual intensities during their respective campaigns are set to the same intervention-reduced reproductive number R₀. The impacts of these interventions, measured as each campaign’s ability over time to reduce infections in a community, are found based on the transmission setting, coverage, and their associated durations. These impacts are compared for both interventions and their joint deployment. Synchronous campaigns of IRS deployed with MDA have a cooperative, synergistic effect whose impact exceeds that when the campaigns are deployed in isolation. Simulations with openmalaria, with its more complex model of transmission, are separately performed and show a similar impact enhancement with these interventions. A new, associated analysis yields simple scaling relationships that estimate the dynamical resurgence time, post-intervention, to infection proliferation in a community.

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.

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.

Interplay between insecticide-treated bed-nets and mosquito demography: implications for malaria control

Although malaria prevalence has witnessed a significant reduction within the past decade, malaria still constitutes a major health and economic problem, especially to low-income countries. Insecticide-treated nets (ITNs) remain one of the primary measures for preventing the malignant disease. Unfortunately, the success of ITN campaigns is hampered by improper use and natural decay in ITN-efficacy over time. Many models aimed at studying malaria transmission and control fail to account for this decay, as well as mosquito demography and feeding preferences exhibited by mosquitoes towards humans. Omitting these factors can misrepresent disease risk, while understanding their effects on malaria dynamics can inform control policy. We present a model for malaria dynamics that incorporates these factors, and a systematic analysis, including stability and sensitivity analyses of the model under different conditions. The model with constant ITN-efficacy exhibits a backward bifurcation emphasizing the need for sustained control measures until the basic reproduction number, R0, drops below a critical value at which control is feasible. The infectious and partially immune human populations and R0 are highly sensitive to the probability that a mosquito feeds successfully on a human, ITN coverage and the maximum biting rate of mosquitoes, irrespective of whether ITN-efficacy is constant or declines over time. This implies that ITNs play an important role in disease control. When ITN-efficacy wanes over time, we identify disease risks and corresponding ITN coverage, as well as feeding preference levels for which the disease can be controlled or eradicated. Our study leads to important insights that could assist in the design and implementation of better malaria control strategies. We conclude that ITNs that can retain their effectiveness for longer periods will be more appropriate in the fight against malaria and that making more ITNs available to highly endemic regions is necessary for malaria containment.

Operational strategies of anti-malarial drug campaigns for malaria elimination in Zambia's southern province: a simulation study

Background

Malaria elimination requires reducing both the potential of mosquitoes to transmit parasites to humans and humans to transmit parasites to mosquitoes. To achieve this goal in Southern province, Zambia a mass test and treat (MTAT) campaign was conducted from 2011–2013 to complement high coverage of long-lasting insecticide-treated nets (LLIN). To identify factors likely to increase campaign effectiveness, a modelling approach was applied to investigate the simulated effect of alternative operational strategies for parasite clearance in southern province.

Methods

OpenMalaria, a discrete-time, individual-based stochastic model of malaria, was parameterized for the study area to simulate anti-malarial drug administration for interruption of transmission. Simulations were run for scenarios with a range of artemisinin-combination therapies, proportion of the population reached by the campaign, targeted age groups, time between campaign rounds, Plasmodium falciparum test protocols, and the addition of drugs aimed at preventing onward transmission. A sensitivity analysis was conducted to assess uncertainty of simulation results. Scenarios were evaluated based on the reduction in all-age parasite prevalence during the peak transmission month one year following the campaign, compared to the currently-implemented strategy of MTAT 19 % population coverage at pilot and 40 % coverage during the first year of implementation in the presence of 56 % LLIN use and 18 % indoor residual spray coverage.

Results

Simulation results suggest the most important determinant of success in reducing prevalence is the population coverage achieved in the campaign, which would require more than 1 year of campaign implementation for elimination. The inclusion of single low-dose primaquine, which acts as a gametocytocide, or ivermectin, which acts as an endectocide, to the drug regimen did not further reduce parasite prevalence one year following the campaign compared to the currently-implemented strategy. Simulation results indicate a high proportion of low-density infections were missed by rapid diagnostic tests that would be treated and cleared with mass drug administration (MDA).

Conclusions

The optimal implementation strategy for MTAT or MDA will vary by background level of prevalence, by rate of infections imported to the area, and by ability to operationally achieve high population coverage. Overall success with new parasite clearance strategies depends on continued coverage of vector control interventions to ensure sustained gains in reduction of disease burden.

Endectocide-treated cattle for malaria control: A coupled entomological-epidemiological model

The malaria vector landscape is dynamic and dependence on indoor control tools has drastically affected both species compositions and local mosquito biting behaviours. In the advent of spreading behavioural resilience and physiological resistance to insecticidal nets and house spray, approaches to target more zoophilic, outdoor-biting vectors are being sought with increased urgency. Endectocides are insecticides applied to hosts which are taken up by the vectors during biting, and recent field assessments have demonstrated favourable results of cattle treated with ivermectin, diflubenzuron, eprinomectin and fipronil. Models were constructed to account for the modern, diverse vector feeding behaviours and assess their role in shaping malaria transmission and control with cattle-treated endectocides. Efficacy of this novel approach to malaria control is shown to be strongly dependent not only on intrinsic host preferences of the vector but also on how this preference is augmented by variation in the encounter rates with alternative blood-hosts. Ecological scenarios are presented whereby endectocides used on cattle yield equivalent, and in some cases improved, efficacy over nets and spray in controlling malaria transmission. Interactions between mosquito biting behaviours and relative availabilities of alternative blood-host species have largely been neglected in malaria programmatic strategy but will increasingly underlie sustaining the successes of vector control initiatives.

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.

Distribution of malaria exposure in endemic countries in Africa considering country levels of effective treatment

Background

Malaria prevalence, clinical incidence, treatment, and transmission rates are dynamically interrelated. Prevalence is often considered a measure of malaria transmission, but treatment of clinical malaria reduces prevalence, and consequently also infectiousness to the mosquito vector and onward transmission. The impact of the frequency of treatment on prevalence in a population is generally not considered. This can lead to potential underestimation of malaria exposure in settings with good health systems. Furthermore, these dynamical relationships between prevalence, treatment, and transmission have not generally been taken into account in estimates of burden.

Methods

Using prevalence as an input, estimates of disease incidence and transmission [as the distribution of the entomological inoculation rate (EIR)] for Plasmodium falciparum have now been made for 43 countries in Africa using both empirical relationships (that do not allow for treatment) and OpenMalaria dynamic micro-simulation models (that explicitly include the effects of treatment). For each estimate, prevalence inputs were taken from geo-statistical models fitted for the year 2010 by the Malaria Atlas Project to all available observed prevalence data. National level estimates of the effectiveness of case management in treating clinical attacks were used as inputs to the estimation of both EIR and disease incidence by the dynamic models.

Results and conclusions

When coverage of effective treatment is taken into account, higher country level estimates of average EIR and thus higher disease burden, are obtained for a given prevalence level, especially where access to treatment is high, and prevalence relatively low. These methods provide a unified framework for comparison of both the immediate and longer-term impacts of case management and of preventive interventions.

Electronic supplementary material

The online version of this article (doi:10.1186/s12936-015-0864-3) contains supplementary material, which is available to authorized users.

Seasonality of Plasmodium falciparum transmission: a systematic review

Background

Although Plasmodium falciparum transmission frequently exhibits seasonal patterns, the drivers of malaria seasonality are often unclear. Given the massive variation in the landscape upon which transmission acts, intra-annual fluctuations are likely influenced by different factors in different settings. Further, the presence of potentially substantial inter-annual variation can mask seasonal patterns; it may be that a location has “strongly seasonal” transmission and yet no single season ever matches the mean, or synoptic, curve. Accurate accounting of seasonality can inform efficient malaria control and treatment strategies. In spite of the demonstrable importance of accurately capturing the seasonality of malaria, data required to describe these patterns is not universally accessible and as such localized and regional efforts at quantifying malaria seasonality are disjointed and not easily generalized.

Methods

The purpose of this review was to audit the literature on seasonality of P. falciparum and quantitatively summarize the collective findings. Six search terms were selected to systematically compile a list of papers relevant to the seasonality of P. falciparum transmission, and a questionnaire was developed to catalogue the manuscripts.

Results and discussion

152 manuscripts were identified as relating to the seasonality of malaria transmission, deaths due to malaria or the population dynamics of mosquito vectors of malaria. Among these, there were 126 statistical analyses and 31 mechanistic analyses (some manuscripts did both).

Discussion

Identified relationships between temporal patterns in malaria and climatological drivers of malaria varied greatly across the globe, with different drivers appearing important in different locations. Although commonly studied drivers of malaria such as temperature and rainfall were often found to significantly influence transmission, the lags between a weather event and a resulting change in malaria transmission also varied greatly by location.

Conclusions

The contradicting results of studies using similar data and modelling approaches from similar locations as well as the confounding nature of climatological covariates underlines the importance of a multi-faceted modelling approach that attempts to capture seasonal patterns at both small and large spatial scales.

Electronic supplementary material

The online version of this article (doi:10.1186/s12936-015-0849-2) contains supplementary material, which is available to authorized users.

Age-shifting in malaria incidence as a result of induced immunological deficit: a simulation study

Effective population-level interventions against Plasmodium falciparum malaria lead to age-shifts, delayed morbidity or rebounds in morbidity and mortality whenever they are deployed in ways that do not permanently interrupt transmission. When long-term intervention programmes target specific age-groups of human hosts, the age-specific morbidity rates ultimately adjust to new steady-states, but it is very difficult to study these rates and the temporal dynamics leading up to them empirically because the changes occur over very long time periods. This study investigates the age and magnitude of age- and time- shifting of incidence induced by either pre-erythrocytic vaccination (PEV) programmes or seasonal malaria chemo-prevention (SMC), using an ensemble of individual-based stochastic simulation models of P. falciparum dynamics. The models made various assumptions about immunity decay, transmission heterogeneity and were parameterized with data on both age-specific infection and disease incidence at different levels of exposure, on the durations of different stages of the parasite life-cycle and on human demography. Effects of transmission intensity, and of levels of access to malaria treatment were considered. While both PEV and SMC programmes are predicted to have overall strongly positive health effects, a shift of morbidity into older children is predicted to be induced by either programme if transmission levels remain static and not reduced by other interventions. Predicted shifting of burden continue into the second decade of the programme. Even if long-term surveillance is maintained it will be difficult to avoid mis-attribution of such long-term changes in age-specific morbidity patterns to other factors. Conversely, short-lived transient changes in incidence measured soon after introduction of a new intervention may give over-positive views of future impacts. Complementary intervention strategies could be designed to specifically protect those age-groups at risk from burden shift.

Transmission dynamics of vivax malaria in the republic of Korea: Effectiveness of anti-malarial mass chemoprophylaxis

BACKGROUND

Vivax malaria with two distinct (short- and long-term) incubation periods has been prevalent in the Republic of Korea since its re-emergence in 1993. As part of countermeasures, mass chemoprophylaxis has been conducted since 1997 among military personnel, a high risk group. To assess the population effectiveness of chemoprophylaxis, the time-dependent reproduction number was estimated in the present study.

METHODS

A renewal process has been employed, estimating the yearly effective reproduction number (Ry) from 1993 to 2012 using a maximum likelihood estimation method. Akaike Information Criterion (AIC) was computed to identify the best-fit model with a time-dependent trend that coincides with the timing of mass chemoprophylaxis.

RESULTS

The estimates of Ry revealed an overall declining trend from 1997 to 2012. Despite small fluctuations in 2005 and 2009, Ry was brought to be close to unity since 2000. An extrapolated model of the time-dependent reproduction number with the smallest AIC indicated that there was an abrupt decline in secondary transmission from 1997 to 1998.

CONCLUSION

The epidemic of vivax malaria in the Republic of Korea has been on the whole brought under control in the last decades. Mass chemoprophylaxis assisted the decline in secondary transmissions from its second year, which presumed to have reflected the effect of long incubation period and expansion of the coverage.

Schistosomiasis japonica: modelling as a tool to explore transmission patterns

Modelling is an important tool for the exploration of Schistosoma japonicum transmission patterns. It provides a general theoretical framework for decision-makers and lends itself specifically to assessing the progress of the national control programme by following the outcome of surveys. The challenge of keeping up with the many changes of social, ecological and environmental factors involved in control activities is greatly facilitated by modelling that can also indicate which activities are critical and which are less important. This review examines the application of modelling tools in the epidemiological study of schistosomiasis japonica during the last 20 years and explores the application of enhanced models for surveillance and response. Updated and timely information for decision-makers in the national elimination programme is provided but, in spite of the new modelling techniques introduced, many questions remain. Issues on application of modelling are discussed with the view to improve the current situation with respect to schistosomiasis japonica.

Modeling the cost effectiveness of malaria control interventions in the highlands of western Kenya

INTRODUCTION

Tools that allow for in silico optimization of available malaria control strategies can assist the decision-making process for prioritizing interventions. The OpenMalaria stochastic simulation modeling platform can be applied to simulate the impact of interventions singly and in combination as implemented in Rachuonyo South District, western Kenya, to support this goal.

METHODS

Combinations of malaria interventions were simulated using a previously-published, validated model of malaria epidemiology and control in the study area. An economic model of the costs of case management and malaria control interventions in Kenya was applied to simulation results and cost-effectiveness of each intervention combination compared to the corresponding simulated outputs of a scenario without interventions. Uncertainty was evaluated by varying health system and intervention delivery parameters.

RESULTS

The intervention strategy with the greatest simulated health impact employed long lasting insecticide treated net (LLIN) use by 80% of the population, 90% of households covered by indoor residual spraying (IRS) with deployment starting in April, and intermittent screen and treat (IST) of school children using Artemether lumefantrine (AL) with 80% coverage twice per term. However, the current malaria control strategy in the study area including LLIN use of 56% and IRS coverage of 70% was the most cost effective at reducing disability-adjusted life years (DALYs) over a five year period.

CONCLUSIONS

All the simulated intervention combinations can be considered cost effective in the context of available resources for health in Kenya. Increasing coverage of vector control interventions has a larger simulated impact compared to adding IST to the current implementation strategy, suggesting that transmission in the study area is not at a level to warrant replacing vector control to a school-based screen and treat program. These results have the potential to assist malaria control program managers in the study area in adding new or changing implementation of current interventions.

Seasonally dependent relationships between indicators of malaria transmission and disease provided by mathematical model simulations

Evaluating the effectiveness of malaria control interventions on the basis of their impact on transmission as well as impact on morbidity and mortality is becoming increasingly important as countries consider pre-elimination and elimination as well as disease control. Data on prevalence and transmission are traditionally obtained through resource-intensive epidemiological and entomological surveys that become difficult as transmission decreases. This work employs mathematical modeling to examine the relationships between malaria indicators allowing more easily measured data, such as routine health systems data on case incidence, to be translated into measures of transmission and other malaria indicators. Simulations of scenarios with different levels of malaria transmission, patterns of seasonality and access to treatment were run with an ensemble of models of malaria epidemiology and within-host dynamics, as part of the OpenMalaria modeling platform. For a given seasonality profile, regression analysis mapped simulation results of malaria indicators, such as annual average entomological inoculation rate, prevalence, incidence of uncomplicated and severe episodes, and mortality, to an expected range of values of any of the other indicators. Results were validated by comparing simulated relationships between indicators with previously published data on these same indicators as observed in malaria endemic areas. These results allow for direct comparisons of malaria transmission intensity estimates made using data collected with different methods on different indicators. They also address key concerns with traditional methods of quantifying transmission in areas of differing transmission intensity and sparse data. Although seasonality of transmission is often ignored in data compilations, the models suggest it can be critically important in determining the relationship between transmission and disease. Application of these models could help public health officials detect changes of disease dynamics in a population and plan and assess the impact of malaria control interventions.

While malaria is still a major public health problem in many parts of the world, control programs have greatly reduced the burden of disease in recent years and many countries are now considering the goal of elimination. Unfortunately, malaria transmission becomes more difficult to measure when it is low because traditional methods involve capturing mosquitoes; an expensive and time-consuming technique. To measure transmission in areas without adequate field data, we run simulations of a mathematical model of malaria over a range of transmission intensities and seasonal patterns to examine how different measurements of malaria (prevalence, clinical disease, and death) relate to each other, how they relate to transmission, and if the relationships are likely to vary by seasonal pattern of transmission. These simulated relationships allow us to translate easily measured data, such as clinical case incidence seen at health facilities, into estimates of transmission. This technique can help public health officials plan and assess the impact of malaria control interventions, even in areas without intensive research activities.

Needs for monitoring mosquito transmission of malaria in a pre-elimination world

As global efforts to eliminate malaria intensify, accurate information on vector populations and transmission dynamics is critical for directing control efforts, developing new control tools, and predicting the effects of these interventions under various conditions. Currently available sampling tools for mosquito population monitoring suffer from well-recognized limitations. As reported in this workshop summary, a recent gathering of medical entomologists, modelers, and malaria experts reviewed these issues and agreed that efforts are needed to improve methods to monitor key transmission parameters. Identified needs include standardized methods for sampling of both mosquito adults and larvae, improved tools for mosquito species identification and age-grading, and a better means for determining the entomological inoculation rate.

Estimating malaria transmission through mathematical models

Evaluating the effectiveness of malaria control interventions on the basis of their impact on transmission is increasingly important as countries move from malaria control to pre-elimination programs. Mathematical modeling can examine relationships between malaria indicators, allowing translation of easily measured data into measures of transmission, and addressing key concerns with traditional methods for quantifying transmission. Simulations show these indicators are statistically correlated, allowing direct comparisons of malaria transmission using data collected using different methods across a range of transmission intensities and seasonal patterns. Results from such models can provide public health officials with accurate estimates of transmission, by seasonal pattern, that are necessary for assessing and tailoring malaria control and elimination programs to specific settings.

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

Background

Agent-based models (ABMs) have been used to estimate the effects of malaria-control interventions. Early studies have shown the efficacy of larval source management (LSM) and insecticide-treated nets (ITNs) as vector-control interventions, applied both in isolation and in combination. However, the robustness of results can be affected by several important modelling assumptions, including the type of boundary used for landscapes, and the number of replicated simulation runs reported in results. Selection of the ITN coverage definition may also affect the predictive findings. Hence, by replication, independent verification of prior findings of published models bears special importance.

Methods

A spatially-explicit entomological ABM of Anopheles gambiae is used to simulate the resource-seeking process of mosquitoes in grid-based landscapes. To explore LSM and replicate results of an earlier LSM study, the original landscapes and scenarios are replicated by using a landscape generator tool, and 1,800 replicated simulations are run using absorbing and non-absorbing boundaries. To explore ITNs and evaluate the relative impacts of the different ITN coverage schemes, the settings of an earlier ITN study are replicated, the coverage schemes are defined and simulated, and 9,000 replicated simulations for three ITN parameters (coverage, repellence and mortality) are run. To evaluate LSM and ITNs in combination, landscapes with varying densities of houses and human populations are generated, and 12,000 simulations are run.

Results

General agreement with an earlier LSM study is observed when an absorbing boundary is used. However, using a non-absorbing boundary produces significantly different results, which may be attributed to the unrealistic killing effect of an absorbing boundary. Abundance cannot be completely suppressed by removing aquatic habitats within 300 m of houses. Also, with density-dependent oviposition, removal of insufficient number of aquatic habitats may prove counter-productive. The importance of performing large number of simulation runs is also demonstrated. For ITNs, the choice of coverage scheme has important implications, and too high repellence yields detrimental effects. When LSM and ITNs are applied in combination, ITNs’ mortality can play more important roles with higher densities of houses. With partial mortality, increasing ITN coverage is more effective than increasing LSM coverage, and integrating both interventions yields more synergy as the densities of houses increase.

Conclusions

Using a non-absorbing boundary and reporting average results from sufficiently large number of simulation runs are strongly recommended for malaria ABMs. Several guidelines (code and data sharing, relevant documentation, and standardized models) for future modellers are also recommended.

Effects of changing mosquito host searching behaviour on the cost effectiveness of a mass distribution of long-lasting, insecticidal nets: a modelling study

Background

The effectiveness of long-lasting, insecticidal nets (LLINs) in preventing malaria is threatened by the changing biting behaviour of mosquitoes, from nocturnal and endophagic to crepuscular and exophagic, and by their increasing resistance to insecticides.

Methods

Using epidemiological stochastic simulation models, we studied the impact of a mass LLIN distribution on Plasmodium falciparum malaria. Specifically, we looked at impact in terms of episodes prevented during the effective life of the batch and in terms of net health benefits (NHB) expressed in disability adjusted life years (DALYs) averted, depending on biting behaviour, resistance (as measured in experimental hut studies), and on pre-intervention transmission levels.

Results

Results were very sensitive to assumptions about the probabilistic nature of host searching behaviour. With a shift towards crepuscular biting, under the assumption that individual mosquitoes repeat their behaviour each gonotrophic cycle, LLIN effectiveness was far less than when individual mosquitoes were assumed to vary their behaviour between gonotrophic cycles. LLIN effectiveness was equally sensitive to variations in host-searching behaviour (if repeated) and to variations in resistance. LLIN effectiveness was most sensitive to pre-intervention transmission level, with LLINs being least effective at both very low and very high transmission levels, and most effective at around four infectious bites per adult per year. A single LLIN distribution round remained cost effective, except in transmission settings with a pre-intervention inoculation rate of over 128 bites per year and with resistant mosquitoes that displayed a high proportion (over 40%) of determined crepuscular host searching, where some model variants showed negative NHB.

Conclusions

Shifts towards crepuscular host searching behaviour can be as important in reducing LLIN effectiveness and cost effectiveness as resistance to pyrethroids. As resistance to insecticides is likely to slow down the development of behavioural resistance and vice versa, the two types of resistance are unlikely to occur within the same mosquito population. LLINs are likely cost effective interventions against malaria, even in areas with strong resistance to pyrethroids or where a large proportion of host-mosquito contact occurs during times when LLIN users are not under their nets.

The importance of mosquito behavioural adaptations to malaria control in Africa

Over the past decade the use of long-lasting insecticidal nets (LLINs), in combination with improved drug therapies, indoor residual spraying (IRS), and better health infrastructure, has helped reduce malaria in many African countries for the first time in a generation. However, insecticide resistance in the vector is an evolving threat to these gains. We review emerging and historical data on behavioral resistance in response to LLINs and IRS. Overall the current literature suggests behavioral and species changes may be emerging, but the data are sparse and, at times unconvincing. However, preliminary modeling has demonstrated that behavioral resistance could have significant impacts on the effectiveness of malaria control. We propose seven recommendations to improve understanding of resistance in malaria vectors. Determining the public health impact of physiological and behavioral insecticide resistance is an urgent priority if we are to maintain the significant gains made in reducing malaria morbidity and mortality.

Effects of pyrethroid resistance on the cost effectiveness of a mass distribution of long-lasting insecticidal nets: a modelling study

Background

The effectiveness of insecticide-treated nets in preventing malaria is threatened by developing resistance against pyrethroids. Little is known about how strongly this affects the effectiveness of vector control programmes.

Methods

Data from experimental hut studies on the effects of long-lasting, insecticidal nets (LLINs) on nine anopheline mosquito populations, with varying levels of mortality in World Health Organization susceptibility tests, were used to parameterize malaria models. Both simple static models predicting population-level insecticidal effectiveness and protection against blood feeding, and complex dynamic epidemiological models, where LLINs decayed over time, were used. The epidemiological models, implemented in OpenMalaria, were employed to study the impact of a single mass distribution of LLINs on malaria, both in terms of episodes prevented during the effective lifetime of the batch of LLINs, and in terms of net health benefits (NHB) expressed in disability-adjusted life years (DALYs) averted during that period, depending on net type (standard pyrethroid-only LLIN or pyrethroid-piperonyl butoxide combination LLIN), resistance status, coverage and pre-intervention transmission level.

Results

There were strong positive correlations between insecticide susceptibility status and predicted population level insecticidal effectiveness of and protection against blood feeding by LLIN intervention programmes. With the most resistant mosquito population, the LLIN mass distribution averted up to about 40% fewer episodes and DALYs during the effective lifetime of the batch than with fully susceptible populations. However, cost effectiveness of LLINs was more sensitive to the pre-intervention transmission level and coverage than to susceptibility status. For four out of the six Anopheles gambiae sensu lato populations where direct comparisons between standard LLINs and combination LLINs were possible, combination nets were more cost effective, despite being more expensive. With one resistant population, both net types were equally effective, and with one of the two susceptible populations, standard LLINs were more cost effective.

Conclusion

Despite being less effective when compared to areas with susceptible mosquito populations, standard and combination LLINs are likely to (still) be cost effective against malaria even in areas with strong pyrethroid resistance. Combination nets are likely to be more cost effective than standard nets in areas with resistant mosquito populations.

Modelling the cost-effectiveness of mass screening and treatment for reducing Plasmodium falciparum malaria burden

Background

Past experience and modelling suggest that, in most cases, mass treatment strategies are not likely to succeed in interrupting Plasmodium falciparum malaria transmission. However, this does not preclude their use to reduce disease burden. Mass screening and treatment (MSAT) is preferred to mass drug administration (MDA), as the latter involves massive over-use of drugs. This paper reports simulations of the incremental cost-effectiveness of well-conducted MSAT campaigns as a strategy for P. falciparum malaria disease-burden reduction in settings with varying receptivity (ability of the combined vector population in a setting to transmit disease) and access to case management.

Methods

MSAT incremental cost-effectiveness ratios (ICERs) were estimated in different sub-Saharan African settings using simulation models of the dynamics of malaria and a literature-based MSAT cost estimate. Imported infections were simulated at a rate of two per 1,000 population per annum. These estimates were compared to the ICERs of scaling up case management or insecticide-treated net (ITN) coverage in each baseline health system, in the absence of MSAT.

Results

MSAT averted most episodes, and resulted in the lowest ICERs, in settings with a moderate level of disease burden. At a low pre-intervention entomological inoculation rate (EIR) of two infectious bites per adult per annum (IBPAPA) MSAT was never more cost-effective than scaling up ITNs or case management coverage. However, at pre-intervention entomological inoculation rates (EIRs) of 20 and 50 IBPAPA and ITN coverage levels of 40 or 60%, respectively, the ICER of MSAT was similar to that of scaling up ITN coverage further.

Conclusions

In all the transmission settings considered, achieving a minimal level of ITN coverage is a “best buy”. At low transmission, MSAT probably is not worth considering. Instead, MSAT may be suitable at medium to high levels of transmission and at moderate ITN coverage. If undertaken as a burden-reducing intervention, MSAT should be continued indefinitely and should complement, not replace, case management and vector control interventions.

Simulation of malaria epidemiology and control in the highlands of Western Kenya

BACKGROUND

Models of Plasmodium falciparum malaria epidemiology that provide realistic quantitative predictions of likely epidemiological outcomes of existing vector control strategies have the potential to assist in planning for the control and elimination of malaria. This work investigates the applicability of mathematical modelling of malaria transmission dynamics in Rachuonyo South, a district with low, unstable transmission in the highlands of western Kenya.

METHODS

Individual-based stochastic simulation models of malaria in humans and a deterministic model of malaria in mosquitoes as part of the OpenMalaria platform were parameterized to create a scenario for the study area based on data from ongoing field studies and available literature. The scenario was simulated for a period of two years with a population of 10,000 individuals and validated against malaria survey data from Rachuonyo South. Simulations were repeated with multiple random seeds and an ensemble of 14 model variants to address stochasticity and model uncertainty. A one-dimensional sensitivity analysis was conducted to address parameter uncertainty.

RESULTS

The scenario was able to reproduce the seasonal pattern of the entomological inoculation rate (EIR) and patent infections observed in an all-age cohort of individuals sampled monthly for one year. Using an EIR estimated from serology to parameterize the scenario resulted in a closer fit to parasite prevalence than an EIR estimated using entomological methods. The scenario parameterization was most sensitive to changes in the timing and effectiveness of indoor residual spraying (IRS) and the method used to detect P. falciparum in humans. It was less sensitive than expected to changes in vector biting behaviour and climatic patterns.

CONCLUSIONS

The OpenMalaria model of P. falciparum transmission can be used to simulate the impact of different combinations of current and potential control interventions to help plan malaria control in this low transmission setting. In this setting and for these scenarios, results were highly sensitive to transmission, vector exophagy, exophily and susceptibility to IRS, and the detection method used for surveillance. The level of accuracy of the results will thus depend upon the precision of estimates for each. New methods for analysing and evaluating uncertainty in simulation results will enhance the usefulness of simulations for malaria control decision-making. Improved measurement tools and increased primary data collection will enhance model parameterization and epidemiological monitoring. Further research is needed on the relationship between malaria indices to identify the best way to quantify transmission in low transmission settings. Measuring EIR through mosquito collection may not be the optimal way to estimate transmission intensity in areas with low, unstable transmission.

The time distribution of sulfadoxine-pyrimethamine protection from malaria

Sulfadoxine-pyrimethamine (SP) has been one of the most widely used antimalarial treatments world-wide, and is also used prophylactically in vulnerable populations. In this paper, we develop a mathematical model which allows us to infer the time distribution of SP protection from drug-trial data. Fitting our model to data from a controlled field study in Mali, we find that SP provided protection from malaria for an average of 37.9 days in this pediatric population. We demonstrate that the duration of SP protection is not well described by an exponential distribution, and in fact has a much narrower dispersal about the mean; the best-fit standard deviation predicted by our model was only 17.0 days, as opposed to 41.8 days for the exponential model. We estimate the monthly entomological inoculation rate and the basic reproductive number for malaria in this population, and demonstrate that extremely high SP treatment rates would be necessary to maintain an effective reproductive number below one throughout a single rainy season. These results have implications for further efforts to model the impact of SP treatment, or for investigations of the optimal timing of prophylactic SP.

Mathematical modeling of biological systems

Mathematical and computational models are increasingly used to help interpret biomedical data produced by high-throughput genomics and proteomics projects. The application of advanced computer models enabling the simulation of complex biological processes generates hypotheses and suggests experiments. Appropriately interfaced with biomedical databases, models are necessary for rapid access to, and sharing of knowledge through data mining and knowledge discovery approaches.

Importance of factors determining the effective lifetime of a mass, long-lasting, insecticidal net distribution: a sensitivity analysis

BACKGROUND

Long-lasting insecticidal nets (LLINs) reduce malaria transmission by protecting individuals from infectious bites, and by reducing mosquito survival. In recent years, millions of LLINs have been distributed across sub-Saharan Africa (SSA). Over time, LLINs decay physically and chemically and are destroyed, making repeated interventions necessary to prevent a resurgence of malaria. Because its effects on transmission are important (more so than the effects of individual protection), estimates of the lifetime of mass distribution rounds should be based on the effective length of epidemiological protection.

METHODS

Simulation models, parameterised using available field data, were used to analyse how the distribution's effective lifetime depends on the transmission setting and on LLIN characteristics. Factors considered were the pre-intervention transmission level, initial coverage, net attrition, and both physical and chemical decay. An ensemble of 14 stochastic individual-based model variants for malaria in humans was used, combined with a deterministic model for malaria in mosquitoes.

RESULTS

The effective lifetime was most sensitive to the pre-intervention transmission level, with a lifetime of almost 10 years at an entomological inoculation rate of two infectious bites per adult per annum (ibpapa), but of little more than 2 years at 256 ibpapa. The LLIN attrition rate and the insecticide decay rate were the next most important parameters. The lifetime was surprisingly insensitive to physical decay parameters, but this could change as physical integrity gains importance with the emergence and spread of pyrethroid resistance.

CONCLUSIONS

The strong dependency of the effective lifetime on the pre-intervention transmission level indicated that the required distribution frequency may vary more with the local entomological situation than with LLIN quality or the characteristics of the distribution system. This highlights the need for malaria monitoring both before and during intervention programmes, particularly since there are likely to be strong variations between years and over short distances. The majority of SSA's population falls into exposure categories where the lifetime is relatively long, but because exposure estimates are highly uncertain, it is necessary to consider subsequent interventions before the end of the expected effective lifetime based on an imprecise transmission measure.