Brajendra K. Singh

A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970-2010

Mathematical models of mosquito-borne pathogen transmission originated in the early twentieth century to provide insights into how to most effectively combat malaria. The foundations of the Ross–Macdonald theory were established by 1970. Since then, there has been a growing interest in reducing the public health burden of mosquito-borne pathogens and an expanding use of models to guide their control. To assess how theory has changed to confront evolving public health challenges, we compiled a bibliography of 325 publications from 1970 through 2010 that included at least one mathematical model of mosquito-borne pathogen transmission and then used a 79-part questionnaire to classify each of 388 associated models according to its biological assumptions. As a composite measure to interpret the multidimensional results of our survey, we assigned a numerical value to each model that measured its similarity to 15 core assumptions of the Ross–Macdonald model. Although the analysis illustrated a growing acknowledgement of geographical, ecological and epidemiological complexities in modelling transmission, most models during the past 40 years closely resemble the Ross–Macdonald model. Modern theory would benefit from an expansion around the concepts of heterogeneous mosquito biting, poorly mixed mosquito-host encounters, spatial heterogeneity and temporal variation in the transmission process.

Recasting the theory of mosquito-borne pathogen transmission dynamics and control

Mosquito-borne diseases pose some of the greatest challenges in public health, especially in tropical and sub-tropical regions of the world. Efforts to control these diseases have been underpinned by a theoretical framework developed for malaria by Ross and Macdonald, including models, metrics for measuring transmission, and theory of control that identifies key vulnerabilities in the transmission cycle. That framework, especially Macdonalds formula for R0 and its entomological derivative, vectorial capacity, are now used to study dynamics and design interventions for many mosquito-borne diseases. A systematic review of 388 models published between 1970 and 2010 found that the vast majority adopted the Ross–Macdonald assumption of homogeneous transmission in a well-mixed population. Studies comparing models and data question these assumptions and point to the capacity to model heterogeneous, focal transmission as the most important but relatively unexplored component in current theory. Fine-scale heterogeneity causes transmission dynamics to be nonlinear, and poses problems for modeling, epidemiology and measurement. Novel mathematical approaches show how heterogeneity arises from the biology and the landscape on which the processes of mosquito biting and pathogen transmission unfold. Emerging theory focuses attention on the ecological and social context for mosquito blood feeding, the movement of both hosts and mosquitoes, and the relevant spatial scales for measuring transmission and for modeling dynamics and control.

Epidemiological inference for partially observed epidemics: The example of the 2001 foot and mouth epidemic in Great Britain

This paper develops a statistical framework for a retrospective analysis for well-observed livestock epidemics during which intervention policies may conceal cases, thus potentially biasing naively derived parameter and final size estimates. We apply the methods to the 2001 foot and mouth epidemic (FMD) in Great Britain, during which a large number of farms (about 7500) were pre-emptively culled as part of the control effort without ever being diagnosed as being infected. We infer farm-level infectivity and susceptibility parameters, a distribution for the delay from infection to report, together with a time varying farm infectivity profile for farms. Hidden infections among proactively culled farms were accounted for using a data augmentation approach utilising reversible jump MCMC methods. Simulated epidemics derived using the parameter estimates obtained reproduced the 2001 epidemic well. Our analysis demonstrates that time-varying infectivity profiles fit the 2001 data better than naive assumptions of constant infectiousness. We estimate that around 210 (or 2.8%) of the farms proactively culled in the 2001 epidemic were infected. However, for the parameter estimated obtained, preliminary simulation results indicate that had contiguous culling not been applied in 2001, the epidemic might have been substantially larger.

Quantitative analyses and modelling to support achievement of the 2020 goals for nine neglected tropical diseases

Quantitative analysis and mathematical models are useful tools in informing strategies to control or eliminate disease. Currently, there is an urgent need to develop these tools to inform policy to achieve the 2020 goals for neglected tropical diseases (NTDs). In this paper we give an overview of a collection of novel model-based analyses which aim to address key questions on the dynamics of transmission and control of nine NTDs: Chagas disease, visceral leishmaniasis, human African trypanosomiasis, leprosy, soil-transmitted helminths, schistosomiasis, lymphatic filariasis, onchocerciasis and trachoma. Several common themes resonate throughout these analyses, including: the importance of epidemiological setting on the success of interventions; targeting groups who are at highest risk of infection or re-infection; and reaching populations who are not accessing interventions and may act as a reservoir for infection,. The results also highlight the challenge of maintaining elimination ‘as a public health problem’ when true elimination is not reached. The models elucidate the factors that may be contributing most to persistence of disease and discuss the requirements for eventually achieving true elimination, if that is possible. Overall this collection presents new analyses to inform current control initiatives. These papers form a base from which further development of the models and more rigorous validation against a variety of datasets can help to give more detailed advice. At the moment, the models’ predictions are being considered as the world prepares for a final push towards control or elimination of neglected tropical diseases by 2020.

Bayesian calibration of simulation models for supporting management of the elimination of the macroparasitic disease, Lymphatic Filariasis

BackgroundMathematical models of parasite transmission can help integrate a large body of information into a consistent framework, which can then be used for gaining mechanistic insights and making predictions. However, uncertainty, spatial variability and complexity, can hamper the use of such models for decision making in parasite management programs.MethodsWe have adapted a Bayesian melding framework for calibrating simulation models to address the need for robust modelling tools that can effectively support management of lymphatic filariasis (LF) elimination in diverse endemic settings. We applied this methodology to LF infection and vector biting data from sites across the major LF endemic regions in order to quantify model parameters, and generate reliable predictions of infection dynamics along with credible intervals for modelled output variables. We used the locally calibrated models to estimate breakpoint values for various indicators of parasite transmission, and simulate timelines to parasite extinction as a function of local variations in infection dynamics and breakpoints, and effects of various currently applied and proposed LF intervention strategies.ResultsWe demonstrate that as a result of parameter constraining by local data, breakpoint values for all the major indicators of LF transmission varied significantly between the sites investigated. Intervention simulations using the fitted models showed that as a result of heterogeneity in local transmission and extinction dynamics, timelines to parasite elimination in response to the current Mass Drug Administration (MDA) and various proposed MDA with vector control strategies also varied significantly between the study sites. Including vector control, however, markedly reduced the duration of interventions required to achieve elimination as well as decreased the risk of recrudescence following stopping of MDA.ConclusionsWe have demonstrated how a Bayesian data-model assimilation framework can enhance the use of transmission models for supporting reliable decision making in the management of LF elimination. Extending this framework for delivering predictions in settings either lacking or with only sparse data to inform the modelling process, however, will require development of procedures to estimate and use spatio-temporal variations in model parameters and inputs directly, and forms the next stage of the work reported here.

Heterogeneous dynamics, robustness/fragility trade-offs, and the eradication of the macroparasitic disease, lymphatic filariasis

BackgroundThe current WHO-led initiative to eradicate the macroparasitic disease, lymphatic filariasis (LF), based on single-dose annual mass drug administration (MDA) represents one of the largest health programs devised to reduce the burden of tropical diseases. However, despite the advances made in instituting large-scale MDA programs in affected countries, a challenge to meeting the goal of global eradication is the heterogeneous transmission of LF across endemic regions, and the impact that such complexity may have on the effort required to interrupt transmission in all socioecological settings.MethodsHere, we apply a Bayesian computer simulation procedure to fit transmission models of LF to field data assembled from 18 sites across the major LF endemic regions of Africa, Asia and Papua New Guinea, reflecting different ecological and vector characteristics, to investigate the impacts and implications of transmission heterogeneity and complexity on filarial infection dynamics, system robustness and control.ResultsWe find firstly that LF elimination thresholds varied significantly between the 18 study communities owing to site variations in transmission and initial ecological parameters. We highlight how this variation in thresholds lead to the need for applying variable durations of interventions across endemic communities for achieving LF elimination; however, a major new result is the finding that filarial population responses to interventions ultimately reflect outcomes of interplays between dynamics and the biological architectures and processes that generate robustness/fragility trade-offs in parasite transmission. Intervention simulations carried out in this study further show how understanding these factors is also key to the design of options that would effectively eliminate LF from all settings. In this regard, we find how including vector control into MDA programs may not only offer a countermeasure that will reliably increase system fragility globally across all settings and hence provide a control option robust to differential locality-specific transmission dynamics, but by simultaneously reducing transmission regime variability also permit more reliable macroscopic predictions of intervention effects.ConclusionsOur results imply that a new approach, combining adaptive modelling of parasite transmission with the use of biological robustness as a design principle, is required if we are to both enhance understanding of complex parasitic infections and delineate options to facilitate their elimination effectively.

Effectiveness of a triple-drug regimen for global elimination of lymphatic filariasis: a modelling study

BACKGROUND Lymphatic filariasis is targeted for elimination as a public health problem by 2020. The principal approach used by current programmes is annual mass drug administration with two pairs of drugs with a good safety profile. However, one dose of a triple-drug regimen (ivermectin, diethylcarbamazine, and albendazole) has been shown to clear the transmissible stage of the helminth completely in treated individuals. The aim of this study was to use modelling to assess the potential value of mass drug administration with the triple-drug regimen for accelerating elimination of lymphatic filariasis in different epidemiological settings. METHODS We used three different transmission models to compare the number of rounds of mass drug administration needed to achieve a prevalence of microfilaraemia less than 1% with the triple-drug regimen and with current two-drug regimens. FINDINGS In settings with a low baseline prevalence of lymphatic filariasis (5%), the triple-drug regimen reduced the number of rounds of mass drug administration needed to reach the target prevalence by one or two rounds, compared with the two-drug regimen. For areas with higher baseline prevalence (10-40%), the triple-drug regimen strikingly reduced the number of rounds of mass drug administration needed, by about four or five, but only at moderate-to-high levels of population coverage (>65%) and if systematic non-adherence to mass drug administration was low. INTERPRETATION Simulation modelling suggests that the triple-drug regimen has potential to accelerate the elimination of lymphatic filariasis if high population coverage of mass drug administration can be achieved and if systematic non-adherence with mass drug administration is low. Future work will reassess these estimates in light of more clinical trial data and to understand the effect on an individual countrys programme. FUNDING Bill & Melinda Gates Foundation.

Sequential Modelling of the Effects of Mass Drug Treatments on Anopheline-Mediated Lymphatic Filariasis Infection in Papua New Guinea

Background Lymphatic filariasis (LF) has been targeted by the WHO for global eradication leading to the implementation of large scale intervention programs based on annual mass drug administrations (MDA) worldwide. Recent work has indicated that locality-specific bio-ecological complexities affecting parasite transmission may complicate the prediction of LF extinction endpoints, casting uncertainty on the achievement of this initiative. One source of difficulty is the limited quantity and quality of data used to parameterize models of parasite transmission, implying the important need to update initially-derived parameter values. Sequential analysis of longitudinal data following annual MDAs will also be important to gaining new understanding of the persistence dynamics of LF. Here, we apply a Bayesian statistical-dynamical modelling framework that enables assimilation of information in human infection data recorded from communities in Papua New Guinea that underwent annual MDAs, into our previously developed model of parasite transmission, in order to examine these questions in LF ecology and control. Results Biological parameters underlying transmission obtained by fitting the model to longitudinal data remained stable throughout the study period. This enabled us to reliably reconstruct the observed baseline data in each community. Endpoint estimates also showed little variation. However, the updating procedure showed a shift towards higher and less variable values for worm kill but not for any other drug-related parameters. An intriguing finding is that the stability in key biological parameters could be disrupted by a significant reduction in the vector biting rate prevailing in a locality. Conclusions Temporal invariance of biological parameters in the face of intervention perturbations indicates a robust adaptation of LF transmission to local ecological conditions. The results imply that understanding the mechanisms that underlie locally adapted transmission dynamics will be integral to identifying points of system fragility, and thus countermeasures to reliably facilitate LF extinction both locally and globally.

The Allee Effect and Elimination of Neglected Tropical Diseases: A Mathematical Modelling Study

Elimination and control programmes for neglected tropical diseases (NTDs) are underway around the world, yet they are generally informed by epidemiological modelling only to a rudimentary degree. Chief among the modelling-derived predictors of disease emergence or controllability is the basic reproduction number R0. The ecological systems of several of the NTDs include density-dependent processes--which alter the rate of e.g. parasite establishment or fecundity--that complicate the calculation of R0. Here we show how the forms of the density-dependent functions for a model of the NTD lymphatic filariasis affect the effective reproduction number Reff. We construct infection transmission models containing various density-dependent functions and show how they alter the shape of the Reff profile, affecting two important epidemiological outcome variables that relate to elimination and control programmes: the parasite transmission breakpoint (or extinction threshold) and the reproduction fitness, as measured by Reff. The current drive to control, eliminate or eradicate several parasitic infections would be substantially aided by the existence of ecological Allee effects. For these control programmes, the findings of this paper are encouraging, since a single positive density dependency (DD) can introduce a reasonable chance of achieving elimination; however, there are diminishing returns to additional positive DDs.

Sero-Prevalence and Incidence of A/H1N1 2009 Influenza Infection in Scotland in Winter 2009–2010

Background Sero-prevalence is a valuable indicator of prevalence and incidence of A/H1N1 2009 infection. However, raw sero-prevalence data must be corrected for background levels of cross-reactivity (i.e. imperfect test specificity) and the effects of immunisation programmes. Methods and Findings We obtained serum samples from a representative sample of 1563 adults resident in Scotland between late October 2009 and April 2010. Based on a microneutralisation assay, we estimate that 44% (95% confidence intervals (CIs): 40–47%) of the adult population of Scotland were sero-positive for A/H1N1 2009 influenza by 1 March 2010. Correcting for background cross-reactivity and for recorded vaccination rates by time and age group, we estimated that 34% (27–42%) were naturally infected with A/H1N1 2009 by 1 March 2010. The central estimate increases to >40% if we allow for imperfect test sensitivity. Over half of these infections are estimated to have occurred during the study period and the incidence of infection in late October 2009 was estimated at 4.3 new infections per 1000 people per day (1.2 to 7.2), falling close to zero by April 2010. The central estimate increases to over 5.0 per 1000 if we allow for imperfect test specificity. The rate of infection was higher for younger adults than older adults. Raw sero-prevalences were significantly higher in more deprived areas (likelihood ratio trend statistic = 4.92,1 df, P = 0.03) but there was no evidence of any difference in vaccination rates. Conclusions We estimate that almost half the adult population of Scotland were sero-positive for A/H1N1 2009 influenza by early 2010 and that the majority of these individuals (except in the oldest age classes) sero-converted as a result of natural infection with A/H1N1 2009. Public health planning should consider the possibility of higher rates of infection with A/H1N1 2009 influenza in more deprived areas.