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The authors have declared that no competing interests exist.

Neglected tropical diseases affect more than one billion people worldwide. The populations most impacted by such diseases are typically the most resource-limited. Mathematical modeling of disease transmission and cost-effectiveness analyses can play a central role in maximizing the utility of limited resources for neglected tropical diseases. We review the contributions that mathematical modeling has made to optimizing intervention strategies of vector-borne neglected diseases. We propose directions forward in the modeling of these diseases, including integrating new knowledge of vector and pathogen ecology, incorporating evolutionary responses to interventions, and expanding the scope of sensitivity analysis in order to achieve robust results.

Mathematical modeling of vector-borne infectious diseases originated with Sir Ronald Ross's study of malaria transmission in 1916

The use of mathematical models has been gaining momentum in recent decades. Models are being used to address an ever-expanding number of diseases and public health questions, as well as to explore the importance of biological and ecological details on disease transmission

We searched PubMed, Web of Science, and SciELO using the terms “mathematical model”, “modeling”, “cost-effectiveness analysis”, and “economic analysis”. For the theoretical literature, we included studies that, in our opinion, addressed important technicalities of mathematical models applied to infectious diseases, including, for example, dynamic modeling, sensitivity analysis, and cost-effectiveness analysis. Modeling analyses conducted for diseases not considered to be neglected vector-borne diseases were excluded. We report on studies that evaluate the impact of interventions on vector-borne neglected tropical diseases.

Model development involves several steps and considerations. Once the modeler identifies the essential components of the biological processes necessary to address the questions of interest, the information needs to be translated into equations that describe the transmission dynamics. The most popular mathematical model is the SIR model, which divides hosts into compartments on the basis of whether they are susceptible, infectious, or recovered/immune (

Schematic representation, differential equations, and plot for the basic SIR (susceptible, infectious, and recovered) model. Model parameters are

Model parameterization can be achieved using published studies and from fitting a model to observed data

Multivariate sensitivity analysis consists of simultaneously measuring the impact of multiple parameters. One approach for multivariate sensitivity analysis is through Monte Carlo simulations. For this procedure, probability distributions are assigned to parameters and the values of those parameters are sampled repeatedly from these distributions. Model simulations with each set of these parameters are then computed to generate a distribution of model outcomes from which summary statistics can be calculated. Statistical regression models can then be used to determine which parameters most strongly influence model outcome

Mathematical models and cost-effectiveness analysis have been used to assess the impact of various control strategies for a wide range of neglected tropical diseases, which we review here.

Many neglected vector-borne diseases can be treated and controlled with drugs

Vector control _{0}) is the number of secondary infections generated from a single infected individual introduced into a susceptible population. In order to curtail transmission, vector control efforts need to decrease the value of _{0} below the critical value of 1. For example, _{0} was used to determine the extent of vector control necessary to eliminate the transmission of Chagas disease in Brazil _{0} for Chagas disease in Brazil is 1.25, it was shown that a 25% increase in vector control mortality induced by insecticides was sufficient to reduce _{0} below 1. Nonetheless, a differential equation model showed that a vector control strategy that reduced _{0} just below 1 would require more than half a century to achieve disease eradication due to disease persistence in chronically infected individuals.

Two models incorporating vector control have also evaluated insecticide-based vector control strategies for dengue prevention

Field evaluations have shown that resistance evolution currently threatens dengue vector control strategies

One of the most significant obstacles to the implementation of optimal vaccination policies is public adherence to recommendations. Concerns about risks of vaccinations, whether real or perceived

When the risk of serious adverse events from vaccination and infection were taken into account, actual vaccination levels were predicted to be lower than the vaccination levels required to prevent an outbreak

Models can be used to evaluate the benefit of innovative control strategies before devoting resources to the actual development and implementation. For example, a mathematical model of onchocerciasis transmission was used to evaluate the impact of a hypothetical macrofilaricidal drug

Other studies have assessed the potential impact of zooprophylaxis interventions, that is, the use of animals resistant against disease to divert bites from humans, with regard to the household transmission of Chagas disease

Another promising avenue for the control of vector-borne disease is through the genetic manipulation of vectors, an approach that could be used synergistically with current control strategies

Transgenic strategies can be categorized as strategies that block transmission, either from humans to mosquitoes or from mosquitoes to humans; strategies that reduce mosquito biting by interfering with host-seeking behavior; strategies that raise overall mosquito mortality, i.e., through the release of engineered males homozygous for a dominant female-killing gene; or strategies that raise mosquito infection-induced mortality, i.e., lethal genes only expressed in the presence of infection. The evolutionary impact of these different transgenic strategies must be incorporated to fully evaluate the benefits, risks, and research priorities associated with using genetically manipulated insects to control vector-borne diseases

Given that pathogens rapidly evolve to evade interventions, the greatest promise for successful long-term control of vector-borne disease may be a combined approach. The optimal combination of control strategies can be assessed with mathematical models. The dynamic aspect of all infectious diseases lends itself to adaptive responses, which may translate into different optimal combinations of interventions in different locations or at different times.

A modeling study evaluated the duration of mass treatment, drug coverage, the added benefit of vector control, and the possibility of resistance to drugs used in the mass drug administration program for the control of lymphatic filariasis

A more complex model incorporating host age-structured and vector transmission dynamics was used to estimate the impact of intervention strategies that consider two community-based interventions for filariasis control, vector control, and/or single-dose mass chemotherapy

Traditional cost-effectiveness analyses that compare the relative costs and effects of competing health interventions have been conducted for some neglected vector-borne diseases. For example, vector control of Chagas disease through residual spraying was shown to be highly cost-effective in Guatemala

Other examples of traditional cost-effectiveness studies are the analyses of drug schemes and of diagnostic/therapeutic strategies that were assessed for visceral leishmaniasis

A traditional cost-effectiveness analysis of vector control interventions has also been carried out for dengue in urban areas of Cambodia. Insecticide-based larval control performed twice a year was found to be cost-effective in reducing dengue burden

We have come a long way since Ronald Ross's early seminal work. However, the increasing availability of complex data poses additional challenges regarding their efficient use by expanding the modeler's horizons into new micro and macro model structures. Recent advances in molecular biology and genetics provide new tools to monitor micro diversity among pathogens and vertebrate and invertebrate hosts. On the other extreme, spatial and social dimensions push the limits of heterogeneities at the macro level. Although macro heterogeneity has received more attention in the past from modelers

Complex models, where spatial structure, seasonal “forcing”, and/or stochasticity influence the dynamics and the impact of interventions, and where computer simulation needs to be used to generate theory, must be reliable and precise in order to be trusted by the scientific community. Improvements in model sensitivity analysis, validation and diagnostics against independent data, and the availability of alternative model fitting techniques based on Monte Carlo or resampling methods, along with the power of today's computing platforms, are expected to fulfill the demand for formal estimation procedures of confidence intervals for model parameters and predictions

Another important future direction is the merger of cost-effectiveness analysis with models of transmission dynamics to address both the short- and long-term impact of resource allocation, while also addressing parameter and model uncertainty

Indeed, the future directions of modeling pose an interesting challenge. As the field of modeling expands, taking into account biological and ecological details, incorporating dynamic and evolutionary aspects, considering the short- and long-term benefits and consequences, and incorporating uncertainty in parameters and predictions, the need to clearly and properly state a model's results and predictions becomes paramount so that the insights may inform policy.

Mathematical modeling and cost-effectiveness analysis are essential tools for addressing research questions related to the control of neglected vector-borne diseases. Modelers need to take into consideration a variety of factors, such as pathogen and vector evolution, combined intervention strategies, novel interventions, and the temporal dynamics of disease transmission in order to accurately estimate the benefits and costs of interventions, as well as to predict outcomes.

We have outlined approaches to model parameterization and sensitivity analysis that are fundamental to the interpretation of modeling results. We argue that sensitivity analyses are necessary to handle uncertainty in disease systems, including our incomplete knowledge of “true” parameter values. However, it is important to keep in mind that models should only be as complicated as needed to avoid unnecessary “pseudo-realism” derived from complex models that cannot be parameterized

We advocate the use of mathematical models in the analysis of control programs. Several steps in this process are active areas of research, notably the merging of transmission dynamics with cost-effectiveness analysis. As a future trend, we anticipate an increasing partnership between theoretical and field researchers. Such interactions would facilitate the development of a data-driven model that could offer practical guidance to inform policy decisions.

The dynamics of an infectious disease in a population and the impact of control measures are not necessarily intuitive because of the dependence structure of transmission of pathogens between individuals through vectors, which gives rise to nonlinear dynamics.

Quantitative methods, including mathematical models and cost-effectiveness analysis, can help understand nonlinearities, aid prediction of future dynamics, and allow comparisons among competing control strategies.

Control strategies targeting the pathogen, such as drug administration, or the vector, such as insecticide control, can lead to resistance and/or virulence evolution. These factors should be acknowledged in evaluating the long-term impact of control strategies.

Increasingly, data on pathogen diversity will become available, allowing for more realistic models. Control measures, such as vaccination or mass drug administration, can change pathogen diversity.

Merging transmission dynamics modeling with cost-effectiveness analysis allows for the short- and long-term assessment of optimal control strategies.

“Mathematical models of disease transmission” by N. C. Grassly and C. Fraser

“Uses and abuses of mathematics in biology” by R. M. May

“Evaluating the cost-effectiveness of vaccination programmes: a dynamic perspective” by W. J. Edmunds, G. F. Medley, and D. J. Nokes

“Uncertainty and sensitivity analyses of a dynamic economic evaluation model for vaccination programs” by R. J. D. Tebbens et al.

“Antibiotic and insecticide resistance modeling–is it time to start talking?” by S. L. Peck

Translation of the Abstract into Portuguese by Paula Mendes Luz

(0.03 MB DOC)

We would like to thank Angie Hoffman for editorial assistance.