Prioritization-Driven Congestion Control in Networks for the Internet of Medical Things: A Cross-Layer Proposal.

Real-life implementation of the Internet of Things (IoT) in healthcare requires sufficient quality of service (QoS) to transmit the collected data successfully. However, unsolved challenges in prioritization and congestion issues limit the functionality of IoT networks by increasing the likelihood of packet loss, latency, and high-power consumption in healthcare systems. This study proposes a priority-based cross-layer congestion control protocol called QCCP, which is managed by communication devices' transport and medium access control (MAC) layers. Unlike existing methods, the novelty of QCCP is how it estimates and resolves wireless channel congestion because it does not generate control packets, operates in a distributed manner, and only has a one-bit overhead. Furthermore, at the same time, QCCP offers packet scheduling considering each packet's network load and QoS. The results of the experiments demonstrated that with a 95% confidence level, QCCP achieves sufficient performance to support the QoS requirements for the transmission of health signals. Finally, the comparison study shows that QCCP outperforms other TCP protocols, with 64.31% higher throughput, 18.66% less packet loss, and 47.87% less latency.

A review of deep learning applications for genomic selection.

BACKGROUND: Several conventional genomic Bayesian (or no Bayesian) prediction methods have been proposed including the standard additive genetic effect model for which the variance components are estimated with mixed model equations. In recent years, deep learning (DL) methods have been considered in the context of genomic prediction. The DL methods are nonparametric models providing flexibility to adapt to complicated associations between data and output with the ability to adapt to very complex patterns. MAIN BODY: We review the applications of deep learning (DL) methods in genomic selection (GS) to obtain a meta-picture of GS performance and highlight how these tools can help solve challenging plant breeding problems. We also provide general guidance for the effective use of DL methods including the fundamentals of DL and the requirements for its appropriate use. We discuss the pros and cons of this technique compared to traditional genomic prediction approaches as well as the current trends in DL applications. CONCLUSIONS: The main requirement for using DL is the quality and sufficiently large training data. Although, based on current literature GS in plant and animal breeding we did not find clear superiority of DL in terms of prediction power compared to conventional genome based prediction models. Nevertheless, there are clear evidences that DL algorithms capture nonlinear patterns more efficiently than conventional genome based. Deep learning algorithms are able to integrate data from different sources as is usually needed in GS assisted breeding and it shows the ability for improving prediction accuracy for large plant breeding data. It is important to apply DL to large training-testing data sets.

A guide for kernel generalized regression methods for genomic-enabled prediction.

The primary objective of this paper is to provide a guide on implementing Bayesian generalized kernel regression methods for genomic prediction in the statistical software R. Such methods are quite efficient for capturing complex non-linear patterns that conventional linear regression models cannot. Furthermore, these methods are also powerful for leveraging environmental covariates, such as genotype × environment (G×E) prediction, among others. In this study we provide the building process of seven kernel methods: linear, polynomial, sigmoid, Gaussian, Exponential, Arc-cosine 1 and Arc-cosine L. Additionally, we highlight illustrative examples for implementing exact kernel methods for genomic prediction under a single-environment, a multi-environment and multi-trait framework, as well as for the implementation of sparse kernel methods under a multi-environment framework. These examples are followed by a discussion on the strengths and limitations of kernel methods and, subsequently by conclusions about the main contributions of this paper.

Using an incomplete block design to allocate lines to environments improves sparse genome-based prediction in plant breeding.

Genomic selection (GS) is a predictive methodology that trains statistical machine-learning models with a reference population that is used to perform genome-enabled predictions of new lines. In plant breeding, it has the potential to increase the speed and reduce the cost of selection. However, to optimize resources, sparse testing methods have been proposed. A common approach is to guarantee a proportion of nonoverlapping and overlapping lines allocated randomly in locations, that is, lines appearing in some locations but not in all. In this study we propose using incomplete block designs (IBD), principally, for the allocation of lines to locations in such a way that not all lines are observed in all locations. We compare this allocation with a random allocation of lines to locations guaranteeing that the lines are allocated to the same number of locations as under the IBD design. We implemented this benchmarking on several crop data sets under the Bayesian genomic best linear unbiased predictor (GBLUP) model, finding that allocation under the principle of IBD outperformed random allocation by between 1.4% and 26.5% across locations, traits, and data sets in terms of mean square error. Although a wide range of performance improvements were observed, our results provide evidence that using IBD for the allocation of lines to locations can help improve predictive performance compared with random allocation. This has the potential to be applied to large-scale plant breeding programs.

Comparing gradient boosting machine and Bayesian threshold BLUP for genome-based prediction of categorical traits in wheat breeding.

Genomic selection (GS) is a predictive methodology that is changing plant breeding. Genomic selection trains a statistical machine-learning model using available phenotypic and genotypic data with which predictions are performed for individuals that were only genotyped. For this reason, some statistical machine-learning methods are being implemented in GS, but in order to improve the selection of new genotypes early in the prediction process, the exploration of new statistical machine-learning algorithms must continue. In this paper, we performed a benchmarking study between the Bayesian threshold genomic best linear unbiased predictor model (TGBLUP; popular in GS) and the gradient boosting machine (GBM). This comparison was done using four real wheat (Triticum aestivum L.) data sets with categorical traits measured in terms of two metrics: the proportion of cases correctly classified (PCCC) and the Kappa coefficient in the testing set. Under 10 random partitions with four different sizes of testing proportions (20, 40, 60, and 80%), we compared the two algorithms and found that in three of the four data sets, the GBM outperformed the TGBLUP model in terms of both metrics (PCCC and Kappa coefficient). In the larger data sets (Data Sets 3 and 4), the gain in terms of prediction accuracy of the GBM was considerably significant. For this reason, we encourage more research using the GBM in GS to evaluate its virtues in terms of prediction performance in the context of GS.

Genomic-enabled prediction was used for categorical traits to capture data patterns in different environments. Two different genome-based models were used for predicting categorical traits. Genome-based prediction with genotype × environment interaction was used.

Accounting for Correlation Between Traits in Genomic Prediction.

Genomic enabled prediction is playing a key role for the success of genomic selection (GS). However, according to the No Free Lunch Theorem, there is not a universal model that performs well for all data sets. Due to this, many statistical and machine learning models are available for genomic prediction. When multitrait data is available, models that are able to account for correlations between phenotypic traits are preferred, since these models help increase the prediction accuracy when the degree of correlation is moderate to large. For this reason, in this chapter we review multitrait models for genome-enabled prediction and we illustrate the power of this model with real examples. In addition, we provide details of the software (R code) available for its application to help users implement these models with its own data. The multitrait models were implemented under conventional Bayesian Ridge regression and best linear unbiased predictor, but also under a deep learning framework. The multitrait deep learning framework helps implement prediction models with mixed outcomes (continuous, binary, ordinal, and count, measured on different scales), which is not easy in conventional statistical models. The illustrative examples are very detailed in order to make the implementation of multitrait models in plant and animal breeding friendlier for breeders and scientists.

Automated Machine Learning: A Case Study of Genomic "Image-Based" Prediction in Maize Hybrids.

Machine learning methods such as multilayer perceptrons (MLP) and Convolutional Neural Networks (CNN) have emerged as promising methods for genomic prediction (GP). In this context, we assess the performance of MLP and CNN on regression and classification tasks in a case study with maize hybrids. The genomic information was provided to the MLP as a relationship matrix and to the CNN as "genomic images." In the regression task, the machine learning models were compared along with GBLUP. Under the classification task, MLP and CNN were compared. In this case, the traits (plant height and grain yield) were discretized in such a way to create balanced (moderate selection intensity) and unbalanced (extreme selection intensity) datasets for further evaluations. An automatic hyperparameter search for MLP and CNN was performed, and the best models were reported. For both task types, several metrics were calculated under a validation scheme to assess the effect of the prediction method and other variables. Overall, MLP and CNN presented competitive results to GBLUP. Also, we bring new insights on automated machine learning for genomic prediction and its implications to plant breeding.

Genome and Environment Based Prediction Models and Methods of Complex Traits Incorporating Genotype × Environment Interaction.

Genomic-enabled prediction models are of paramount importance for the successful implementation of genomic selection (GS) based on breeding values. As opposed to animal breeding, plant breeding includes extensive multienvironment and multiyear field trial data. Hence, genomic-enabled prediction models should include genotype × environment (G × E) interaction, which most of the time increases the prediction performance when the response of lines are different from environment to environment. In this chapter, we describe a historical timeline since 2012 related to advances of the GS models that take into account G × E interaction. We describe theoretical and practical aspects of those GS models, including the gains in prediction performance when including G × E structures for both complex continuous and categorical scale traits. Then, we detailed and explained the main G × E genomic prediction models for complex traits measured in continuous and noncontinuous (categorical) scale. Related to G × E interaction models this review also examine the analyses of the information generated with high-throughput phenotype data (phenomic) and the joint analyses of multitrait and multienvironment field trial data that is also employed in the general assessment of multitrait G × E interaction. The inclusion of nongenomic data in increasing the accuracy and biological reliability of the G × E approach is also outlined. We show the recent advances in large-scale envirotyping (enviromics), and how the use of mechanistic computational modeling can derive the crop growth and development aspects useful for predicting phenotypes and explaining G × E.

Bayesian multitrait kernel methods improve multienvironment genome-based prediction.

When multitrait data are available, the preferred models are those that are able to account for correlations between phenotypic traits because when the degree of correlation is moderate or large, this increases the genomic prediction accuracy. For this reason, in this article, we explore Bayesian multitrait kernel methods for genomic prediction and we illustrate the power of these models with three-real datasets. The kernels under study were the linear, Gaussian, polynomial, and sigmoid kernels; they were compared with the conventional Ridge regression and GBLUP multitrait models. The results show that, in general, the Gaussian kernel method outperformed conventional Bayesian Ridge and GBLUP multitrait linear models by 2.2-17.45% (datasets 1-3) in terms of prediction performance based on the mean square error of prediction. This improvement in terms of prediction performance of the Bayesian multitrait kernel method can be attributed to the fact that the proposed model is able to capture nonlinear patterns more efficiently than linear multitrait models. However, not all kernels perform well in the datasets used for evaluation, which is why more than one kernel should be evaluated to be able to choose the best kernel.

A General-Purpose Machine Learning R Library for Sparse Kernels Methods With an Application for Genome-Based Prediction.

The adoption of machine learning frameworks in areas beyond computer science have been facilitated by the development of user-friendly software tools that do not require an advanced understanding of computer programming. In this paper, we present a new package (sparse kernel methods, SKM) software developed in R language for implementing six (generalized boosted machines, generalized linear models, support vector machines, random forest, Bayesian regression models and deep neural networks) of the most popular supervised machine learning algorithms with the optional use of sparse kernels. The SKM focuses on user simplicity, as it does not try to include all the available machine learning algorithms, but rather the most important aspects of these six algorithms in an easy-to-understand format. Another relevant contribution of this package is a function for the computation of seven different kernels. These are Linear, Polynomial, Sigmoid, Gaussian, Exponential, Arc-Cosine 1 and Arc-Cosine L (with L = 2, 3, … ) and their sparse versions, which allow users to create kernel machines without modifying the statistical machine learning algorithm. It is important to point out that the main contribution of our package resides in the functionality for the computation of the sparse version of seven basic kernels, which is indispensable for reducing computational resources to implement kernel machine learning methods without a significant loss in prediction performance. Performance of the SKM is evaluated in a genome-based prediction framework using both a maize and wheat data set. As such, the use of this package is not restricted to genome prediction problems, and can be used in many different applications.

Prediction of count phenotypes using high-resolution images and genomic data.

Genomic selection (GS) is revolutionizing plant breeding since the selection process is done with the help of statistical machine learning methods. A model is trained with a reference population and then it is used for predicting the candidate individuals available in the testing set. However, given that breeding phenotypic values are very noisy, new models must be able to integrate not only genotypic and environmental data but also high-resolution images that have been collected by breeders with advanced image technology. For this reason, this paper explores the use of generalized Poisson regression (GPR) for genome-enabled prediction of count phenotypes using genomic and hyperspectral images. The GPR model allows integrating input information of many sources like environments, genomic data, high resolution data, and interaction terms between these three sources. We found that the best prediction performance was obtained when the three sources of information were taken into account in the predictor, and those measures of high-resolution images close to the harvest day provided the best prediction performance.

Deep-learning power and perspectives for genomic selection.

Deep learning (DL) is revolutionizing the development of artificial intelligence systems. For example, before 2015, humans were better than artificial machines at classifying images and solving many problems of computer vision (related to object localization and detection using images), but nowadays, artificial machines have surpassed the ability of humans in this specific task. This is just one example of how the application of these models has surpassed human abilities and the performance of other machine-learning algorithms. For this reason, DL models have been adopted for genomic selection (GS). In this article we provide insight about the power of DL in solving complex prediction tasks and how combining GS and DL models can accelerate the revolution provoked by GS methodology in plant breeding. Furthermore, we will mention some trends of DL methods, emphasizing some areas of opportunity to really exploit the DL methodology in GS; however, we are aware that considerable research is required to be able not only to use the existing DL in conjunction with GS, but to adapt and develop DL methods that take the peculiarities of breeding inputs and GS into consideration.

A zero altered Poisson random forest model for genomic-enabled prediction.

In genomic selection choosing the statistical machine learning model is of paramount importance. In this paper, we present an application of a zero altered random forest model with two versions (ZAP_RF and ZAPC_RF) to deal with excess zeros in count response variables. The proposed model was compared with the conventional random forest (RF) model and with the conventional Generalized Poisson Ridge regression (GPR) using two real datasets, and we found that, in terms of prediction performance, the proposed zero inflated random forest model outperformed the conventional RF and GPR models.

Maximum a posteriori Threshold Genomic Prediction Model for Ordinal Traits.

Due to the ever-increasing data collected in genomic breeding programs, there is a need for genomic prediction models that can deal better with big data. For this reason, here we propose a Maximum a posteriori Threshold Genomic Prediction (MAPT) model for ordinal traits that is more efficient than the conventional Bayesian Threshold Genomic Prediction model for ordinal traits. The MAPT performs the predictions of the Threshold Genomic Prediction model by using the maximum a posteriori estimation of the parameters, that is, the values of the parameters that maximize the joint posterior density. We compared the prediction performance of the proposed MAPT to the conventional Bayesian Threshold Genomic Prediction model, the multinomial Ridge regression and support vector machine on 8 real data sets. We found that the proposed MAPT was competitive with regard to the multinomial and support vector machine models in terms of prediction performance, and slightly better than the conventional Bayesian Threshold Genomic Prediction model. With regard to the implementation time, we found that in general the MAPT and the support vector machine were the best, while the slowest was the multinomial Ridge regression model. However, it is important to point out that the successful implementation of the proposed MAPT model depends on the informative priors used to avoid underestimation of variance components.

A Multivariate Poisson Deep Learning Model for Genomic Prediction of Count Data.

The paradigm called genomic selection (GS) is a revolutionary way of developing new plants and animals. This is a predictive methodology, since it uses learning methods to perform its task. Unfortunately, there is no universal model that can be used for all types of predictions; for this reason, specific methodologies are required for each type of output (response variables). Since there is a lack of efficient methodologies for multivariate count data outcomes, in this paper, a multivariate Poisson deep neural network (MPDN) model is proposed for the genomic prediction of various count outcomes simultaneously. The MPDN model uses the minus log-likelihood of a Poisson distribution as a loss function, in hidden layers for capturing nonlinear patterns using the rectified linear unit (RELU) activation function and, in the output layer, the exponential activation function was used for producing outputs on the same scale of counts. The proposed MPDN model was compared to conventional generalized Poisson regression models and univariate Poisson deep learning models in two experimental data sets of count data. We found that the proposed MPDL outperformed univariate Poisson deep neural network models, but did not outperform, in terms of prediction, the univariate generalized Poisson regression models. All deep learning models were implemented in Tensorflow as back-end and Keras as front-end, which allows implementing these models on moderate and large data sets, which is a significant advantage over previous GS models for multivariate count data.

Validation of an instrument to measure tutor performance in promoting self-directed learning by using confirmatory factor analysis.

OBJECTIVE: This work sought to validate and propose an instrument to measure the performance of tutors in promoting self-directed learning in students involved in processes of problem-based learning. METHODS: Confirmatory factor analysis (CFA) was applied to validate the instrument composed of 60 items and six factors (self-assessment of learning gaps within the United Nations specific context: self-assessment, reflexion, critical thinking, administration of information, group skills), using a sample of 207 students from a total of 279, which comprise the student population of the Faculty of Nursing at Universidad de Colima in Mexico. (2007). RESULTS: The CFA results demonstrated that the instrument is acceptable to measure performance of tutors in promoting self-directed learning, given that all the indicators, variances, covariances, and thresholds are statistically significant. CONCLUSION: The instrument permits obtaining students' opinions on how much professors contribute for them to develop each of the 60 skills described in the scale. Lastly, the results could report if professors are placing more emphasis in some areas than in other areas they should address during the problem-based learning (PBL) process, or if definitely their actions are removed from the premises of PBL, information that will be useful for school management in decision making on the direction of teaching as a whole.

Sample size under inverse negative binomial group testing for accuracy in parameter estimation.

BACKGROUND: The group testing method has been proposed for the detection and estimation of genetically modified plants (adventitious presence of unwanted transgenic plants, AP). For binary response variables (presence or absence), group testing is efficient when the prevalence is low, so that estimation, detection, and sample size methods have been developed under the binomial model. However, when the event is rare (low prevalence <0.1), and testing occurs sequentially, inverse (negative) binomial pooled sampling may be preferred. METHODOLOGY/PRINCIPAL FINDINGS: This research proposes three sample size procedures (two computational and one analytic) for estimating prevalence using group testing under inverse (negative) binomial sampling. These methods provide the required number of positive pools ([Formula: see text]), given a pool size (k), for estimating the proportion of AP plants using the Dorfman model and inverse (negative) binomial sampling. We give real and simulated examples to show how to apply these methods and the proposed sample-size formula. The Monte Carlo method was used to study the coverage and level of assurance achieved by the proposed sample sizes. An R program to create other scenarios is given in Appendix S2. CONCLUSIONS: The three methods ensure precision in the estimated proportion of AP because they guarantee that the width (W) of the confidence interval (CI) will be equal to, or narrower than, the desired width ([Formula: see text]), with a probability of [Formula: see text]. With the Monte Carlo study we found that the computational Wald procedure (method 2) produces the more precise sample size (with coverage and assurance levels very close to nominal values) and that the samples size based on the Clopper-Pearson CI (method 1) is conservative (overestimates the sample size); the analytic Wald sample size method we developed (method 3) sometimes underestimated the optimum number of pools.

Validation of an instrument to measure tutor performance in promoting self-directed learning by using confirmatory factor analysis / Validación de un instrumento para medir el desempeño de los tutores en la promoción del aprendizaje autodirigido usando análisis factorial confirmatorio / Validação de um instrumento para medir o desempenho dos tutores na promoção da aprendizagem autodirigido usando análise fatorial confirmatório

Objective.This work sought to validate and propose an instrument to measure the performance of tutors in promoting self-directed learning in students involved in processes of problem-based learning. Methods. Confirmatory factor analysis (CFA) was applied to validate the instrument composed of 60 items and six factors (self-assessment of learning gaps within the United Nations specific context: self-assessment, reflexion, critical thinking, administration of information, group skills), using a sample of 207 students from a total of 279, which comprise the student population of the Faculty of Nursing at Universidad de Colima in Mexico. (2007). Results. The CFA results demonstrated that the instrument is acceptable to measure performance of tutors in promoting self-directed learning, given that all the indicators, variances, covariances, and thresholds are statistically significant. Conclusion. The instrument permits obtaining students' opinions on how much professors contribute for them to develop each of the 60 skills described in the scale. Lastly, the results could report if professors are placing more emphasis in some areas than in other areas they should address during the problem-based learning (PBL) process, or if definitely their actions are removed from the premises of PBL, information that will be useful for school management in decision making on the direction of teaching as a whole.

Objetivo.Validar y proponer un instrumento que mide el desempeño de los tutores en la promoción del aprendizaje autodirigido en los estudiantes involucrados en procesos de ABP. Métodos. Se aplicó el Análisis Factorial Confirmatorio (AFC) para validar el instrumento compuesto por 60 ítems y seis factores (Autoevaluación de las Brechas de Aprendizaje dentro de las Naciones Unidas Contexto Especifico: Autoevaluación, Reflexión, Pensamiento Crítico, Administración de la Información, Habilidades de Grupo), utilizando una muestra de 207 estudiantes de un total de 279, que conforman la población estudiantil de la Facultad de Enfermería de la Universidad de Colima, México. (2007). Resultados. Los resultados del AFC demostraron que el instrumento es aceptable para medir el desempeño de los tutores en la promoción del aprendizaje autodirigido ya que todos los indicadores, las varianzas, covarianzas y thresholds son estadísticamente significativos. Conclusión. El instrumento permite obtener la opinión de los estudiantes sobre cuánto el profesor contribuye para que ellos desarrollen cada una de las 60 habilidades descritas en la escala. Al final, los resultados podrían informar si el profesor está haciendo más énfasis en una área que debe atender durante el proceso del ABP o en otra, o si definitivamente su actuación se aleja de las premisas del ABP, información que será útil para la administración escolar en la toma de decisiones sobre el rumbo de la docencia en su conjunto.

Objetivo.Validar e propor um instrumento que meça o desempenho dos tutores na promoção da aprendizagem autodirigido nos estudantes envolvidos em processos de ABP. Métodos. Se aplicou uma Análise Fatorial Confirmatório (AFC) para validar o instrumento composto por 60 itens e seis fatores (Auto-avaliação das Brechas de Aprendizagem dentro das Nações Unidas Contexto Especifico: Auto-avaliação, Reflexão, Pensamento Crítico, Administração da Informação, habilidades de Grupo), utilizando uma amostra de 207 estudantes de um total de 279, que conformam a população estudantil da Faculdade de Enfermagem da Universidad de Colima, México. (2007). Resultados. Os resultados do AFC demostraram que o instrumento é aceitável para medir o desempenho dos tutores na promoção da aprendizagem autodirigido já que todos os indicadores, as variâncias, covariâncias e thresholds são estatisticamente significativos. Conclusão. O instrumento permite obter a opinião dos estudantes sobre quanto o professor contribui para que eles desenvolvam cada uma das 60 habilidades descritas na escala. Ao final, os resultados poderiam informar se o professor está fazendo mais ênfase em uma do que em outras das áreas que deve atender durante o processo do ABP, ou se definitivamente sua atuação se afasta e as premissas do ABP, informação que será útil para a administração escolar na toma de decisões sobre o rumo da docência em seu conjunto.

[Mathematical models for infectious diseases]. / Modelos matemáticos para enfermedades infecciosas.

OBJECTIVE: To describe the importance of mathematical models in the understanding of infectious disease transmission dynamics, as well as in the design of effective strategies for control. MATERIAL AND METHODS: International literature was reviewed on the subject through digital means. Around 60 papers about the subject were identified; nevertheless, this study is based on only 27 of these, due to the fact that they were directly related to the subject. RESULTS: This work presents a brief explanation of the antecedents, importance and classification of mathematical models for infectious diseases. In addition, a detailed description of some classical models is discussed as well as other more recent models used in the modeling of infectious disease. CONCLUSIONS: The use of mathematical models for infectious diseases has grown significantly in the last few years and has proven to be of great help in designing efficient strategies for control and eradication of infectious diseases.

Modelos matemáticos para enfermedades infecciosas / Mathematical models for infectious diseases

OBJETIVO: Describir la importancia de los modelos matemáticos en la comprensión de la dinámica de transmisión de las enfermedades infecciosas, así como en el diseño de medidas eficaces de control. MATERIAL Y MÉTODOS: Se revisaron las publicaciones internacionales sobre el tema a través de medios digitales; se identificaron alrededor de 60 artículos, aunque sólo se revisaron 27 de éstos por su estrecha relación con el tema. RESULTADOS: Este trabajo explica de manera sinóptica los antecedentes, importancia y clasificación de los modelos matemáticos en padecimientos infecciosos. De modo adicional se describen con detalle algunos modelos comunes de transmisión de enfermedades y otros de uso más reciente que se utilizan en la modelación de trastornos infecciosos. CONCLUSIONES: El empleo de modelos matemáticos ha crecido en grado significativo en los últimos años y son de gran ayuda para idear medidas eficaces de control y erradicación de las enfermedades infecciosas.

OBJECTIVE: To describe the importance of mathematical models in the understanding of infectious disease transmission dynamics, as well as in the design of effective strategies for control. MATERIAL AND METHODS: International literature was reviewed on the subject through digital means. Around 60 papers about the subject were identified; nevertheless, this study is based on only 27 of these, due to the fact that they were directly related to the subject. RESULTS:This work presents a brief explanation of the antecedents, importance and classification of mathematical models for infectious diseases. In addition, a detailed description of some classical models is discussed as well as other more recent models used in the modeling of infectious disease. CONCLUSIONS: The use of mathematical models for infectious diseases has grown significantly in the last few years and has proven to be of great help in designing efficient strategies for control and eradication of infectious diseases.