Mathematical modeling tendencies in plant pathology

Nowadays plant diseases represent one of the major threats for crops around the world, because they carry healthy, economical, environmental and social problems. Considering this, it is necessary to have a description of the dynamics of plant disease in order to have sustainable strategies to prevent and diminish the impact of the diseases in crops. Mathematical tools have been employed to create models which give a description of epidemic dynamics; the commonly mathematical tools used are: Diseaseprogress curves, Linked Differential Equation (LDE), Area Under disease Progress Curve (AUDPC) and computer simulation. Nevertheless, there are other tools that have been employed in epidemiology of plant disease like: statistical tools, visual evaluations and pictorial assessment. Each tool has its own advantages and disadvantages. The nature of the problem and the epidemiologist necessities determine the mathematical tool to be used and the variables to be included into the model. This paperpresents review of the tools used in epidemiology of plant disease remarking their advantages and disadvantages and mathematical modeling tendencies in plant pathology

Parameter estimation for a mathematical model predicting the COVID-19 spread in the Àrea Metropolitana de Barcelona

Epidemiology is the medical discipline in charge of sudying the dynamics of a disease in a given population; particularly, we are interested in human infectious diseases. In the 18th century, with Daniel Bernouilli, a new branch appeared: mathematical epidemiology. During this project, we will first establish some basic concepts and a motivational introduction in order to present some common results on mathematical epidemiology. For that, it will be introduced some theory using the basic SIRS model so as to understand well the involved tools, such as Lyapunov theory on equilibrium points and their stability or the basic reproduction number R0, which will be crucial to determine the future of the disease. Finally, we will try to apply all the learned concepts to study a more complex mathematical model, still in developement, whose aim is trying to reproduce the behaviour of the well-known COVID-19; concretely, there will be shown some numerical results for its evolution in the Metropolitan Area of Barcelona

A critical review of mathematical models and data used in diabetology

The literature dealing with mathematical modelling for diabetes is abundant. During the last decades, a variety of models have been devoted to different aspects of diabetes, including glucose and insulin dynamics, management and complications prevention, cost and cost-effectiveness of strategies and epidemiology of diabetes in general. Several reviews are published regularly on mathematical models used for specific aspects of diabetes. In the present paper we propose a global overview of mathematical models dealing with many aspects of diabetes and using various tools. The review includes, side by side, models which are simple and/or comprehensive; deterministic and/or stochastic; continuous and/or discrete; using ordinary differential equations, partial differential equations, optimal control theory, integral equations, matrix analysis and computer algorithms

Mathematical Manipulative Models: In Defense of Beanbag Biology

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education

Mathematical Analysis and Computational Integration of Massive Heterogeneous Data from the Human Retina

Modern epidemiology integrates knowledge from heterogeneous collections of data consisting of numerical, descriptive and imaging. Large-scale epidemiological studies use sophisticated statistical analysis, mathematical models using differential equations and versatile analytic tools that handle numerical data. In contrast, knowledge extraction from images and descriptive information in the form of text and diagrams remain a challenge for most fields, in particular, for diseases of the eye. In this article we provide a roadmap towards extraction of knowledge from text and images with focus on forthcoming applications to epidemiological investigation of retinal diseases, especially from existing massive heterogeneous collections of data distributed around the globe.Comment: 9 pages, 3 figures, submitted and accepted in Damor2012 conference: http://www.uninova.pt/damor2012/index.php?page=author

Estimating the Causal Effects of Marketing Interventions Using Propensity Score Methodology

Propensity score methods were proposed by Rosenbaum and Rubin [Biometrika 70 (1983) 41--55] as central tools to help assess the causal effects of interventions. Since their introduction more than two decades ago, they have found wide application in a variety of areas, including medical research, economics, epidemiology and education, especially in those situations where randomized experiments are either difficult to perform, or raise ethical questions, or would require extensive delays before answers could be obtained. In the past few years, the number of published applications using propensity score methods to evaluate medical and epidemiological interventions has increased dramatically. Nevertheless, thus far, we believe that there have been few applications of propensity score methods to evaluate marketing interventions (e.g., advertising, promotions), where the tradition is to use generally inappropriate techniques, which focus on the prediction of an outcome from background characteristics and an indicator for the intervention using statistical tools such as least-squares regression, data mining, and so on. With these techniques, an estimated parameter in the model is used to estimate some global ``causal'' effect. This practice can generate grossly incorrect answers that can be self-perpetuating: polishing the Ferraris rather than the Jeeps ``causes'' them to continue to win more races than the Jeeps $\Leftrightarrow$ visiting the high-prescribing doctors rather than the low-prescribing doctors ``causes'' them to continue to write more prescriptions. This presentation will take ``causality'' seriously, not just as a casual concept implying some predictive association in a data set, and will illustrate why propensity score methods are generally superior in practice to the standard predictive approaches for estimating causal effects.Comment: Published at http://dx.doi.org/10.1214/088342306000000259 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org