We present a new SIR epidemiological model whose exact analytical solution can be calculated. In this model, unlike previous models, the infective population becomes zero at a finite time. Remarkably, these results can be derived from only an elementary knowledge of differential equations.

Measuring teacher effectiveness is challenging since no direct estimate exists; teacher effectiveness can be measured only indirectly through student responses. Traditional value-added assessment (VAA) models generally attempt to estimate the value that an individual teacher adds to students' knowledge as measured by scores on successive…

In this article, the author reports results in their efforts to model sublimation of carbon dioxide and the associated kinetics order and parameter estimation issues in their model. They have offered the reader two sets of data and several approaches to determine the rate of sublimation of a piece of solid dry ice. They presented several models…

This article addresses modeling oscillation in continuous time. It criticizes Steele and Ferrer's article "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011), particularly the approximate estimation procedure applied. This procedure is the latent version of the local linear approximation procedure…

In this article we examine 2 x 2 first-order systems of ordinary differential equations and show how to identify separatrices for phase plane portraits when the system has a saddle point critical value. We describe how to use a computer algebra system to generate trajectories from contour plots, when possible, and determine the equation of the…

The estimate of the time since death and, thus, the time of death is strictly that, an estimate. However, the time of death can be an important piece of information in some coroner's cases, especially those that involve criminal or insurance investigations. It has been known almost from the beginning of time that bodies cool after the internal…

Considering a dyad as a dynamic system whose current state depends on its past state has allowed researchers to investigate whether and how partners influence each other. Some researchers have also focused on how differences between dyads in their interaction patterns are related to other differences between them. A promising approach in this area…

This article presents our response to Oud and Folmer's "Modeling Oscillation, Approximately or Exactly?" (2011), which criticizes aspects of our article, "Latent Differential Equation Modeling of Self-Regulatory and Coregulatory Affective Processes" (2011). In this response, we present a conceptual explanation of the derivative-based estimation…

The fitting of dynamical systems to psychological data offers the promise of addressing new and innovative questions about how people change over time. One method of fitting dynamical systems is to estimate the derivatives of a time series and then examine the relationships between derivatives using a differential equation model. One common…

Population models are often discussed in algebra, calculus, and differential equations courses. In this article we will use the human population of the world as our application. After quick looks at two common models we'll investigate more deeply a model which incorporates the negative effect that accumulated pollution may have on population.

In this article a continuous-time stochastic model (the Ornstein-Uhlenbeck process) is presented to model the perpetually altering states of the core affect, which is a 2-dimensional concept underlying all our affective experiences. The process model that we propose can account for the temporal changes in core affect on the latent level. The key…

The objective of the present paper is to provide a simple approach to statistical inference using the method of transformations of variables. We demonstrate performance of this powerful tool on examples of constructions of various estimation procedures, hypothesis testing, Bayes analysis and statistical inference for the stress-strength systems.…

A method is presented to calculate accurate approximations to the half-life values of elimination systems modelled by one compartment. The major advantage of this method is that only algebraic mathematical operations are required. The results will be of value not only to students beginning the study of elimination kinetics, but also to…

This article discusses the incorporation of biological content into existing calculus courses without significantly changing the courses. This is exemplified by the common laboratory course taken by students in all first semester calculus courses at Benedictine University. Several biologically oriented projects are implemented in this laboratory…

In this article we provide two detailed examples of how we incorporate biological examples into two mathematics courses: Linear Algebra and Ordinary Differential Equations. We use Leslie matrix models to demonstrate the biological properties of eigenvalues and eigenvectors. For Ordinary Differential Equations, we show how using a logistic growth…