Modeling Super-spreading Events for Infectious Diseases: Case Study SARS

Super-spreading events for infectious diseases occur when some infected individuals infect more than the average number of secondary cases. Several super-spreading individuals have been identified for the 2003 outbreak of severe acute respiratory syndrome (SARS). We develop a model for super-spreading events of infectious diseases, which is based on the outbreak of SARS. Using this model we describe two methods for estimating the parameters of the model, which we demonstrate with the small-scale SARS outbreak at the Amoy Gardens, Hong Kong, and the large-scale outbreak in the entire Hong Kong Special Administrative Region. One method is based on parameters calculated for the classical susceptible - infected - removed (SIR) disease model. The second is based on parameter estimates found in the literature. Using the parameters calculated for the SIR model, our model predicts an outcome similar to that for the SIR model. On the other hand, using parameter estimates from SARS literature our model predicts a much more serious epidemic.Comment: 8 pages, 1 figure, 7 table

Modeling super-spreading events for SARS

One of the intriguing characteristics of the 2003 severe acute respiratory syndrome (SARS) epidemics was the occurrence of super spreading events (SSEs). Super-spreading events for a specific infectious disease occur when infected individuals infect more than the average number of secondary cases. The understanding of these SSEs is critical to under- standing the spread of SARS. In this thesis, we present a modification of the basic SIR (Susceptible - Infected - Removed) disease model, an SIPR (Susceptible - Regular Infected - Super-spreader - Removed) model, which captures the effect of the SSEs

Business Calculus Students’ Reasoning about Optimization Problems: A Study of Quantitative Reasoning in an Economic Context

While the opportunity to learn mathematics via textbooks is well documented at the secondary and elementary levels, research on the opportunity to learn mathematics via textbooks at the undergraduate level has received little attention. Furthermore, research that examines the role of mathematics textbooks in students’ learning of important concepts such as marginal change in applied calculus is scarce. Research on students’ quantitative reasoning at the post-secondary level is lacking. This qualitative study investigated the opportunity to learn about optimization problems, marginal change, and quantitative reasoning in an economic context via a business calculus textbook and from lectures in a business calculus course. The study also investigated students’ quantitative reasoning, using task based interviews conducted with 12 pairs of business calculus students, about optimization problems and marginal change in an economic context. This study found that the textbook’s presentation of optimization problems and marginal change was largely procedural with limited attention to the underlying concepts and that opportunities for students to reason about relationships between or among economic quantities such as the relationship between marginal cost and marginal revenue at a profit maximizing quantity received little attention. The presentation of optimization problems and marginal change in course lectures closely followed the presentation of these topics in the textbook. Students’ interpretations of marginal change varied in different contexts and representations depending on the tasks they were given. This study provided insights into students’ quantitative reasoning when analyzing multivariable situations in an economic context: students created new quantities that helped them to solve the problems in the tasks and helped them to reason about relationships among several quantities. Implications for different stakeholders including business calculus instructors and suggestions for further research are included

An exploratory study of calculus students’ understanding of multivariable optimization problems

International audienceContributing to the growing body of research on students’ quantitative reasoning at the undergraduate level, this study reports on students’ reasoning about a multivariable optimization problem that involves finding the dimensions of the largest volume bag a passenger can carry on an American Airlines flight. Analysis of verbal responses and work written by 11 students when solving the problem revealed that finding the required dimensions was easy for nearly all the students. However, showing that these are the dimensions of the largest volume bag was problematic for a majority of the students. Implications for instruction and directions for future research are discussed

An exploratory study of calculus students’ understanding of multivariable optimization problems

International audienceContributing to the growing body of research on students’ quantitative reasoning at the undergraduate level, this study reports on students’ reasoning about a multivariable optimization problem that involves finding the dimensions of the largest volume bag a passenger can carry on an American Airlines flight. Analysis of verbal responses and work written by 11 students when solving the problem revealed that finding the required dimensions was easy for nearly all the students. However, showing that these are the dimensions of the largest volume bag was problematic for a majority of the students. Implications for instruction and directions for future research are discussed

Students' understanding of marginal change in the context of cost, revenue, and profit

International audienceThis paper describes how eight undergraduate students majoring in economics and business studies reasoned about marginal change (marginal cost, marginal revenue , and marginal profit) in the process of deciding how they would advise the management team of an airline about an economic decision involving the addition of another jet plane. To elicit students' understanding of marginal change in an economic context, pairs of students were engaged in a task-based interview. Nearly all of the students were able to reason correctly about marginal change within the immediate context of the task, while four of the students also did so beyond the context presented in the task. Only one student considered the marginal change information in the task as a rate of change