Applied Mathematics Commons^™

Influence Of Concurrency, Partner Choice, And Viral Suppression On Racial Disparity In The Prevalence Of Hiv Infected Women, Katharine Gurski, Kathleen Hoffman

Biology and Medicine Through Mathematics Conference

No abstract provided.

The Role Of Mathematical Modeling In Designing And Evaluating Antimicrobial Stewardship Programs, Lester Caudill, Joanna R. Wares

Department of Math & Statistics Faculty Publications

Antimicrobial agent effectiveness continues to be threatened by the rise and spread of pathogen strains that exhibit drug resistance. This challenge is most acute in healthcare facilities where the well-established connection between resistance and sub-optimal antimicrobial use has prompted the creation of antimicrobial stewardship programs (ASPs). Mathematical models offer tremendous potential for serving as an alternative to controlled human experimentation for assessing the effectiveness of ASPs. Models can simulate controlled randomized experiments between groups of virtual patients, some treated with the ASP measure under investigation, and some without. By removing the limitations inherent in human experimentation, including health risks, study …

A Comparison Of Five Malaria Transmission Models: Benchmark Tests And Implications For Disease Control, Dorothy I. Wallace, Ben S. Southworth, Xun Shi, Jonathan W. Chipman, Andrew K. Githeko

Dartmouth Scholarship

Background: Models for malaria transmission are usually compared based on the quantities tracked, the form taken by each term in the equations, and the qualitative properties of the systems at equilibrium. Here five models are compared in detail in order to develop a set of performance measures that further illuminate the differences among models.

Methods: Five models of malaria transmission are compared. Parameters are adjusted to correspond to similar biological quantities across models. Nine choices of parameter sets/initial conditions are tested for all five models. The relationship between malaria incidence in humans and (1) malaria incidence in vectors, (2) man-biting …

A Mathematical Model For Dengue Fever In A Virgin Environment, Jason K. Bowman

Senior Honors Projects

Dengue is a mosquito-borne viral infection found in tropical and subtropical regions around the world. The disease was named in 1779 and the first recorded epidemic of it occurred simultaneously on three continents within the following decade. Dengue is characterized by flu-like symptoms and, while its symptoms are generally reported as quite unpleasant, is rarely fatal. However, in some cases patients can contract a more serious form of the disease, known as Dengue Hemorrhagic Fever, which is far more dangerous. The World Health Organization estimates that today over 2.5 billion people are at risk for Dengue (over 40% of the …

Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing

Mathematics and Statistics Faculty Publications

Pertussis (whooping cough) incidence in the United States has oscillated with a period of about four years since data was first collected in 1922. An infection with pertussis confers immunity for several years, but then the immunity wanes, so that reinfection is possible. A pertussis reinfection is mild after partial loss of immunity, but the reinfection can be severe after complete loss of immunity. Three pertussis transmission models with waning of immunity are examined for periodic solutions. Equilibria and their stability are determined. Hopf bifurcation of periodic solutions around the endemic equilibrium can occur for some parameter values in two …