One can use mathematical techniques to model disease outbreaks such as COVID-19, Ebola, or HIV/AIDS. We can then use model simulations to make future projections about the number of cases, consider the impact of intervention strategies, or analyze other key characteristics of an epidemic.

This presentation will begin by introducing the compartmental framework commonly used to model infectious diseases, which will be illustrated by some simple models. After we lay some groundwork, a specific application to modeling HIV/AIDS in Kenya will be presented. In this application we formulate a compartmental system of ordinary differential equations (ODEs) to consider how stigma towards people living with HIV/AIDS has impeded the response to the disease. We take a data-driven approach to embed a time-dependent stigma function within our model for HIV dynamics and estimate model parameters from published data. We then explore a range of scenarios to understand the potential impact of different public health interventions on key HIV metrics such as prevalence and disease-related death, and to see how close Kenya will get to achieving UN Goals for these HIV and stigma metrics by 2030.

In many situations we are faced with the problem of choosing among several alternatives. We may want to make a decision about which alternative(s) are the best. Considering a typical clinical trial setting, we set the goal of selecting among k ( > 0) experimental Bernoulli treatments the t (1 < t < k) best treatments provided that they are significantly better than the control. If fewer than t treatments are significantly better than the control, our goal is to retain the control. A fixed-sample-size procedure and a curtailed procedure are proposed to reach the goal. We adopt the two-stage selection/testing approach considered by Thall, Simon, and Ellenberg (1988) in both procedures. Properties of the proposed procedures will be presented through theorems and numerical results.

“One if by Land Two if by Sea”

This line from Longfellow’s poem describes a secret signal to the patriots about approaching British troops and goes on to commemorate Paul Revere’s Midnight Ride. At the same time, the poem reveals that Revere served as a spy and that the colonists engaged in early attempts at cryptology — sending, receiving, and decoding secret messages. We will explore the role that spycraft and cryptology played in the American Revolution and in the U.S. Civil War. 

Shall we play a game? Hawks, Doves, and More

In the 1960's, ecologists began to use game theory to study evolutionary questions on topics such as animal aggression, the sex ratio, and altruism. Further study led to the creation of evolutionary game theory. In contrast to traditional game theory, evolutionary game theory seeks to describe changes in the frequency of strategies over repeated iterations of a game. Typically, the number of players in the game is fixed. In this talk, I will describe recent efforts to integrate population dynamics and evolutionary game theory models to answer questions about the evolution of animal aggression.

Part 1: Data and Donations, Joshua Hayden

A talk on using data to help project donations and find top donor prospects for the Ithaca State Theatre. How data analysis and machine learning can be put to work in the non-profit space to help communities.

Part 2: Application of Math in Real Life, Heetisha Inderjeet

As a math major, people sometimes expect that the only career goal is to teach. However, math can be a career in different ways. This project which involves working with Matthew LeRoux from the Cornell Cooperative Extension (Tompkins County) is a good example. This project consists of working with the cooperative extension partner to evaluate a meat pricing calculator and drill down on significant statistical numbers which will be able to be used for workshops and grant writing.