More on the Cohort-Component Model of Population Projection in the Context of HIV/AIDS: A Leslie Matrix Representation and New Estimates

This article presents an extension of the cohort component model of population projection (CCMPP) first formulated by Heuveline that is capable of modeling a population affected by HIV. We extend this work by developing the Leslie matrix representation of the CCMPP that greatly facilitates implementation of the model for parameter estimation and projecting. The Leslie matrix also contains information about the stable tendencies of the corresponding population, such as the stable age distribution and time to stability. We validate our reformulation of the model by comparing parameter estimates obtained through maximum likelihood and bootstrap methods to those presented by Heuveline.Africa, AIDS/HIV, cohort component method, estimation, incidence, Leslie matrices, model, prevalence

Comparing Powers of Edge Ideals

Given a nontrivial homogeneous ideal $I\subseteq k[x_1,x_2,\ldots,x_d]$, a problem of great recent interest has been the comparison of the $r$th ordinary power of $I$ and the $m$th symbolic power $I^{(m)}$. This comparison has been undertaken directly via an exploration of which exponents $m$ and $r$ guarantee the subset containment $I^{(m)}\subseteq I^r$ and asymptotically via a computation of the resurgence $\rho(I)$, a number for which any $m/r > \rho(I)$ guarantees $I^{(m)}\subseteq I^r$. Recently, a third quantity, the symbolic defect, was introduced; as $I^t\subseteq I^{(t)}$, the symbolic defect is the minimal number of generators required to add to $I^t$ in order to get $I^{(t)}$. We consider these various means of comparison when $I$ is the edge ideal of certain graphs by describing an ideal $J$ for which $I^{(t)} = I^t + J$. When $I$ is the edge ideal of an odd cycle, our description of the structure of $I^{(t)}$ yields solutions to both the direct and asymptotic containment questions, as well as a partial computation of the sequence of symbolic defects.Comment: Version 2: Revised based on referee suggestions. Lemma 5.12 was added to clarify the proof of Theorem 5.13. To appear in the Journal of Algebra and its Applications. Version 1: 20 pages. This project was supported by Dordt College's undergraduate research program in summer 201

Mathematical approaches to scale degrees and harmonic functions in analytical dialogue

Published versio

Extending General Equilibrium to the Tariff Line: U.S. Dairy in the Doha Development Agenda

International Relations/Trade,

A contact process with mutations on a tree

Consider the following stochastic model for immune response. Each pathogen gives birth to a new pathogen at rate $\lambda$. When a new pathogen is born, it has the same type as its parent with probability $1 - r$. With probability $r$, a mutation occurs, and the new pathogen has a different type from all previously observed pathogens. When a new type appears in the population, it survives for an exponential amount of time with mean 1, independently of all the other types. All pathogens of that type are killed simultaneously. Schinazi and Schweinsberg (2006) have shown that this model on $\Z^d$ behaves rather differently from its non-spatial version. In this paper, we show that this model on a homogeneous tree captures features from both the non-spatial version and the $\Z^d$ version. We also obtain comparison results between this model and the basic contact process on general graphs