arXiv subjects

Annemarie Grass

Publications and source records attributed to Annemarie Grass.

3 recordsLinked to original sources

arXiv2023

Perkins Embedding for General Starting Laws

The Skorokhod embedding problem (SEP) is to represent a given probability measure as a Brownian motion $B$ at a particular stopping time. In recent years particular attention has gone to solutions which exhibit additional optimality properties due to applications to martingale inequalities and robust pricing in mathematical finance. Among these solutions, the Perkins embedding sticks out through its distinct geometric properties. Moreover is the only optimal solution to the SEP which so far has been limited to the case of Brownian motion started in a dirac distribution. In this paper we provide for the first time an optimal solution to the Skorokhod embedding problem for the general SEP which leads to the Perkins solution when applied to Brownian motion with start in a dirac. This solution to the SEP also suggests a new geometric interpretation of the Perkins solution which better clarifies the relation to other optimal solutions of the SEP.

math.PR↗

arXiv2022

Robust models of SARS-CoV-2 heterogeneity and control

In light of the continuing emergence of new SARS-CoV-2 variants and vaccines, we create a simulation framework for exploring possible infection trajectories under various scenarios. The situations of primary interest involve the interaction between three components: vaccination campaigns, non-pharmaceutical interventions (NPIs), and the emergence of new SARS-CoV-2 variants. Additionally, immunity waning and vaccine boosters are modeled to account for their growing importance. New infections are generated according to a hierarchical model in which people have a random, individual infectiousness. The model thus includes super-spreading observed in the COVID-19 pandemic. Our simulation functions as a dynamic compartment model in which an individual's history of infection, vaccination, and possible reinfection all play a role in their resistance to further infections. We present a risk measure for each SARS-CoV-2 variant, $ρ^\V$, that accounts for the amount of resistance within a population and show how this risk changes as the vaccination rate increases. Furthermore, by considering different population compositions in terms of previous infection and type of vaccination, we can learn about variants which pose differential risk to different countries. Different control strategies are implemented which aim to both suppress COVID-19 outbreaks when they occur as well as relax restrictions when possible. We demonstrate that a controller that responds to the effective reproduction number in addition to case numbers is more efficient and effective in controlling new waves than monitoring case numbers alone. This is of interest as the majority of the public discussion and well-known statistics deal primarily with case numbers.

q-bio.PE↗

arXiv2021

Disease Momentum: Estimating the Reproduction Number in the Presence of Superspreading

A primary quantity of interest in the study of infectious diseases is the average number of new infections that an infected person produces. This so-called reproduction number has significant implications for the disease progression. There has been increasing literature suggesting that superspreading, the significant variability in number of new infections caused by individuals, plays an important role in the spread of SARS-CoV-2. In this paper, we consider the effect that such superspreading has on the estimation of the reproduction number and subsequent estimates of future cases. Accordingly, we employ a simple extension to models currently used in the literature to estimate the reproduction number and present a case-study of the progression of COVID-19 in Austria. Our models demonstrate that the estimation uncertainty of the reproduction number increases with superspreading and that this improves the performance of prediction intervals. Of independent interest is the derivation of a transparent formula that connects the extent of superspreading to the width of credible intervals for the reproduction number. This serves as a valuable heuristic for understanding the uncertainty surrounding diseases with superspreading.

q-bio.PE↗