Talks

Abstract This work connects models for virus spread on networks with their equivalent neural network representations. Based on this connection, we propose a new neural network architecture, called Transmission Neural Networks (TransNNs) where activation functions are primarily associated with links and are allowed to have different activation levels. This connection also leads to the discovery and the derivation of three new activation functions with tunable or trainable parameters. We show that TransNNs with a single hidden layer and a fixed non-zero bias term are universal function approximators. Moreover, we establish threshold conditions for virus spread on networks where the dynamics are characterized by TransNNs. Finally, we present new derivations of continuous time epidemic models on networks based on TransNNs. *This is joint work with Peter E. Caines.

Abstract Dengue virus is the most significant viral mosquito-borne infection in terms of its human impact. Mathematical modeling has contributed to our understanding of its transmission and control strategies aimed at halting its spread. We consider the spread of dengue at the level of a city. Because the Aedes aegypti mosquito that transmits dengue has relatively low dispersal over its lifetime, human movement plays a major role in its spread and the household is a key spatial scale on which transmission occurs. Simple multi-patch deterministic models---metapopulation models, which consider the population to be described as a network of well-mixed patches---have been used to model city-level spatial spread and can provide expressions for key epidemiological quantities such as the basic reproduction number, $R_0$. We compare dynamics predicted by such models with results from individual-based network models and illustrate several discrepancies. We argue that the small size of households and local depletion of susceptibles are key features of the dynamics that are not captured in the standard $R_0$ analysis of the ODE model. In order to gain analytic understanding, we propose the use of household-level models, which can be analyzed using branching process theory. Our work, which echoes results previously found for directly-transmitted infections, highlights the importance of correctly accounting for the relevant spatial scales on which transmission occurs

Abstract The ongoing COVID-19 pandemic has had devastating impacts on global public health and socioeconomic stability. Although highly efficacious COVID-19 vaccines were developed at an unprecedented rate, the ongoing evolution of SARS-CoV-2 and consequential changes in infectivity and immunological resistance of new variants continues to present challenges. Computing the growth rates of emerging variants is complicated by many issues, including vaccine uptake, regional levels of prior infection, viral resistance to protective antibodies, and the relative infectivity of new variants in complex populations. While epidemic forecasting has played an important role in decision-making, forecast accuracy has been limited, especially at key tipping points in the pandemic, by the inability to incorporate important factors, such as the emergence of phenotypically novel variants. In this talk, I will describe a flexible strategy to characterize variant transition dynamics through three simple summaries, the speed, the relative timing, and the magnitude of the variant transition. This foundational research is intended to better understand the implication of SARS-CoV-2 evolution to ultimately inform regional epidemiological forecasting.  

Bang Nucleosynthesis (BBN) is one of the greatest outcome of the Standard Model of Particle Physics when put next to ΛCDM cosmology. In this talk, I will first review the key aspects of standard BBN and illustrate a new code -- PRyMordial -- to make state-of-the-art predictions of primordial light-element abundances within and beyond the Standard Model. I will then highlight the latest measurements regarding the primordial abundance of helium-4 and deuterium, and present evidence at the 2 sigma level for a nonzero lepton asymmetry from BBN data jointly with the Cosmic Microwave Background. I will leave some final comments on how a large total lepton asymmetry can be consistently realized in the Early Universe.

Zoom Link: https://pitp.zoom.us/j/95011247645?pwd=S0EwZG9nSHQvTjV0QjBxeHNUWWtmUT09