Grzegorz Rempala

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  Mathematics of Modeling a Pandemic: The Journey Continues
  Grzegorz Rempala
  Over the last several weeks many mathematicians, statisticians, and data scientists have found themselves involved with various efforts in response to the public health crisis caused by the COVID-19 pandemic. Did predictive modeling really help with COVID preparedness and decision making? Can we use it to slowly move away from the current measures of social distancing and reopen our economy. Following up on my earlier seminar on the topic, I will try to give a perspective of how various mathematical methods turned out to work (or not) in practical settings of the daily predictions of the pandemic size in Ohio. In particular, I will briefly outline some new ideas and possible improvements in the methodology of "dynamic survival analysis developed by the OSU COVID response team to help predict COVID hospital burden.
  
  This is a Follow-up on the talk Prof. Rempala gave on March 24, 2020 titled Mathematical Models of Epidemics: Tracking Coronavirus using Dynamic Survival Analysis.
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  Mathematical Models of Epidemics: Tracking Coronavirus using Dynamic Survival Analysis
  Grzegorz Rempala
  As the outbreak of COVID-19 in the city of Wuhan appears to be the beginning of a global pandemic, there is much public interest in predicting both the dynamics and the size of the ongoing regional outbreaks in different countries. It is also important to ascertain the potential effects of early interventions such as school closures and mandatory or self-imposed quarantines. To answer some of these questions, we propose a general framework for analyzing the ongoing outbreak trend using data from a partially observed epidemic curve under minimal assumptions that are clearly speci- fied. In particular, this framework does not assume any specific infectious or recovery periods (which are often unknown) or observable prevalence of the disease (allowing, for instance, for silent infectives). We show that this analysis can help anticipate both the likely temporal trends of an ongoing epidemic as well as its final size in a commu- nity with or without social distancing. We use our approach to predict the trajectory of the epidemic curve from Wuhan city in Hubei province, which is most detailed one available to date from the COVID-19 outbreak.
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  Correlation equations, US elections, and modeling SIR-epidemics on dynamic random graphs
  Grzegorz Rempala
  Stochastic SIR-type epidemic processes on random graphs are a special class of interaction networks that have become of interest lately for modeling contact-type epidemics (Ebola, HIV, election choices etc). I will discuss a particular case of the SIR epidemic evolving on a configuration model random graph with given degree distribution. In particular, I will describe the relevant large graph limit result which yields the law of large numbers (LLN) for the edge-based SIR process and is useful in building a "network-free" SIR Markov hybrid model for epidemic parameters inference.
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  Deterministic and Stochastic SIR Dynamics on Random Graphs with Given Degree
  Grzegorz Rempala

  I will present some recent work of Mbi based group which investigated a mathematical model of a large pandemic,  leading to the Law of Large number result for the SIR type epidemics on random contact networks.   I will also discuss the applications of the LLN approximation in building a "network-free" SIR Markov hybrid model which can be used for epidemic parameters inference. The hybrid model idea appears particularly relevant in the context of the recent Ebola and the current Zika virus epidemics.

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  Omics Data: Testing for Differential Expressions
  Maciej Pietrzak, Grzegorz Rempala
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  Omics Data: Differential Expressions via GLM
  Maciej Pietrzak, Grzegorz Rempala