Bayesian Inference of State-Level COVID-19 Basic Reproduction Numbers across the United States

Abhishek Mallela, Jacob Neumann, Ely F. Miller, Ye Chen, Richard G. Posner, Yen Ting Lin, William S. Hlavacek

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Although many persons in the United States have acquired immunity to COVID-19, either through vaccination or infection with SARS-CoV-2, COVID-19 will pose an ongoing threat to non-immune persons so long as disease transmission continues. We can estimate when sustained disease transmission will end in a population by calculating the population-specific basic reproduction number R0, the expected number of secondary cases generated by an infected person in the absence of any interventions. The value of R0 relates to a herd immunity threshold (HIT), which is given by 1 − 1/R0 . When the immune fraction of a population exceeds this threshold, sustained disease transmission becomes exponentially unlikely (barring mutations allowing SARS-CoV-2 to escape immunity). Here, we report state-level R0 estimates obtained using Bayesian inference. Maximum a posteriori estimates range from 7.1 for New Jersey to 2.3 for Wyoming, indicating that disease transmission varies considerably across states and that reaching herd immunity will be more difficult in some states than others. R0 estimates were obtained from compartmental models via the next-generation matrix approach after each model was parameterized using regional daily confirmed case reports of COVID-19 from 21 January 2020 to 21 June 2020. Our R0 estimates characterize the infectiousness of ancestral strains, but they can be used to determine HITs for a distinct, currently dominant circulating strain, such as SARS-CoV-2 variant Delta (lineage B.1.617.2), if the relative infectiousness of the strain can be ascertained. On the basis of Delta-adjusted HITs, vaccination data, and seroprevalence survey data, we found that no state had achieved herd immunity as of 20 September 2021.

Original languageEnglish (US)
Article number157
Issue number1
StatePublished - Jan 2022


  • Basic reproduction number
  • Bayesian inference
  • Coronavirus disease 2019 (COVID-19)
  • Herd immunity
  • Mathematical model

ASJC Scopus subject areas

  • Infectious Diseases
  • Virology


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