Effective immunity and second waves: A dynamic causal modelling study

Karl J. Friston, Thomas Parr, Peter Zeidman, Adeel Razi, Guillaume Flandin, Jean Daunizeau, Oliver J. Hulme, Alexander J. Billig, Vladimir Litvak, Cathy J. Price, Rosalyn J. Moran, Anthony M.D.L. Costello, Deenan Pillay, Christian Lambert

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)


This technical report addresses a pressing issue in the trajectory of the coronavirus outbreak; namely, the rate at which effective immunity is lost following the first wave of the pandemic. This is a crucial epidemiological parameter that speaks to both the consequences of relaxing lockdown and the propensity for a second wave of infections. Using a dynamic causal model of reported cases and deaths from multiple countries, we evaluated the evidence models of progressively longer periods of immunity. The results speak to an effective population immunity of about three months that, under the model, defers any second wave for approximately six months in most countries. This may have implications for the window of opportunity for tracking and tracing, as well as for developing vaccination programmes, and other therapeutic interventions.

Original languageEnglish
Article number204
Number of pages16
JournalWellcome Open Research
Publication statusPublished - Sept 2020


  • Bayesian
  • Compartmental models
  • Coronavirus
  • Dynamic causal modelling
  • Epidemiology
  • Variational

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