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Abstract One clear aspect of behaviour in the COVID-19 pandemic has been people’s focus on, and response to, reported or observed infection numbers in their community. We describe a simple model of infectious disease spread in a pandemic situation where people’s behaviour is influenced by the current risk of infection and where this behavioural response acts homeostatically to return infection risk to a certain preferred level. This homeostatic response is active until approximate herd immunity is reached: in this domain the model predicts that the reproduction rate R will be centred around a median of 1, that proportional change in infection numbers will follow the standard Cauchy distribution with location and scale parameters 0 and 1, and that high infection numbers will follow a power-law frequency distribution with exponent 2. To test these predictions we used worldwide COVID-19 data from 1st February 2020 to 30th June 2022 to calculate $$95\%$$ 95 % confidence interval estimates across countries for these R, location, scale and exponent parameters. The resulting median R estimate was $$95\%\; CI=[0.99, 1.01]$$ 95 % C I = [ 0.99 , 1.01 ] (predicted value 1) the proportional change location estimate was $$95\%\; CI=[-0.01, 0.02]$$ 95 % C I = [ - 0.01 , 0.02 ] (predicted value 0), the proportional change scale estimate was $$95\%\; CI=[0.99, 1.08]$$ 95 % C I = [ 0.99 , 1.08 ] (predicted value 1), and the frequency distribution exponent estimate was $$95\%\; CI=[1.97, 2.15]$$ 95 % C I = [ 1.97 , 2.15 ] (predicted value 2); in each case the observed estimate agreed with model predictions.