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Most countries are suffering severely from the ongoing covid-19 pandemicdespite various levels of preventive measures. A common question is if and whena country or region will reach herd immunity $h$. The classical herd immunitylevel $h_C$ is defined as $h_C=1-1/R_0$, where $R_0$ is the basic reproductionnumber, for covid-19 estimated to lie somewhere in the range 2.2-3.5 dependingon country and region. It is shown here that the disease-induced herd immunitylevel $h_D$, after an outbreak has taken place in a country/region with a setof preventive measures put in place, is actually substantially smaller than$h_C$. As an illustration we show that if $R_0=2.5$ in an age-structuredcommunity with mixing rates fitted to social activity studies, and alsocategorizing individuals into three categories: low active, average active andhigh active, and where preventive measures affect all mixing ratesproportionally, then the disease-induced herd immunity level is $h_D=43\%$rather than $h_C=1-1/2.5=60\%$. Consequently, a lower fraction infected isrequired for herd immunity to appear. The underlying reason is that whenimmunity is induced by disease spreading, the proportion infected in groupswith high contact rates is greater than that in groups with low contact rates.Consequently, disease-induced immunity is stronger than when immunity isuniformly distributed in the community as in the classical herd immunity level.

The disease-induced herd immunity level for Covid-19 is substantially lower than the classical herd immunity level