We propose a novel thermal production mechanism for dark matter based on the idea that dark matter particles $chi$ can transform (`infect) heat bath particles $psi$: $chi psi rightarrow chi chi$. For a small initial abundance of $chi$ this induces an exponential growth in the dark matter number density, closely resembling the epidemic curves of a spreading pathogen after an initial outbreak. To quantify this relation we present a sharp duality between the Boltzmann equation for the dark matter number density and epidemiological models for the spread of infectious diseases. Finally we demonstrate that the exponential growth naturally stops before $chi$ thermalizes with the heat bath, corresponding to a triumphant `flattening of the curve that matches the observed dark matter abundance.
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