  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.
