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An infection caused by bacteria.

An infection involves invasion and multiplication of an infectious agent in a host. Bacteria are one possible cause; an agent capable of causing disease is a pathogen. The National Cancer Institute defines infection through invasion and growth in the body. ^[ref].

In a SIR model, acquiring infection moves a member of the susceptible compartment into the infectious compartment. That immediate transition is a model assumption: the SEIR model instead includes an exposed stage before infectiousness. Specify these states when translating a biological process into compartmental models.

An epidemic is a period of growing infection incidence in a population. Compartmental models describe transmission, recovery and depletion or renewal of susceptible hosts. An epidemic invasion threshold concerns growth after a small introduction; a final size relation for an epidemic concerns the total susceptible depletion of a closed outbreak. These are distinct from an endemic equilibrium with continuing transmission.

For a closed homogeneous epidemic, integrating $dS/dR$ relates the ultimately susceptible population to cumulative infections through an exponential equation.

The relation constrains the final outcome of compartmental models rather than describing their whole time-dependent solution.