Figure 2. Four compartment model of an epidemic.

A. Cartoon of the compartment model. Note that, in the model, permanent immunity is gained with probability α for mathematical convenience. Alternatively, temporary immunity can be gained with a probability of 1 and lost at rate k _L. Although the dynamics are different, the corresponding endemic equilibria can be identified by expressing k _L as function of α and compartment frequencies. B. Disease free equilibrium (gray), endemic equilibrium (striped), and unsustainable (red) regions for three analyzed viruses over a range of host contact rates. The unsustainable region for smallpox-like viruses is narrow and not shown to scale. C. For endemic equilibrium (contact rates correspond to the midrange shown in B), the fraction of the host population infected and the death rate. Note that, representing equilibrium, the choice of timescale (years) is arbitrary.