The logistic function maps the real line (from minus infinity to plus infinity) to the range zero to one in a monotonically increasing manner. It is the same as a scaled and offset hyperbolic tangent hence at minus infinity it is approximately exponential growth but diverges from that rapidly as it approximates exponential decay. The inverse function is the logit.

| 1910 AD | Lotka & Volterra | Lotka-Volterra predator-prey model |
| 1927 AD | Kermack & McKendrick | Standard SIR model |
| 1987 AD | Anderson & May | Anderson-May model for HIV |
| 2024 AD | Mason | Minimal SIR model |