DTM.4:4.2 - Test a rare variant in a specified resident regime

Place the proposed variant at a small positive amount in an otherwise specified regime. Determine its initial growth from the modeled receiving events and losses.

For one rare quantity y, a local form y’=r y plus smaller terms gives growth when r>0 and decline when r<0. r concerns this surrounding regime and these assumptions. If r=0 or the neglected terms can dominate at the relevant scale, the first-order test does not decide.

With several linked rare states, use the appropriate coupled linearization or generation-to-generation operator supplied by the mathematical modeling method. Do not assign one scalar “reproduction number” until its construction and threshold apply to that model.

A zero initial amount can remain zero in a deterministic model with no external introduction. The rare-variant test asks about a small positive amount; it does not predict that an introduction will occur.