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Modeling fire spread as an infection process is intuitive: An ignition lights a patch of fuel, which infects its neighbor, and so on. Infection models produce nonlinear thresholds, whereby fire spreads only when fuel connectivity and infection probability are sufficiently high. These thresholds are fundamental both to managing fire and to theoretical models of fire spread, whereas applied fire models more often apply quasi-empirical approaches. Here, we resolve this tension by quantifying thresholds in fire spread locally, using field data from individual fires ( n = 1,131) in grassy ecosystems across a precipitation gradient (496 to 1,442 mm mean annual precipitation) and evaluating how these scaled regionally (across 533 sites) and across time (1989 to 2012 and 2016 to 2018) using data from Kruger National Park in South Africa. An infection model captured observed patterns in individual fire spread better than competing models. The proportion of the landscape that burned was well described by measurements of grass biomass, fuel moisture, and vapor pressure deficit. Regionally, averaging across variability resulted in quasi-linear patterns. Altogether, results suggest that models aiming to capture fire responses to global change should incorporate nonlinear fire spread thresholds but that linear approximations may sufficiently capture medium-term trends under a stationary climate.