SIRtype

SIRtype is a conceptual framework and, in some contexts, a software toolkit used to categorize and analyze SIR-type epidemiological models. It provides a typology of dynamical regimes that can arise in susceptible–infected–recovered systems, focusing on how transmission and recovery rates, population structure, and interventions shape qualitative behavior. The framework commonly considers the standard SIR model and its extensions, including vital dynamics, seasonality, waning immunity, vaccination, and age structure.

Key concepts include disease-free equilibrium, endemic equilibrium, transient outbreaks, and oscillatory or boom-bust dynamics. A central criterion is the basic reproduction number R0; when R0 > 1 the disease can invade, whereas R0 < 1 leads to disease fade-out. Beyond this threshold, SIRtype emphasizes how parameter changes or structural features create different regimes, identified by qualitative features of trajectories such as peak prevalence, duration, and whether the system settles into a steady state or continues to oscillate.

Methods used in SIRtype include equilibrium analysis, Jacobian stability, and bifurcation analysis, complemented by numerical simulation. Typing is accomplished by classifying time-series data or model output into regimes and by mapping parameter space to regime boundaries. Extensions address more complex dynamics such as age-structured mixing, vaccination impact, and seasonal forcing.

Applications span study design, intervention evaluation, and educational purposes in epidemiology. Limitations include reliance on the chosen model structure and parameter values; real-world data may be noisy, and simplified SIR-type models may not capture all heterogeneity or network effects present in populations.

Origin and usage vary across literature; SIRtype is not a single universal standard but a descriptive approach used to discuss the qualitative behavior of SIR-type systems.