SusceptibleInfectedRecovered

Susceptibleinfectedrecovered refers to the classic compartmental framework in epidemiology that models disease dynamics by dividing a population into three groups: susceptible individuals who can become infected, infected individuals who can transmit the disease, and recovered individuals who have gained immunity. This trio—susceptible, infected, and recovered—forms the basis of the SIR model, a foundational tool in understanding how infections spread and decline over time.

In the SIR model, the population size is typically treated as constant, with transitions between compartments governed by transmission and recovery processes. The dynamics are commonly written with differential equations: dS/dt = -β S I / N, dI/dt = β S I / N - γ I, and dR/dt = γ I, where S, I, and R are the numbers of individuals in each compartment, N is the total population, β is the transmission rate, and γ is the recovery rate. The basic reproduction number, R0 = β/γ, indicates how many new infections one infectious person would generate in a fully susceptible population. If R0 exceeds 1, an outbreak can spread; if it is below 1, it tends to die out.

The model relies on simplifying assumptions, such as a closed population, homogeneous mixing, and lasting immunity after recovery. Real-world settings exhibit heterogeneity, varying contact patterns, and waning immunity, leading to extensions like SEIR (including an exposed stage), SIRS (allowing loss of immunity), and age-structured variants. Despite limitations, SIR and its variants remain central to planning vaccination strategies and evaluating interventions, tracing their origins to the work of Kermack and McKendrick in 1927.