Contagion Models 2 SIS Model

SIS models include recovery that returns an infected unit to susceptibility. Some deterministic versions have an endemic equilibrium under specified conditions.

The susceptible–infected–susceptible model allows infection followed by recovery back into susceptibility. In a basic homogeneous deterministic model for infected fraction i, the rate of change is βi(1−i)−γi. With positive transmission and recovery rates, R0=β/γ; when R0 exceeds one, the model has a positive equilibrium i=1−1/R0, in addition to the disease-free state.

That mathematical equilibrium is not a claim that every real infection lasts forever. Finite stochastic populations can reach extinction, and parameters, contact patterns, importation, and interventions can change. SIR’s removed state also does not mean that every problem is permanently solved. The useful distinction is the transition structure, not a classification of life’s problems into solvable and eternally recurring.

When to use it

When a spreading process plausibly permits repeated transitions between susceptible and infected states.

How it can help

Inspect the transition structure and assumptions, then distinguish equilibrium predictions from stochastic extinction, changing conditions, and external reintroduction.