Stability of a stochastic SIR system

By E. Tornatore, Stefania Maria Buccellato, Pasquale Vetro. 2005

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A Stochastic Differential Equation SIS Epidemic Model (2011, methodology): “This is a well-established method [7, 10, 11, 12, 19, 22, 29], although both methods are biologically reasonable.”
STABILITY OF STOCHASTIC DELAYED SIR MODEL (2009, background): “For a specific SIR model with distributed delay, the stability of the boundary equilibrium (1, 0, 0) is studied in [23].”
Qualitative Behavior of Giving Up Smoking Models (2011, background): “There is a lot of mathematical theory on the concept of diseases and epidemics, (see for example [1, 3, 6, 7, 14, 17–19]).”
Long-time behaviour of a perturbed SIR model by white noise (2013, background): “And they deduce the globally asymptotic stability of the disease-free equilibrium when R0 ≤ 1, which greatly improved the corresponding result in [27].”
Local Lipschitz Continuity in the Initial Value and Strong Completeness for Nonlinear Stochastic Differential Equations (2013, background): “For the stochastic SIR model it is well known that the sum of the first two coordinates serves as a Lyapunov-type function (cf., e.g., Tornatore, Buccellato & Vetro [50]).”