Abstract:In Gray et al. [A stochastic differential equation SIS epidemic model, SIAM J. Appl. Math. 71 (3) (2011) 876–902] a susceptible‐infected‐susceptible (SIS) stochastic differential equation (SDE), obtained via a suitable random perturbation of the disease transmission coefficient in the classic SIS model, has been studied. Such random perturbation enters via an informal manipulation of stochastic differentials and leads to an Itô's‐type SDE. The authors identify a stochastic reproduction number, which differs fr… Show more
“…The previous theorem asserts that in the Stratonovich model (1.5) the conditions for extinction and persistence of the disease coincide with those of the deterministic system (1.1). This result extends to the SIR model an equivalent feature shown recently for the SIS model: see [4], [1], [9]. It also contributes to the fundamental modelling issues discussed for instance in [3] and [13].…”
Section: Introduction and Statement Of The Main Resultssupporting
“…The previous theorem asserts that in the Stratonovich model (1.5) the conditions for extinction and persistence of the disease coincide with those of the deterministic system (1.1). This result extends to the SIR model an equivalent feature shown recently for the SIS model: see [4], [1], [9]. It also contributes to the fundamental modelling issues discussed for instance in [3] and [13].…”
Section: Introduction and Statement Of The Main Resultssupporting
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