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SIR epidemic models; stochastic epidemic models; stochastic differential equation; strong solution; weak solution; absorption; Kermack–McKendrick model
A two dimensional stochastic differential equation is suggested as a stochastic model for the Kermack–McKendrick epidemics. Its strong (weak) existence and uniqueness and absorption properties are investigated. The examples presented in Section 5 are meant to illustrate possible different asymptotics of a solution to the equation.
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