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.
stochastic differential equation, SIR epidemic models, weak solution, stochastic epidemic models, strong solution, absorption, Kermack--McKendrick model
92D25, 37N25