On a simulation of the oscillation excited by a random force
We consider a stochastic SIR system and we prove the existence, uniqueness and positivity of solution. Moreover the existence of an invariant measure under a suitable condition on the coefficients is studied.
We consider the equation where is a given increasing sequence of positive numbers, and is chosen at random so that are totally independent random variables uniformly distributed on interval . We determine the probability of the event that all solutions of the equation tend to zero as .