When the initial state of an epidemic is uncertain, mathematical descriptions of that epidemic in terms of initial conditions must be modified by regarding these initial conditions as random variables having particular distribution functions. In this paper we assume a beta distribution as the initial proportion of infected in an SIR epidemic model. Numerical simulations are carried out on the various classes of the model as the uncertainties are propagated. The probability density functions of the random solutions of these classes over time are also calculated numerically. Some properties of the random solution and the effect of the parameters of the beta distribution on the behaviour of the epidemic are investigated.

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In this work, the predator-prey model with the ratio-dependent functional response is considered,  where the randomness enters into the equations only through their initial conditions. It is done by assuming normal distribution as the initial states of the model to treat the randomness. The passage from the deterministic situation to the random one for these equations is also the most transparent. In addition, a numerical simulation will be offered using the modified approach founded on the fifth-order improved Runge-Kutta method. Furthermore, the stability of the equilibrium points, and certain statistical properties related to the random behaviour of predators and their prey, will be analyzed and discussed.