Statistical analysis of biological models with uncertainty

In this contribution relevant biological models, based on random differential equations, are studied. For the sake of generality, we assume that the initial condition and the biological model parameters are dependent random variables with arbitrary probability distributions. We present a general methodology that enables us to provide a full probabilistic description of the solution stochastic process for each stochastic model. The statistical analysis is performed through the calculation of the first probability function by applying the random variable transformation technique. From the first probability density function, we can calculate any one-dimensional moment of the solution, including the mean and the variance as important particular cases. Our theoretical findings are applied to describe the probabilistic dynamics of Spirulina sp. biomass production in a particular medium using real data.