Simulation or statistically based models are often used to explore the outcomes and dynamics of physical systems or scientific experiments. In this work, we consider the use of a mixed effects differential equations model and the use of a stochastic agent based model to model data from competition infection experiments of Equine Infectious Anemia Virus (EIAV). EIAV is a retrovirus that presents with a lifelong persistent infection. Vaccine development for this and other retroviruses has been impeded due to the genetic variation that the virus exhibits in the presence of host immune pressure. To assess if genetic variation has an impact on replicative capacity, variants of EIAV that differ phenotypically were competed in dual infection assays. Data from these experiments were used to develop models that are aimed at being able to detect if there are differences in replicative capacity among the variants.

We first consider a mixed effects model of data from an in vivo competition assay. Parameters of the model are estimated through the use of Markov Chain Monte Carlo (MCMC) methods. In vitro competition experiments were also conducted. These experiments offer more controlled experimental conditions than the in vivo assays. We then propose an agent based computer model that is able to simulate cell free and cell associated virus spread to model the data from the in vitro competition assays. To estimate the parameters of the agent based model, a surrogate Gaussian process model is used. Finally, we propose an extension of the Gaussian process model to account for the additional variance present in stochastic computer models.