This chapter focuses on the use of deterministic models based on differential or partial differential equations (PDEs), with a special focus on reaction–diffusion models. Parameters inference rely on the definition of a probabilistic observation model depending on the outputs of the mechanistic model. Ordinary differential equations (ODEs) are used in population dynamics to describe the evolution of the size of one or more populations of individuals over time. SIR models are a form of ODE model widely used in epidemiology. The reaction–diffusion model is simulated by producing a numerical approximation of the solution of the PDE. The chapter presents an approach to establishing the link between latent variables and data, which are generally noisy, partial and/or non-commensurable. It focuses on the estimation of parameters and the inference of latent processes; for cases requiring the estimation of functions, readers may wish to consult the literature on semi-parametric and non-parametric models.