Reproducibility of Two Innate Immune System Models

In this paper we present the first step towards the development of a mathematical model of human immune system for advanced individualized healthcare, where medication plan is fine-tuned for each patient to fit his conditions. We reproduce two representative models of the innate immune system. The first model by Rocha et al. describes the dynamics of the innate immune response by ordinary differential equations, focusing on LPS, neutrophils, resting macrophages, and activated macrophages. The second model by Pigozzo et al. describes the spatial dynamics of LPS, neutrophils, and pro-inflammatory cytokines by partial differential equations. We found that the results of the first model are fully reproducible. However, the second model is only partially reproducible. Several parameters had to be adjusted in order to reproduce the dynamics of the immune response: diffusion coefficients and the rates of LPS phagocytosis, cytokine production, neutrophils chemotaxis and apoptosis.