2022/01/14 by Eugenia Franco, Odo Diekmann, Franco, Eugenia +3 · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #45A05 #45D05 #45M05 #92D25 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.2201.05323
openalex publication_date 2022/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyse the long term behaviour of the measure-valued solutions of a class of linear renewal equations modelling physiologically structured populations. The renewal equations that we consider are characterised by a regularisation property of the kernel. This regularisation property allows to deduce the large time behaviour of the measure-valued solutions from the asymptotic behaviour of their absolutely continuous, with respect to the Lebesgue measure, component. We apply the results to a model of cell growth and fission and to a model of waning and boosting of immunity. For both models we relate the renewal equation (RE) to the partial differential equation (PDE) formulation and draw conclusions about the asymptotic behaviour of the solutions of the PDEs.