11 papers
On a phenotype-structured phase-field model of nutrient-limited tumour growth
Tommaso Lorenzi, Giulia Pozzi, Andrea Signori
Phase-field models of tumour growth have proved useful as theoretical tools to investigate cancer invasion. A key implicit assumption underlying mathematical models of this type wh…
Phenotype-structuring of non-local kinetic models of cell migration driven by environmental sensing
Tommaso Lorenzi, Nadia Loy, Chiara Villa
The capability of cells to form surface extensions to non-locally probe the surrounding environment plays a key role in cell migration. The existing mathematical models for migrati…
Kinetic and mean-field modeling of muscular dystrophies
Tommaso Lorenzi, Horacio Tettamanti, Mattia Zanella
We present a new class of models for assessing the cell dynamics characterising muscular dystrophies. The proposed approach comprises a system of integro-differential equations for…
Derivation and quasi-invariant asymptotics of phenotype-structured integro-differential models
Emanuele Bernardi, Tommaso Lorenzi, Andrea Tosin
Building upon kinetic theory approaches for multi-agent systems and generalising them to scenarios where the total mass of the system is not conserved, we develop a modelling frame…
A phenotype-structured reaction-diffusion model of avascular glioma growth
Francesca Ballatore, Xinran Ruan, Chiara Giverso +1
We consider a phenotype-structured reaction-diffusion model of avascular glioma growth. The model describes the interaction dynamics between tumour cells and oxygen, and takes into…
Heterogeneously structured compartmental models of epidemiological systems: from individual-level processes to population-scale dynamics
Emanuele Bernardi, Tommaso Lorenzi, Mattia Sensi +1
We develop a general modelling framework for compartmental epidemiological systems structured by continuous variables which are linked to the levels of expression of compartment-sp…