Continuous model for collective invasion with leader-follower dynamics

Collective invasion plays a pivotal role in cancer metastasis, characterized by coordinated movement of leader and follower cells into surrounding tissues. This study presents a continuous mathematical model to investigate the dynamics underlying this process, focusing on leader chemotaxis, cell-cell adhesion, and the conservation of cell numbers. The model incorporates diffusion, chemotaxis, and adhesion terms, governed by parameters for leader-leader ($\alpha_l$), follower-follower ($\alpha_f$), and leader-follower ($\alpha_{fl}$) interactions. Using a nondimensionalized system of partial differential equations solved numerically via the finite element method, we explored invasion dynamics across diverse parameter settings. Preliminary simulations model the leader cells migrating directionally towards a chemoattractant gradient, forming invasion fronts that pull follower cells via strong leader-follower adhesion. Collective invasion is observed when leader-follower adhesion dominated over leader-leader adhesion. Our results aim to provide early insights into the interplay between chemotaxis and adhesion in driving metastatic behavior, and our objective is to further characterize these dynamics based on our model parameters in future work.