Mathematical modelling of cancer cell invasion of tissue

By Ignacio Ramis-Conde, M. Chaplain, A. Anderson. Mathematical and computer modelling, 2005

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Global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening (2014, background): “in colonies of Salmonella typhimurium ([35]), but also medically relevant processes such as tumor invasion ([3], [17]) and self-organization during embryonic development ([24]).”
Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production (2016, background): “ation, spatial pattern formation, embryonic morphogenesis, cell sorting, immune response, wounding healing, tumor-induced angiogenesis, and also tumor invasion (see [35], [20], [28], [11], [1], [10], [6] and [7], for instance). The renowned Keller-Segel model (cf. (1.4) below), describing the collec”
Boundedness in a two-dimensional chemotaxis-haptotaxis system (2014, background): “ x ∈ Ω, (1.3) where ∂ ∂ν denotes diﬀerentiation with respect to outward normal on ∂Ω, and the parameters χ,ξ and µ are assumed to be positive. This system was initially proposed by Chaplain and Lolas [3, 4] to model the process of cancer cell invasion of surrounding tissue. In this context, u repres”