From the Modeling of the Immune Hallmarks of Cancer to a Black Swan in Biology

Abstract

This paper deals with the modeling of the early stage of cancer phenomena, namely mutations, onset, progression of cancer cells, and their competition with the immune system. The mathematical approach is based on the kinetic theory of active particles developed to describe the dynamics of large systems of interacting cells, called active particles. Their microscopic state is modeled by a scalar variable which expresses the main biological function. The modeling focuses on an interpretation of the immune-hallmarks of cancer.

On Entropy Dynamics for Active “Living” Particles

“…In addition, it can contribute to the assessment of chaotic behaviors which may be related to the onset of pathological states [5]. In some cases, these are enhanced by segregation phenomena already mentioned in the preceding paragraph.…”

“…Two possible approaches have been developed. The first one starts with a detailed modeling of the interactions involving not only social-biological states at the microscopic scale, but also localization of the interacting active particles; applications refer to crowd dynamics [9], vehicular traffic [5,6], and multicellular systems [27]. The second approach is based on the conjecture that space dynamics is induced by a velocity jump perturbation of the spatially homogeneous activity dynamics; see for example [25,30].…”

“…The interested reader is referred to the book [3] for theoretical aspects and for the rationale to develop specific applications which have been produced to model, for instance, the dynamics of collective learning [4], the immune competition [5], vehicular traffic [6][7][8], the dynamics of crowds [9][10][11], and the collective motion of swarms [12].…”

“…In several applications, the qualitative analysis of the initial value problem has generated proofs of the existence of solutions for arbitrarily large time; as an example, see [5]. However, information on the shape of the solution has been achieved only by computational solutions.…”

“…However, the concept of entropy is far less developed in the case of living systems which have the ability to express collective strategies and extract energy from the surrounding environment. In addition, biological systems can aggregate or fragment due to consent versus dissent dynamics [17,18], or even undergo Darwinist-type dynamics [5]. The utility of the information which can be obtained from the dynamics of entropy functional is well recognized.…”