How and how much to invest for fighting cheaters: from an ODE to a Cellular Automata model

Abstract

In this paper, we present a study which is the completion of the problem left open in the appendix of the paper Nuño et al. (Eur J Appl Math 21:459-478, 2010). The goal of the paper is to offer a deeper analysis of the type of the ODE system featured in the paper above concerning the evolution of the total wealth and cheater population and, mainly, the purpose is to generalize this one to a Cellular Automata model introducing spatial and local effects. The work presented shows the original interaction between an Ordinary Differential Equations model and a Cellular Automata model.

Mathematical models for tumours with cancer stem cells

“…An interesting generalization of system (1)-(2) is presented inRodriguez-Brenes et al (2011, 2015 where the proliferation rate ρ u and the fraction of symmetric mitosis δ depend on v. This produces a sort of feedback regulation of the system that can be broken by phenotypical mutations, thus leading to abnormal cellular growth.…”

A two-component model of the red blood cell membrane and other mathematical models in medicine

“…Possibly, this term could be modified by a different function of u + v vanishing when the whole region is filled by tumour cells.2 For an application to a social problem seeNUÑO;PRIMICERIO, 2012) and(MEACCI, 2015).…”