abstract: We present an extension of a standard stochastic individual-based model for evolution in an asexual population which broadens the range of biological applications and is in particular able to describe some experiments in cancer immunotherapy, where tumours avoid detection through inflammation induced reversible dedifferentiation to a therapy resistant form.
In the standard model a population consisting of different traits with a large but non-constant population size is characterized by its natural birth rates, logistic death rates modelling competition, and the probability of mutation at each birth event. The evolution of the population is then described by a measure-valued Markov process.
In the extended model we distinguish between three different types of actors: tumour cells (characterized by their pheno- and genotypes), cytotoxic T-cells, and cytokines. The T-cells interact with the tumour cells displaying the differentiated phenotype in a predator-prey-like way. Furthermore, we include an environment-dependent switch between phenotypes, not affecting the genotype. We argue why understanding purely stochastic events may help to understand the resistance of tumours to various therapeutic approaches and may have non-trivial consequences on tumour treatment protocols.
Recently, new experiments have lead to a further modification of the model. The possibility of mutation to a different genotype that permanently displays the resistant phenotype has been added and also the effects of T-cell exhaustion and the spatial structure of the tumour have gained importance in the new setting and are now included. We study the interplay of genetic mutations and phenotypic switches on different timescales, where the originally unfit resistant mutant can grow under therapy and thus even help the wildtype's survival.
The extended model has been implemented as an Gillespie-like algorithm to simulate the process of immunotherapy. Since the number of cells in a tumour is large, we combine deterministic simulation of frequent events and stochastic simulation of rare events to decrease the running time of the algorithm.