English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Reaction diffusion equations have been used to model a wide range ofbiological phenomenon related to population spread and proliferation fromecology to cancer. It is commonly assumed that individuals in a population havehomogeneous diffusion and growth rates, however, this assumption can beinaccurate when the population is intrinsically divided into many distinctsubpopulations that compete with each other. In previous work, the task ofinferring the degree of phenotypic heterogeneity between subpopulations fromtotal population density has been performed within a framework that combinesparameter distribution estimation with reaction-diffusion models. Here, weextend this approach so that it is compatible with reaction-diffusion modelsthat include competition between subpopulations. We use a reaction-diffusionmodel of Glioblastoma multiforme, an aggressive type of brain cancer, to testour approach on simulated data that are similar to measurements that could becollected in practice. We use Prokhorov metric framework and convert thereaction-diffusion model to a random differential equation model to estimatejoint distributions of diffusion and growth rates among heterogeneoussubpopulations. We then compare the new random differential equation modelperformance against other partial differential equation models' performance. Wefind that the random differential equation is more capable at predicting thecell density compared to other models while being more time efficient. Finally,we use $k$-means clustering to predict the number of subpopulations based onthe recovered distributions.

Estimation of Parameter Distributions for Reaction-Diffusion Equations with Competition using Aggregate Spatiotemporal Data