• Abstract

Human heterogeneity is a critical issue in infectious disease transmission dynamics modelling, and it has recently received much attention in COVID-19 studies. In this article, a general human heterogeneous disease model with mutation is proposed to comprehensively study the effects of human heterogeneity on basic reproduction number, final epidemic size and herd immunity. We show that human heterogeneity may increase or decrease herd immunity level, strongly depending on some convexity of the heterogeneity function, which gives new insights and extends the results in [Britton et al., Science, 369:846–849, 2020]. Moreover, human heterogeneity may decrease the basic reproduction number but increase the level of herd immunity, implying the unreliability of the basic reproduction number in characterizing the spread and control of infectious diseases with human heterogeneity.

• General Summary

• Abstract

Granger causality (GC) stands as a powerful causal inference tool in time series analysis. Typically estimated from time series data with finite sampling rate, the GC value inherently depends on the sampling interval $\tau$. Intuitively, a higher data sampling rate leads to a time series that better approximates the real signal. However, previous studies have shown that the bivariate GC converges to zero linearly as $\tau$ approaches zero, which will lead to mis-inference of causality due to vanishing GC value even in the presence of causality. In this work, by performing mathematical analysis, we show this asymptotic behavior remains valid in the case of conditional GC when applying to a system composed of more than two variables. We validate the analytical result by computing GC value with multiple sampling rates for the simulated data of Hodgkin-Huxley neuronal networks and the experimental data of intracranial EEG signals. Our result demonstrates the hazard of GC inference with high sampling rate, and we propose an accurate inference approach by calculating the ratio of GC to $\tau$ as $\tau$ approaches zero.

• General Summary

• Abstract

Cancer is a multifaceted disease caused by dynamic interaction between genetic mutations and environmental factors. Understanding the genetic mutations underlying the development and progression of cancer is the stepstone for developing effective treatments and therapies. However, these mutations occurred in only a small fraction of cancer patients and it is extremely difficult to associate with cancer. Here, we propose MutNet, a heterogeneous network embedding method which integrate biomolecular network with cancer genomics data. Using pan cancer genomic data from The Cancer Genome Atlas program and public protein-protein interaction and pathway data, MutNet identifies rarely mutated cancer genes often overlooked by conventional genetic studies. In addition, the unified vector representation of biological entities allows us to reveal the tumor type specific cancer genes, cancer gene modules, and potential relationships among different tumor types. Our heterogeneous network embedding method holds the promise for the underlying mechanisms of cancer and potential therapeutic targets.

• General Summary