# Analysis and simulation of a novel stochastic RNA silencing model

## TL;DR

This paper introduces a new model to study how random environmental changes impact RNA silencing processes in cells.

## Contribution

A novel stochastic RNA silencing model is proposed, incorporating white noise to capture random fluctuations.

## Key findings

- The stochastic model shows a unique global positive solution, ensuring biological relevance.
- Numerical simulations reveal that stochasticity significantly affects RNA silencing dynamics.
- The model provides new insights into gene regulatory processes under random environmental fluctuations.

## Abstract

The current work aims to investigate how random environmental fluctuations affect the dynamics of the RNA Silencing model. To capture this complexity, a novel stochastic RNA Silencing model is proposed by incorporating four distinct white noise terms into key system parameters. Unlike previous deterministic approaches, our model explicitly accounts for stochastic perturbations using Brownian motion processes. A comprehensive analysis of both the deterministic as well as the stochastic one are presented. Employing Lyapunov analysis, the stochastic system yields a unique global positive solution for any initial value, ensuring its biological relevance. Lastly, numerical simulations based on the Milstein’s higher-order-method are conducted for the two models. The findings highlight the significant influence of stochasticity on RNA silencing dynamics, offering new insights into the stability and behavior of gene regulatory processes under random fluctuations.