# Anomalous diffusion in run-and-tumble motion

## TL;DR

This paper models bacterial run-and-tumble motion using a combined Brownian and Lévy walk scheme, analyzing how different dwelling time distributions lead to various diffusion behaviors.

## Contribution

It introduces a continuous-time random walk model capturing diverse diffusion regimes in bacterial motion based on dwelling time distributions.

## Key findings

- Normal diffusion, superdiffusion, and ballistic spreading can result from different dwelling time distributions.
- The model explains how microscopic phase durations influence macroscopic diffusion behavior.
- Long-time and short-time behaviors of mean squared displacement are characterized.

## Abstract

A random walk scheme, consisting of alternating phases of regular Brownian motion and L\'evy walks, is proposed as a model for run-and-tumble bacterial motion. Within the continuous-time random walk approach we obtain the long-time and short-time behavior of the mean squared displacement of the walker as depending on the properties of dwelling time distribution in each phase. Depending on these distributions, normal diffusion, superdiffusion and ballistic spreading may arise.