A Simple Noise Model with Memory for Biological Systems

TL;DR

This paper introduces a noise model with adjustable memory that produces various correlated noise types, useful for modeling biological systems with delays, and demonstrates its impact on epidemiological infection dynamics.

Contribution

The paper presents a novel noise model with memory for biological systems and explores its effects on epidemiological models, highlighting the role of noise parameters.

Findings

Noise model can generate white to quasi-periodic noise.

Memory influences the spectral density of the noise.

Noise parameters affect infection dynamics in the epidemiological model.

Abstract

A noise source model, consisting of a pulse sequence at random times with memory, is presented. By varying the memory we can obtain variable randomness of the stochastic process. The delay time between pulses, i. e. the noise memory, produces different kinds of correlated noise ranging from white noise, without delay, to quasi-periodical process, with delay close to the average period of the pulses. The spectral density is calculated. This type of noise could be useful to describe physical and biological systems where some delay is present. In particular it could be useful in population dynamics. A simple dynamical model for epidemiological infection with this noise source is presented. We find that the time behavior of the illness depends on the noise parameters. Specifically the amplitude and the memory of the noise affect the number of infected people.