Analysis of a stochastic SIR model with fractional Brownian motion

Caraballo, Tomás; Keraani, Sami

doi:10.1080/07362994.2018.1490912

Cited by 6 publications

(3 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [37], a link between sun-climate complexity and integrated global temperature anomalies is described by a fractional Brownian motion. Moreover, in [38], a stochastic model from epidemiology with fractional Brownian motion is studied to account for long range memory.…”

Section: Introductionmentioning

confidence: 99%

Warning signs for non-Markovian bifurcations: colour blindness and scaling laws

2022

View full text Add to dashboard Cite

Warning signs for tipping points (or critical transitions) have been very actively studied. Although the theory has been applied successfully in models and in experiments for many complex systems such as for tipping in climate systems, there are ongoing debates as to when warning signs can be extracted from data. In this work, we shed light on this debate by considering different types of underlying noise. Thereby, we significantly advance the general theory of warning signs for nonlinear stochastic dynamics. A key scenario deals with stochastic systems approaching a bifurcation point dynamically upon slow parameter variation. The stochastic fluctuations are generically able to probe the dynamics near a deterministic attractor to reveal critical slowing down. Using scaling laws near bifurcations, one can then anticipate the distance to a bifurcation. Previous warning signs results assume that the noise is Markovian, most often even white. Here, we study warning signs for non-Markovian systems including coloured noise and α -regular Volterra processes (of which fractional Brownian motion and the Rosenblatt process are special cases). We prove that early warning scaling laws can disappear completely or drastically change their exponent based upon the parameters controlling the noise process. This provides a clear explanation as to why applying standard warning signs results to reduced models of complex systems may not agree with data-driven studies. We demonstrate our results numerically in the context of a box model of the Atlantic Meridional Overturning Circulation.

show abstract

Section: Introductionmentioning

confidence: 99%

Warning signs for non-Markovian bifurcations: colour blindness and scaling laws

2022

View full text Add to dashboard Cite

show abstract

“…In a different approach, the spreading process of the epidemic dynamics has been also analyzed through some random, self-propelled particles, moving and interacting in a synthetic society [ 23 , 26 – 28 ]. As people often move and interact without following any deterministic or probabilistic rules, thus, the interactions and movements of a group be well approximated using Brownian motion-like Dynamics (BMD) [ 23 ].…”

Section: Introductionmentioning

confidence: 99%

How surface and fomite infection affect contagion dynamics: a study with self-propelled particles

Ghosh

Chakraborty

Bhattacharya

2022

Eur. Phys. J. Spec. Top.

View full text Add to dashboard Cite

Self-propelled particles have been a tool of choice for many studies for understanding spatial interaction of people and propagation of infectious diseases. Other than the direct contagion process through face-to-face contacts with an infected agent, in some diseases, like COVID-19, the disease can spread by indirect ways, through contaminated object surfaces and puff-clouds created by the infected individual. However, this dual spreading process and the impact of these indirect infections in the entire dynamics are not properly explored. In this work, we consider epidemic spreading in an artificial society, with realistic parameters and movements of people, along with the possibilities of indirect exposure through contaminated surfaces and puff-clouds. This particular simulation based infectious disease dynamics is associated with the movements of some self-propelled free agents executing random motion which is investigated in conjunction with the rules of a realistic contagion process. With mathematical formulation and extensive computational studies, we have accommodated the indirect infection possibilities into the dynamics by incorporating an infectious ‘tail’ with the infected individuals. Analytical expressions of survival distance and infection probability of individuals have been explicitly calculated and reported. Results of precise and comparative simulation study have revealed the seriousness of indirect infections in connection with several dynamical parameters. Using this framework, interpretation of multiple waves in local as well as global scenarios have been established for COVID-19 infection statistics. Furthermore, the importance of indirect infections are also pointed out through data fitting, showing that ignoring this component might cause a misinterpretation of the dynamical parameters, like, imposed restrictions.

show abstract

“…These systems were generated by taking into account some facts such as duration of disease, availability and resistance against vaccination, immune systems of individuals in the population and so on. There are mathematical models employing deterministic [4][5][6][7] , stochastic [1][2][3] , fractional-order [8][9][10][11][12][13][14][15] system of differential equations. Almost each of these models were generated by compartmental models considering each compartment as individuals of susceptible (denoted by S), infected (I), exposed (E), and recovered (R) ones.…”

Section: Introductionmentioning

confidence: 99%

Solutions of a disease model with fractional white noise

Akinlar

Gómez‐Aguilar

Boutarfa

2020

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre-including this research content-immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active.

show abstract

Analysis of a stochastic SIR model with fractional Brownian motion

Cited by 6 publications

References 11 publications

Warning signs for non-Markovian bifurcations: colour blindness and scaling laws

Warning signs for non-Markovian bifurcations: colour blindness and scaling laws

How surface and fomite infection affect contagion dynamics: a study with self-propelled particles

Solutions of a disease model with fractional white noise

Contact Info

Product

Resources

About