Statistical Analysis of a New Markov Chain Model for Rumor Dynamics in Heterogeneous Complex Social Networks

Divine Wanduku

doi:10.1007/978-3-031-69706-7_13

Statistical Analysis of a New Markov Chain Model for Rumor Dynamics in Heterogeneous Complex Social Networks

Divine Wanduku

Mathematical Sciences

Research output: Contribution to book or proceeding › Conference article › peer-review

Abstract

A new Markov chain (MC) model for rumor epidemic dynamics in heterogeneous complex social networks (HCSN) is investigated. The epidemic model is also a compartmental SEIR (susceptible-exposed-infected-removed), with an expanded multidimensional state space for the MC by utilizing two discrete time measures for representing both the “disease” states and the age in each state of the nodes in the HCSN. Moreover, characterizations of the MC at both the mean-field and global levels of the HCSN are given. A statistical analysis of the MC is conducted to find a parameter for the basic reproduction number, ℜ₀, of the “disease” in the network; and to find an unbiased and precise estimator for ℜ₀. The goodness-of-fit of the estimator is investigated by employing the mean squared error.

Original language	English
Title of host publication	Applied Mathematical Analysis and Computations I - 1st SGMC
Editors	Divine Wanduku, Shijun Zheng, Zhan Chen, Andrew Sills, Haomin Zhou, Ephraim Agyingi
Publisher	Springer
Pages	323-363
Number of pages	41
ISBN (Print)	9783031697050
DOIs	https://doi.org/10.1007/978-3-031-69706-7_13
State	Published - 2024
Event	1st Southern Georgia Mathematics Conference, SGMC 2021 - Virtual, Online Duration: Apr 2 2021 → Apr 3 2021

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	471
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	1st Southern Georgia Mathematics Conference, SGMC 2021
City	Virtual, Online
Period	04/2/21 → 04/3/21

Scopus Subject Areas

General Mathematics

Access to Document

10.1007/978-3-031-69706-7_13

Cite this

Wanduku, D. (2024). Statistical Analysis of a New Markov Chain Model for Rumor Dynamics in Heterogeneous Complex Social Networks. In D. Wanduku, S. Zheng, Z. Chen, A. Sills, H. Zhou, & E. Agyingi (Eds.), Applied Mathematical Analysis and Computations I - 1st SGMC (pp. 323-363). (Springer Proceedings in Mathematics and Statistics; Vol. 471). Springer. https://doi.org/10.1007/978-3-031-69706-7_13

Wanduku, Divine. / Statistical Analysis of a New Markov Chain Model for Rumor Dynamics in Heterogeneous Complex Social Networks. Applied Mathematical Analysis and Computations I - 1st SGMC. editor / Divine Wanduku ; Shijun Zheng ; Zhan Chen ; Andrew Sills ; Haomin Zhou ; Ephraim Agyingi. Springer, 2024. pp. 323-363 (Springer Proceedings in Mathematics and Statistics).

@inproceedings{5d38e3475c7b4271a086a7058dff289a,

title = "Statistical Analysis of a New Markov Chain Model for Rumor Dynamics in Heterogeneous Complex Social Networks",

abstract = "A new Markov chain (MC) model for rumor epidemic dynamics in heterogeneous complex social networks (HCSN) is investigated. The epidemic model is also a compartmental SEIR (susceptible-exposed-infected-removed), with an expanded multidimensional state space for the MC by utilizing two discrete time measures for representing both the “disease” states and the age in each state of the nodes in the HCSN. Moreover, characterizations of the MC at both the mean-field and global levels of the HCSN are given. A statistical analysis of the MC is conducted to find a parameter for the basic reproduction number, ℜ0, of the “disease” in the network; and to find an unbiased and precise estimator for ℜ0. The goodness-of-fit of the estimator is investigated by employing the mean squared error.",

author = "Divine Wanduku",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.; 1st Southern Georgia Mathematics Conference, SGMC 2021 ; Conference date: 02-04-2021 Through 03-04-2021",

year = "2024",

doi = "10.1007/978-3-031-69706-7_13",

language = "English",

isbn = "9783031697050",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "323--363",

editor = "Divine Wanduku and Shijun Zheng and Zhan Chen and Andrew Sills and Haomin Zhou and Ephraim Agyingi",

booktitle = "Applied Mathematical Analysis and Computations I - 1st SGMC",

address = "Germany",

}

Wanduku, D 2024, Statistical Analysis of a New Markov Chain Model for Rumor Dynamics in Heterogeneous Complex Social Networks. in D Wanduku, S Zheng, Z Chen, A Sills, H Zhou & E Agyingi (eds), Applied Mathematical Analysis and Computations I - 1st SGMC. Springer Proceedings in Mathematics and Statistics, vol. 471, Springer, pp. 323-363, 1st Southern Georgia Mathematics Conference, SGMC 2021, Virtual, Online, 04/2/21. https://doi.org/10.1007/978-3-031-69706-7_13

Statistical Analysis of a New Markov Chain Model for Rumor Dynamics in Heterogeneous Complex Social Networks. / Wanduku, Divine.
Applied Mathematical Analysis and Computations I - 1st SGMC. ed. / Divine Wanduku; Shijun Zheng; Zhan Chen; Andrew Sills; Haomin Zhou; Ephraim Agyingi. Springer, 2024. p. 323-363 (Springer Proceedings in Mathematics and Statistics; Vol. 471).

Research output: Contribution to book or proceeding › Conference article › peer-review

TY - GEN

T1 - Statistical Analysis of a New Markov Chain Model for Rumor Dynamics in Heterogeneous Complex Social Networks

AU - Wanduku, Divine

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

PY - 2024

Y1 - 2024

N2 - A new Markov chain (MC) model for rumor epidemic dynamics in heterogeneous complex social networks (HCSN) is investigated. The epidemic model is also a compartmental SEIR (susceptible-exposed-infected-removed), with an expanded multidimensional state space for the MC by utilizing two discrete time measures for representing both the “disease” states and the age in each state of the nodes in the HCSN. Moreover, characterizations of the MC at both the mean-field and global levels of the HCSN are given. A statistical analysis of the MC is conducted to find a parameter for the basic reproduction number, ℜ0, of the “disease” in the network; and to find an unbiased and precise estimator for ℜ0. The goodness-of-fit of the estimator is investigated by employing the mean squared error.

AB - A new Markov chain (MC) model for rumor epidemic dynamics in heterogeneous complex social networks (HCSN) is investigated. The epidemic model is also a compartmental SEIR (susceptible-exposed-infected-removed), with an expanded multidimensional state space for the MC by utilizing two discrete time measures for representing both the “disease” states and the age in each state of the nodes in the HCSN. Moreover, characterizations of the MC at both the mean-field and global levels of the HCSN are given. A statistical analysis of the MC is conducted to find a parameter for the basic reproduction number, ℜ0, of the “disease” in the network; and to find an unbiased and precise estimator for ℜ0. The goodness-of-fit of the estimator is investigated by employing the mean squared error.

UR - http://www.scopus.com/inward/record.url?scp=85210324350&partnerID=8YFLogxK

U2 - 10.1007/978-3-031-69706-7_13

DO - 10.1007/978-3-031-69706-7_13

M3 - Conference article

AN - SCOPUS:85210324350

SN - 9783031697050

T3 - Springer Proceedings in Mathematics and Statistics

SP - 323

EP - 363

BT - Applied Mathematical Analysis and Computations I - 1st SGMC

A2 - Wanduku, Divine

A2 - Zheng, Shijun

A2 - Chen, Zhan

A2 - Sills, Andrew

A2 - Zhou, Haomin

A2 - Agyingi, Ephraim

PB - Springer

T2 - 1st Southern Georgia Mathematics Conference, SGMC 2021

Y2 - 2 April 2021 through 3 April 2021

ER -

Statistical Analysis of a New Markov Chain Model for Rumor Dynamics in Heterogeneous Complex Social Networks

Abstract

Publication series

Conference

Scopus Subject Areas

Access to Document

Other files and links

Fingerprint

Cite this