Parameter Estimation in a New Markov Jump Process Compartmental Model with Missing Data

Divine Wanduku; Ivy Collins

doi:10.1007/978-3-031-69710-4_7

Parameter Estimation in a New Markov Jump Process Compartmental Model with Missing Data

Divine Wanduku
, Ivy Collins

Mathematical Sciences

Georgia Southern University

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

1 Scopus citations

Abstract

In this paper, a novel compartmental model for a disease epidemic dynamics with both symptomatic and asymptomatic disease transmissions; exposure, vaccinated and hospitalized states; and recovery and death states is derived and studied. The dynamic model is a discrete-time approximation of a Markov jump processes with inter-jump times between states that are exponentially distributed. This study addresses the statistical inference challenges in compartmental models for disease dynamics exhibiting numerous states with missing data, such as, asymptomatic infectiousness, exposure to disease, and recovery from an asymptomatic infectious state. The rigorous method of EM-algorithm is employed to find Maximum-Likelihood estimators for the disease parameters in the model. This research is motivated by infectious diseases such as COVID-19, with non-observable compartments requiring data imputation statistical methods for parameter estimation. Numerical simulation results are presented.

Original language	English
Title of host publication	Applied Mathematical Analysis and Computations II - 1st SGMC
Editors	Divine Wanduku, Shijun Zheng, Zhan Chen, Andrew Sills, Haomin Zhou, Ephraim Agyingi
Publisher	Springer
Pages	141-179
Number of pages	39
ISBN (Print)	9783031697098
DOIs	https://doi.org/10.1007/978-3-031-69710-4_7
State	Published - Aug 7 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	472
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

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Scopus Subject Areas

General Mathematics

Keywords

62F10
92B15
Conditional expectation
EM-algorithm
Markov jump process
Maximum-likelihood estimator
Multinomial distribution
SVIS model
Serial exponential distribution

Access to Document

10.1007/978-3-031-69710-4_7

Cite this

Wanduku, D., & Collins, I. (2024). Parameter Estimation in a New Markov Jump Process Compartmental Model with Missing Data. In D. Wanduku, S. Zheng, Z. Chen, A. Sills, H. Zhou, & E. Agyingi (Eds.), Applied Mathematical Analysis and Computations II - 1st SGMC (pp. 141-179). (Springer Proceedings in Mathematics and Statistics; Vol. 472). Springer. https://doi.org/10.1007/978-3-031-69710-4_7

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title = "Parameter Estimation in a New Markov Jump Process Compartmental Model with Missing Data",

abstract = "In this paper, a novel compartmental model for a disease epidemic dynamics with both symptomatic and asymptomatic disease transmissions; exposure, vaccinated and hospitalized states; and recovery and death states is derived and studied. The dynamic model is a discrete-time approximation of a Markov jump processes with inter-jump times between states that are exponentially distributed. This study addresses the statistical inference challenges in compartmental models for disease dynamics exhibiting numerous states with missing data, such as, asymptomatic infectiousness, exposure to disease, and recovery from an asymptomatic infectious state. The rigorous method of EM-algorithm is employed to find Maximum-Likelihood estimators for the disease parameters in the model. This research is motivated by infectious diseases such as COVID-19, with non-observable compartments requiring data imputation statistical methods for parameter estimation. Numerical simulation results are presented.",

keywords = "62F10, 92B15, Conditional expectation, EM-algorithm, Markov jump process, Maximum-likelihood estimator, Multinomial distribution, SVIS model, Serial exponential distribution",

author = "Divine Wanduku and Ivy Collins",

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",

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language = "English",

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series = "Springer Proceedings in Mathematics and Statistics",

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

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}

Wanduku, D & Collins, I 2024, Parameter Estimation in a New Markov Jump Process Compartmental Model with Missing Data. in D Wanduku, S Zheng, Z Chen, A Sills, H Zhou & E Agyingi (eds), Applied Mathematical Analysis and Computations II - 1st SGMC. Springer Proceedings in Mathematics and Statistics, vol. 472, Springer, pp. 141-179, 1st Southern Georgia Mathematics Conference, SGMC 2021, Virtual, Online, 04/2/21. https://doi.org/10.1007/978-3-031-69710-4_7

Parameter Estimation in a New Markov Jump Process Compartmental Model with Missing Data. / Wanduku, Divine; Collins, Ivy.
Applied Mathematical Analysis and Computations II - 1st SGMC. ed. / Divine Wanduku; Shijun Zheng; Zhan Chen; Andrew Sills; Haomin Zhou; Ephraim Agyingi. Springer, 2024. p. 141-179 (Springer Proceedings in Mathematics and Statistics; Vol. 472).

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

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AU - Wanduku, Divine

AU - Collins, Ivy

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

PY - 2024/8/7

Y1 - 2024/8/7

N2 - In this paper, a novel compartmental model for a disease epidemic dynamics with both symptomatic and asymptomatic disease transmissions; exposure, vaccinated and hospitalized states; and recovery and death states is derived and studied. The dynamic model is a discrete-time approximation of a Markov jump processes with inter-jump times between states that are exponentially distributed. This study addresses the statistical inference challenges in compartmental models for disease dynamics exhibiting numerous states with missing data, such as, asymptomatic infectiousness, exposure to disease, and recovery from an asymptomatic infectious state. The rigorous method of EM-algorithm is employed to find Maximum-Likelihood estimators for the disease parameters in the model. This research is motivated by infectious diseases such as COVID-19, with non-observable compartments requiring data imputation statistical methods for parameter estimation. Numerical simulation results are presented.

AB - In this paper, a novel compartmental model for a disease epidemic dynamics with both symptomatic and asymptomatic disease transmissions; exposure, vaccinated and hospitalized states; and recovery and death states is derived and studied. The dynamic model is a discrete-time approximation of a Markov jump processes with inter-jump times between states that are exponentially distributed. This study addresses the statistical inference challenges in compartmental models for disease dynamics exhibiting numerous states with missing data, such as, asymptomatic infectiousness, exposure to disease, and recovery from an asymptomatic infectious state. The rigorous method of EM-algorithm is employed to find Maximum-Likelihood estimators for the disease parameters in the model. This research is motivated by infectious diseases such as COVID-19, with non-observable compartments requiring data imputation statistical methods for parameter estimation. Numerical simulation results are presented.

KW - 62F10

KW - 92B15

KW - Conditional expectation

KW - EM-algorithm

KW - Markov jump process

KW - Maximum-likelihood estimator

KW - Multinomial distribution

KW - SVIS model

KW - Serial exponential distribution

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PB - Springer

T2 - 1st Southern Georgia Mathematics Conference, SGMC 2021

Y2 - 2 April 2021 through 3 April 2021

ER -

Parameter Estimation in a New Markov Jump Process Compartmental Model with Missing Data

Abstract

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UN SDGs

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Keywords

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