Continuous Time Markov Modeling and Analysis for Infectious Disease Spread

Sujata Sukhija; Rajeev Kumar; Arni S.R. Srinivasa Rao

doi:10.1007/s13571-025-00393-9

Continuous Time Markov Modeling and Analysis for Infectious Disease Spread

Sujata Sukhija
, Rajeev Kumar
, Arni S.R. Srinivasa Rao

Epidemiology

Research output: Contribution to journal › Article › peer-review

Abstract

A continuous-time Markov model is developed to account for transitions between discrete states of the infected and uninfected disease status of individuals in a population. Home-based quarantining of the infected individual is considered as one of the states of the model. The mean survival time, the mean hospitalisation time and the mean home isolation time have been derived using matrix calculus. Theoretical relationships between transition probabilities, mean times in state, and transition intensities have been obtained. Extended continuous time Markov model is also discussed by taking into account the age of the infected individual that could prove useful in analysing the impact of different age groups on the transition probabilities. Analysis is then conducted to understand elasticity and sensitivity of parameters. Computations have been shown keeping in mind a general hospital data, and some individuals could be under quarantine.

Original language	English (US)
Journal	Sankhya B
DOIs	https://doi.org/10.1007/s13571-025-00393-9
State	Accepted/In press - 2025

Keywords

Absorbing state
Elasticity
Fundamental matrix
Intensity matrix
Markov model
Sensitivity
Transient state

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

UN SDGs

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

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10.1007/s13571-025-00393-9

Cite this

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title = "Continuous Time Markov Modeling and Analysis for Infectious Disease Spread",

abstract = "A continuous-time Markov model is developed to account for transitions between discrete states of the infected and uninfected disease status of individuals in a population. Home-based quarantining of the infected individual is considered as one of the states of the model. The mean survival time, the mean hospitalisation time and the mean home isolation time have been derived using matrix calculus. Theoretical relationships between transition probabilities, mean times in state, and transition intensities have been obtained. Extended continuous time Markov model is also discussed by taking into account the age of the infected individual that could prove useful in analysing the impact of different age groups on the transition probabilities. Analysis is then conducted to understand elasticity and sensitivity of parameters. Computations have been shown keeping in mind a general hospital data, and some individuals could be under quarantine.",

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T1 - Continuous Time Markov Modeling and Analysis for Infectious Disease Spread

AU - Sukhija, Sujata

AU - Kumar, Rajeev

AU - Srinivasa Rao, Arni S.R.

N1 - Publisher Copyright: © Indian Statistical Institute 2025.

PY - 2025

Y1 - 2025

N2 - A continuous-time Markov model is developed to account for transitions between discrete states of the infected and uninfected disease status of individuals in a population. Home-based quarantining of the infected individual is considered as one of the states of the model. The mean survival time, the mean hospitalisation time and the mean home isolation time have been derived using matrix calculus. Theoretical relationships between transition probabilities, mean times in state, and transition intensities have been obtained. Extended continuous time Markov model is also discussed by taking into account the age of the infected individual that could prove useful in analysing the impact of different age groups on the transition probabilities. Analysis is then conducted to understand elasticity and sensitivity of parameters. Computations have been shown keeping in mind a general hospital data, and some individuals could be under quarantine.

AB - A continuous-time Markov model is developed to account for transitions between discrete states of the infected and uninfected disease status of individuals in a population. Home-based quarantining of the infected individual is considered as one of the states of the model. The mean survival time, the mean hospitalisation time and the mean home isolation time have been derived using matrix calculus. Theoretical relationships between transition probabilities, mean times in state, and transition intensities have been obtained. Extended continuous time Markov model is also discussed by taking into account the age of the infected individual that could prove useful in analysing the impact of different age groups on the transition probabilities. Analysis is then conducted to understand elasticity and sensitivity of parameters. Computations have been shown keeping in mind a general hospital data, and some individuals could be under quarantine.

KW - Absorbing state

KW - Elasticity

KW - Fundamental matrix

KW - Intensity matrix

KW - Markov model

KW - Sensitivity

KW - Transient state

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DO - 10.1007/s13571-025-00393-9

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JO - Sankhya B

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Continuous Time Markov Modeling and Analysis for Infectious Disease Spread

Abstract

Keywords

ASJC Scopus subject areas

UN SDGs

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