A Probabilistic Estimation of the Basic Reproduction Number: A Case of Control Strategy of Pneumonia

Ong’ala Jacob Otieno; Mugisha Joseph; Oleche Paul

doi:doi:10.11648/j.sjams.20140202.12

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A Probabilistic Estimation of the Basic Reproduction Number: A Case of Control Strategy of Pneumonia

Ong’ala Jacob Otieno, Mugisha Joseph, Oleche Paul

Published in Science Journal of Applied Mathematics and Statistics (Volume 2, Issue 2)

Received: 13 March 2014 Accepted: 10 April 2014 Published: 20 April 2014

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Abstract

Deterministic models have been used in the past to understand the epidemiology of infectious diseases, most importantly to estimate the basic reproduction number, Ro by using disease parameters. However, the approach overlooks variation on the disease parameter(s) which are function of Ro and can introduce random effect on Ro. In this paper, we estimate the Ro as a random variable by first developing and analyzing a deterministic model for transmission patterns of pneumonia, and then compute the probability distribution of Ro using Monte Carlo Markov Chain (MCMC) simulation approach. A detailed analysis of the simulated transmission data, leads to probability distribution of Ro as opposed to a single value in the convectional deterministic modeling approach. Results indicate that there is sufficient information generated when uncertainty is considered in the computation of Ro and can be used to describe the effect of parameter change in deterministic models

Published in	Science Journal of Applied Mathematics and Statistics (Volume 2, Issue 2)
DOI	10.11648/j.sjams.20140202.12
Page(s)	53-59
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Basic Reproduction Number, MCMC, Pneumonia Model, Uncertainty, Sensitivity Analysis

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APA Style

Ong’ala Jacob Otieno, Mugisha Joseph, Oleche Paul. (2014). A Probabilistic Estimation of the Basic Reproduction Number: A Case of Control Strategy of Pneumonia. Science Journal of Applied Mathematics and Statistics, 2(2), 53-59. https://doi.org/10.11648/j.sjams.20140202.12

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ACS Style

Ong’ala Jacob Otieno; Mugisha Joseph; Oleche Paul. A Probabilistic Estimation of the Basic Reproduction Number: A Case of Control Strategy of Pneumonia. Sci. J. Appl. Math. Stat. 2014, 2(2), 53-59. doi: 10.11648/j.sjams.20140202.12

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AMA Style

Ong’ala Jacob Otieno, Mugisha Joseph, Oleche Paul. A Probabilistic Estimation of the Basic Reproduction Number: A Case of Control Strategy of Pneumonia. Sci J Appl Math Stat. 2014;2(2):53-59. doi: 10.11648/j.sjams.20140202.12

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@article{10.11648/j.sjams.20140202.12,
  author = {Ong’ala Jacob Otieno and Mugisha Joseph and Oleche Paul},
  title = {A Probabilistic Estimation of the Basic Reproduction Number: A Case of Control Strategy of Pneumonia},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {2},
  number = {2},
  pages = {53-59},
  doi = {10.11648/j.sjams.20140202.12},
  url = {https://doi.org/10.11648/j.sjams.20140202.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20140202.12},
  abstract = {Deterministic models have been used in the past to understand the epidemiology of infectious diseases, most importantly to estimate the basic reproduction number, Ro by using disease parameters. However, the approach overlooks variation on the disease parameter(s) which are function of Ro and can introduce random effect on Ro. In this paper, we estimate the Ro as a random variable by first developing and analyzing a deterministic model for transmission patterns of pneumonia, and then compute the probability distribution of Ro using Monte Carlo Markov Chain (MCMC) simulation approach. A detailed analysis of the simulated transmission data, leads to probability distribution of Ro as opposed to a single value in the convectional deterministic modeling approach. Results indicate that there is sufficient information generated when uncertainty is considered in the computation of Ro and can be used to describe the effect of parameter change in deterministic models},
 year = {2014}
}

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TY  - JOUR
T1  - A Probabilistic Estimation of the Basic Reproduction Number: A Case of Control Strategy of Pneumonia
AU  - Ong’ala Jacob Otieno
AU  - Mugisha Joseph
AU  - Oleche Paul
Y1  - 2014/04/20
PY  - 2014
N1  - https://doi.org/10.11648/j.sjams.20140202.12
DO  - 10.11648/j.sjams.20140202.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 53
EP  - 59
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20140202.12
AB  - Deterministic models have been used in the past to understand the epidemiology of infectious diseases, most importantly to estimate the basic reproduction number, Ro by using disease parameters. However, the approach overlooks variation on the disease parameter(s) which are function of Ro and can introduce random effect on Ro. In this paper, we estimate the Ro as a random variable by first developing and analyzing a deterministic model for transmission patterns of pneumonia, and then compute the probability distribution of Ro using Monte Carlo Markov Chain (MCMC) simulation approach. A detailed analysis of the simulated transmission data, leads to probability distribution of Ro as opposed to a single value in the convectional deterministic modeling approach. Results indicate that there is sufficient information generated when uncertainty is considered in the computation of Ro and can be used to describe the effect of parameter change in deterministic models
VL  - 2
IS  - 2
ER  -

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Author Information

Ong’ala Jacob Otieno

School of Mathematics, Statistics and actuarial Science, Maseno University, Kisumu, Kenya
Mugisha Joseph

School of Mathematics, Statistics and actuarial Science, Maseno University, Kisumu, Kenya
Oleche Paul

Department of Mathematics, Makerere University, Kampala, Uganda

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APA Style

Ong’ala Jacob Otieno, Mugisha Joseph, Oleche Paul. (2014). A Probabilistic Estimation of the Basic Reproduction Number: A Case of Control Strategy of Pneumonia. Science Journal of Applied Mathematics and Statistics, 2(2), 53-59. https://doi.org/10.11648/j.sjams.20140202.12

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ACS Style

Ong’ala Jacob Otieno; Mugisha Joseph; Oleche Paul. A Probabilistic Estimation of the Basic Reproduction Number: A Case of Control Strategy of Pneumonia. Sci. J. Appl. Math. Stat. 2014, 2(2), 53-59. doi: 10.11648/j.sjams.20140202.12

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AMA Style

Ong’ala Jacob Otieno, Mugisha Joseph, Oleche Paul. A Probabilistic Estimation of the Basic Reproduction Number: A Case of Control Strategy of Pneumonia. Sci J Appl Math Stat. 2014;2(2):53-59. doi: 10.11648/j.sjams.20140202.12

Copy | Download

@article{10.11648/j.sjams.20140202.12,
  author = {Ong’ala Jacob Otieno and Mugisha Joseph and Oleche Paul},
  title = {A Probabilistic Estimation of the Basic Reproduction Number: A Case of Control Strategy of Pneumonia},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {2},
  number = {2},
  pages = {53-59},
  doi = {10.11648/j.sjams.20140202.12},
  url = {https://doi.org/10.11648/j.sjams.20140202.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20140202.12},
  abstract = {Deterministic models have been used in the past to understand the epidemiology of infectious diseases, most importantly to estimate the basic reproduction number, Ro by using disease parameters. However, the approach overlooks variation on the disease parameter(s) which are function of Ro and can introduce random effect on Ro. In this paper, we estimate the Ro as a random variable by first developing and analyzing a deterministic model for transmission patterns of pneumonia, and then compute the probability distribution of Ro using Monte Carlo Markov Chain (MCMC) simulation approach. A detailed analysis of the simulated transmission data, leads to probability distribution of Ro as opposed to a single value in the convectional deterministic modeling approach. Results indicate that there is sufficient information generated when uncertainty is considered in the computation of Ro and can be used to describe the effect of parameter change in deterministic models},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - A Probabilistic Estimation of the Basic Reproduction Number: A Case of Control Strategy of Pneumonia
AU  - Ong’ala Jacob Otieno
AU  - Mugisha Joseph
AU  - Oleche Paul
Y1  - 2014/04/20
PY  - 2014
N1  - https://doi.org/10.11648/j.sjams.20140202.12
DO  - 10.11648/j.sjams.20140202.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 53
EP  - 59
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20140202.12
AB  - Deterministic models have been used in the past to understand the epidemiology of infectious diseases, most importantly to estimate the basic reproduction number, Ro by using disease parameters. However, the approach overlooks variation on the disease parameter(s) which are function of Ro and can introduce random effect on Ro. In this paper, we estimate the Ro as a random variable by first developing and analyzing a deterministic model for transmission patterns of pneumonia, and then compute the probability distribution of Ro using Monte Carlo Markov Chain (MCMC) simulation approach. A detailed analysis of the simulated transmission data, leads to probability distribution of Ro as opposed to a single value in the convectional deterministic modeling approach. Results indicate that there is sufficient information generated when uncertainty is considered in the computation of Ro and can be used to describe the effect of parameter change in deterministic models
VL  - 2
IS  - 2
ER  -

Copy | Download