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A Probabilistic Estimation of the Basic Reproduction Number: A Case of Control Strategy of Pneumonia
Science Journal of Applied Mathematics and Statistics
Volume 2, Issue 2, April 2014, Pages: 53-59
Received: Mar. 13, 2014; Accepted: Apr. 10, 2014; Published: Apr. 20, 2014
Authors
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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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
Keywords
Basic Reproduction Number, MCMC, Pneumonia Model, Uncertainty, Sensitivity Analysis
Ong’ala Jacob Otieno, Mugisha Joseph, Oleche Paul, A Probabilistic Estimation of the Basic Reproduction Number: A Case of Control Strategy of Pneumonia, Science Journal of Applied Mathematics and Statistics. Vol. 2, No. 2, 2014, pp. 53-59. doi: 10.11648/j.sjams.20140202.12
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