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
Views 3239 Downloads 226
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
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
Ong’ala Jacob Otieno,
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.
A. Brueggemann, D.T. Griffiths, E. Meats, T. Peto, D.W. Crook and B.G. Spratt (2003), “Clonal Relationships between Invasive and Carriage Streptococcus pneumoniae and Serotype- and Clone-Specific Differences in Invasive Disease Potential”, The Journal of Infectious Diseases. Vol 9(187) pp. 1424-1432
A. Brueggemann and V. G. Doern (2000), “Resistance Among treptococcus pneumoniae: Patterns, Mechanisms, Interpreting the Breakpoints”, The American Journal of Managed Care. Vol 6(23) pp.1189-1196.
A. Kuhlmann, U. Theidel, M. W. Pletz and J Schulenburg1, (2012) “Potential cost-effectiveness and benefit-cost ratios of adult pneumococcal vaccination in Germany” Health Economics Review. http://www.healtheconomicsreview.com/content/2/1/4 2 4
B. Ashby and C. Turkington (2007 ),, The encyclopedia of infectious diseases 3rd Edition, Website Publication -http://books.google.co.uk/ books?id =4Xlyaipv3dIC/pg=PA242.
B. Greenwood 354 (1999), “The epidemiology of pneumococcal infection in children in the developing world,” The Royal Society. Pp. 777-785
B.M. Gray, G.M. Converse and J. Dillon (2007), “Epidemiologic Studies of Streptococcus pneumoniae in Infants: Ac-quisition, Carriage, and Infection during the First 24 Months of Life”, The Journal of Infectious Diseases Vol 3 .pp.142
C. Davis (2010), “Pneumoniae”: Retrieved September 2011, from Medicinenet.com, http:// www.medicinenet.com/pneumonia/article.htm 2howdo.
D. Kateete, H. Kajumbula, K. Deogratias and A. Ssevviri, (2012), “Nasopharyngeal carriage rate of Streptococcus pneu-moniae in Ugandan children with sickle cell disease”, BMC Research Notes pp. 321-416
D. Pessoa, (2010), “Modelling the daynamics of Streptococcus pneumoniae Transmmission in children” Masters thesis, University of De Lisboa.
D. T. Jamison, (2006), “Disease control priorities in developing countries, Part 611 Stand Alone Series,” World Bank Publications, http://books.google.co.ke/books?id=Ds93H98Z6D0C 2
GAVI, , (2011), “Statement of Alex Palacios on the Global Alliance for Vaccines and Immunizations (GAVI) Alliance”
G. Aslan, G. Emekdas, M. Bayer, M. Sami, N. Kuyucu and A. Kanik (2007), “Serotype distribution of Streptococcus pneumoniae strains in the nasopharynx of healthy Turkish children” Indian Journal of Medical research Vol. 125pp. 582-587
G. McKenzie (1999), “The Pneumococcus Carrier”, The Mary Imogene Bassett Hospital pp. 88-100
G. Schiffman and C. Melissa (2010), “Pneumonia”, MedicineNet. Retrieved from http://www.medicinenet.com/pneumonia/article.htm 2howdo ,
H. Gazi, S. Kurutepe, S. Surucuoglu and A. Teker, (2004), “Antimicrobial susceptibility of bacterial pathogens in the oropharynx of healthy school children in Turkey.” Indian Journal of Medical research Vol. 120 pp. 489-494
I. Rudan, C. Boschi-Pinto, Z. Biloglav, K. Mulholland and H. Campbell, (2011), “Epidemiology and entomology of childhood pneumonia”., Bulletin of the World Health Organization.
J. Anthony, G. Scott, W. Abdullah,P. Walik, H. Douglas and M. Kim (2008),, Pneumonia research to reduce childhood mortality in the developing world, Journal of Clinical Investigation. Vol 4(118) pp. 1291-1300
J. Dushoff, W. Huang and C.Carlos, (1998), “Backwards birfurcations and catastrophe in simple model of fatal diseases”, Journal of Mathematical Biology Vol.36 pp. 227-248
J. Kodaira and J. Passos(2010), “The Basic Reproduction Number in SI Staged Progression Model: A Probabilistic Approach”, International Conference on Chaos and Nonlioniear Dynamics
J. Nuorti and C. Whitney (2010), “Prevention of Pneumococcal Disease Among Infants and Children Use of 13-Valent Pneumococcal Conjugate Vaccine and 23-Valent Pneumococcal Polysaccharide Vaccine, Division of Bacterial Diseases”, National Center for Immunization and Respiratory Diseases 59
J. M. Heffernan, R.J Smith, and L.M Wahl (2005),, Perspectives on the basic reproductive ratio, Journal of the Royal Society Interface. Vol 4(2) pp. 281-293
J. Starr, G. Fox and J. Clayton, (2008), “Streptococcus pneumoniae: An Update on Resistance Patterns in the United States”, Journal of Pharmacy Practice. Vol 5(21) pp. 363-370
J. Ong’ala, J.Y.T Mugisha and P. Oleche, (2013), “Mathematical Model for Pneumonia Dynamics with Carriers,” Inter-national Journal of Mathematical Analysis, Vol 7 pp. 2457 - 2473
K. Doura and D. Malendez-Morales and G. Mayer and L.E Perez, (2000), “An S-I-S Model of Streptococcal Disease with a Class of Beta Hemolytic Carriers”
K. Todar (2011), “Streptococcus, Online Textbook of Biology”, http://textbookofbacteriology.net/S.pneumoniae.html.
M. Bakir, A. Yagci, C. Akbenlioglu, A. Ilki, N. Ulger and G. Syletir, (2002), “Epidemiology of Streptococcus pneumoniae pharyngeal carriage among healthy Turkish infants and children” European Journal of Pediatrics. Vol. 161 pp. 165-166
M. Darboe, A. Fulford, O. Secka and A. Prentice(2010), “The dynamics of nasopharyngeal streptococcus Pneumoniae carriage among rural Gambian Mother-child pairs”, BioMed Central Infectious Diseases, Vol 95(10) pp. 1471-2334
M. Pergler and A. Freeman (2008), “Probabilstic Modeling as an Exploratory decision Making tool”, McKinseyand Company, Working Paper
M. Sanchez and S. Blower, (1997), “Uncertainty and Sensitivity Analysis of the Basic Reproductive Rate: Tuberculosis as an Example”, American Journal of Epidemiology. Vol. 12(145) pp. 1127-1137
N. W. Schluger, (2006), “Vaccinations Bacterial, for Pneumonia, Encyclopedia of Respiratory Medicine”. Vol 5(21) pp. 389-392
P. C. Appelbaum, (2003), “Resistance among Streptococcus pneumoniae: Implications for Drug Selection”, Oxford Jour-nals of Clinical Infectious Diseases. Vol 12(34), pp 1613-1620
P. Hill, Y. Cheung, A. Akisanya, K. Sankareh, G. Lahai, B. Greenwood and R. Adegbola, (2008), “Nasopharyngeal Carriage of Streptococcus pneumoniae in Gambian Infants: A Longitudinal Study,” Clinical Infectious Disease Journal Vol 6 (46) pp. 807-814
R.E. Black and S. Moris and J. Bryce (2003), Where and why are 10 million children dying every year, Lancet. Vol (361) pp. 2226-2234
R. Thadani, (2011), “Pneumonia Recovery Time”, http://www.buzzle.com/articles/pneumonia-recovery-time.html
S. Cousens, E.R. Black, L. H. Johnson, I. Rudan, D. G. Bassani and R. Cibulskis, Global, (2010), “Regional, and national causes of child mortality in 2008: a systematic analysis”, Lancet. Vol 375 pp. 1969-1987
S. Obaro and R. Adegbola, The pneumococcal: carriage, disease and conjugate vaccine, J Med Microbiol 2 (2002), 98-104
United Nations, (2011), “Milleniam Development Goals,” United Nations website, http://www.un.org/millenniumgoals/
World Health Organization(2010),, “Global Health Observatory Data Repository”, http://apps.who.int/ghodata/?vid=1320.
W. Hethcote, (2000), “The Mathematics of Infectious Diseases”, Society for Industrial and Applied Mathematics Vol. 424 pp. 599-653
Y. Kimura and S. Kotami and Y. Siokawa.(1984), “Recent Advances in streptococci and Streptoccocal Diseases”, Brack-nell