BAYESIAN MARKOV CHAIN MONTE CARLO SIMULATION OF NONLIENAR MODEL FOR INFECTIOUS DISEASES WITH QUARANTINE
DOI:
https://doi.org/10.22487/27765660.2023.v3.i1.16445Keywords:
Bayesian, Disease, Markov Chain Monte Carlo, Runge-Kutta, SIQSAbstract
The SIQS (Susceptible, Infective, Quarantine, and Susceptible) non-linear model is used to describe the dynamics of infectious diseases, especially optimizing individuals who are quarantined. Discretization of the SIQS model using the Runge-Kutta method and its physical interpretation is very useful if the model parameters can be estimated. Bayesian Markov Chain Monte Carlo for its numerical simulation. After 10,000 iterations, convergent and significant parameters were obtained, namely beta = 94.37, beta0 = -10.19, mu = -0.23 and b = 0.5.
References
Allen, L. J. (2003). An introduction to stochastic Epidemic Model-part 1. Lubbock, Texas: Departement of Mathematics and Statistics Texas Tech University.
Bain, L.J, and Engelhardt, M. (2000). Introduction to Probability and Mathematical Statistics. Second Edition. California: Duxbury Press.
Box, G.E.P. and Tiao, G. C. (1973). Bayes Inference in Statistical Analysis. Philippines: Addison-Wesley Publishing Company Inc.
Hethcote, H. W. (2000). The Basic Epidemology Models. Singapura: World Scientific Publishing.
Mukhsar, A. S. Ahmar, M. A. El Safty, H. El-Khawaga and M. El Sayed (2022), Bayesian Convolution for Stochastic Epidemic Model, Intelligent Automation & Soft Computing, Tech Science Press, vol. 34, no. 2, pp.1175-1186.
Mukhsar (2018), The Bayesian zero-inflated negative binomial (t) spatio-temporal model to detect an endemic DHF location, Far East Journal of Mathematical Sciences, vol. 109, no. 2, pp. 357-372.
Mukhsar, B. Abapihi, A. Sani, E. Cahyono, P. Adam and F. A. Abdullah (2016), Extended convolution model to Bayesian spatio-temporal for diagnosing DHF endemic locations, Journal of Interdisciplinary Mathematics, vol.19, no. 2, pp. 233-244.
Mukhsar, N. Iriawan, B. S. S. Ulama and Sutikno (2013), New look for DHF relative risk analysis using Bayesian poisson-lognormal 2-level spatio-temporal, International Journal of Applied Mathematics and Statistics, vol. 47, no. 17, pp. 39-46.
Nakamura, S. (1991). Applied Numerical Methods with Software. New Jersey: A division of Simon & Schuster by Prentice-Hall Inc.
