Dr. Sumit Kumar Banerjee, Analysis of SIR Epidemic Model by Using Stochastic Process, ASIO Journal of Chemistry, Physics, Mathematics & Applied Sciences (ASIO-JCPMAS), 2016, 1(1): 09-11.
ARTICLE TYPE: Research
dids/doi No.: 02.2016-14482937
dids link: http://dids.info/didslink/02.2016-55799898/
A mathematical SIR epidemic model with invariant population size has been studied. Due to incorporation of stochastic process into the mathematical model the term probability has been used instead of rate, which is used in deterministic model. Discrete stochastic process especially Markov chain has been used to analyze the SIR epidemic model and finally validity of the model has been checked by using numerical simulation.
Key words: Epidemic model, probability, stochastic process, Markov chain, simulation.
- W. O. Kermack and A.G. Mckendrick, contributions to the mathematical theory of epidemics, part 1, proc. Roy. Soc. London Ser. A, 115 (1927), PP. 700721.
- A.G. Mckendrick, Applications of mathematics to medical problems, proc. Edinburgh Math. Soc., 44(1926), PP.98130.
- N. Becker, The use of epidemic models, Biometrics, 35 (1978), PP. 295305.
- E. Beretta, Y. Takeuchi, Global stability of a SIR epidemic model with time delay, J. Math. Biol., 33(1998), PP. 250-260.
- C. Castillo-Chavez, ed., Mathematical and Statistical Approaches to AIDS Epidemiology, Lecture Notes in Biomath. 83 (2011), PP. 382-390.
- V. Capasso, G. Serio, A generalization of the Kermack-McKendrick deterministic epidemic model, Math. Bio. sci, 42(2012), PP.43-61.
- W. Ma, Y. Takeuchi, T. Hara, E. Beretta, Permanence of an SIR epidemic model with distributed time delays, Tohoku Math. J., 54(2012), PP.581-591.
- M. song, W. Ma, Y. Takeuchi, permanence of a delayed SIR epidemic model with density dependent birth rate, J. Comput. Appl. Math. 201(2012), PP. 389-394.
- D. Xiao, S. Ruan, Global analysis of an epidemic model with non monotone incidence rate, Math. Bio. sci. 208(2007), PP. 419-429.