Open Access Open Access  Restricted Access Subscription or Fee Access

Final Size of Stochastic SIR Epidemic Model with Infection Rate of General Form


(*) Corresponding author


Authors' affiliations


DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)

Abstract


In this work we consider the SIR (Susceptible - Infected -Removed) epidemic model with infection and removal rates of general form  and  respectively. To calculate the final size of this model we give a recursive method using the embedded chain. Then we make a numerical calculation for some particular infections and removals rates. Our method we allow calculating the final size for a large population and for all values of basic reproduction number, so it is very fast.
Copyright © 2017 Praise Worthy Prize - All rights reserved.

Keywords


Final Size; SIR; Stochastic Model; Markov Process; Embedded Chain

Full Text:

PDF


References


N. T. J. Bailey, The total size of a general stochastic epidemic. Biometrika. 40. 177-85, 1953.

N. T. J. Bailey, The Mathematical Theory of Infectious Diseases. Griffin-London, 2nd. Edition, 1975.

T. Williams, An algebraic proof of the threshold theorem for the general stochastic epidemic, Adv. appl. Prob. 3, 223, 1971.

F. G. Ball, A Note on the Total Size Distribution of Epidemic Models, Journal of Appl. Prob., Vol. 23, No. 3, pp. 832-836, Sep., 1986.

F. G. Ball, The threshold behaviour of epidemic models. J. Appl. Probab., 20, 227-241, 1983.

F. G. Ball and D. Clancy, The final size and severity of a generalised stochastic multitype epidemic models, Adv. App. Prob. 25. 721-736, 1993.

H. El Maroufy, Modèles déterministes et stochastiques des épidémies de type SIE étude quantitative et qualitative, Ph. D. dissertation, Sidi Mohammed Ben Abdellah Univ., Faculty of Science Dhar-Mahraz, Fès, 2001.

H. El Maroufy, T. Ziad, and L. Omari, Closed form of time dependent SIR epidemics with generalized infection mechanisms, Departement of Mathematical Statistics, Chalemers University of Technology Sweden, 21. ISSN 1652-9715, 2008.

I. Nåsell, The threshold concept in stochastic epidemic and endemic models. In Epidemic Models: Their Structure and Relation to Data, ed. D. Mollison, pp. 71–83. Cambridge University Press, 1995.

M. Lindholm, Some approximation results concerning near critical epidemics, Examensarbete 2004:21, Department of Mathematical Statistics, Stockholm University, 2004.


Refbacks

  • There are currently no refbacks.


Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize