Epidemiological models

PDF (ελληνικά)
Published: Dec 3, 2019
DOI: https://doi.org/10.12681/jhvms.21636
Α. Μακρόγλου
Δ/νση Μηχανογράφησης Υπ. Γεωργίας
Σ. Κουιμτζής
Κέντρο τεχν. Σπερμ. και Νοσ. Αναπαρ. Διαβατά, Θεσσαλονίκη
Abstract

In this paper are described some epidemiological models which govern the spread of infectius diseases. These models are deterministic, and have the form of integral and integrodifferential equations. Solving these equations it is possible to predict the inumber of the confected members of a population at time t>0 if it Is known at time t=0.

Article Details
  • Section
  • Articles
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Authors who publish with this journal agree to the following terms:

· Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution Non-Commercial License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

· Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g. post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

· Authors are permitted and encouraged to post their work online (preferably in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.

Downloads
Download data is not yet available.
References
Anderson, R.M. and May, R.M.: Population biology of infectious deseases I, Nature 280, 361 -367 (1979).
Diekmann O. : Integral equations and population dynamics, p. 117-149 in: Colloquium Numerical treatment of integral equations, Ed. H.J.J, te Riele, Mathematisch Centrum, Amsterdam (1979).
Diekmann O.: Thresholds and travelling waves for the geographical spead of infection, J. Math. Biol. 6,109-130 (1978).
Diekmann, O.: On a nonlinear integral equation arising in Mathematical Epidemiology, in: Differential Equations and Applications (W. Eckhaus, E.M. de Jager" Eds), 133-140, North - Holland, Amsterdam, (1978).
Diekmann O.: Run for your life. A note on the asymptotic speed of propagation of an epidemic. To appear in J. Diff. Equ.
Diekmann, O.: A nonlinear integral equation describing the geographical spread of infection: the hair - trigger effect, travelling waves and the asymptotic speed of propagation, Report III, 1 o n '-•i+••*- ««•- le Applicazioni del Calcolo « Mauro Picone », Roma, (1978).
Hethcote, H.W., Stech H.W. and Driessche, P. van der: Periodicity and stability in epidemic models: A survey, in: Differential equations and Applications in Ecology, Epidemics and Population problems, (Busenborg S. and Cooke K.L. Eds), Academic Press, 1981.
Hoppensteadt F.: Mathematical theories of Populations: Demographics, Genetics and Epidemics. SIAM Regional
Conference Series in Applied Math., 20, SIAM, Philadelphia, (1975).
Hoppensteadt F. and Waltman P.: A problem in the theory of epidemics. I. II, Math. Biosci. 9, 71-91: 133-145 (197Û-1971).
Kermack W. O. and McKendrick A.G.: Proc. Roy. Soc. A. 115, p. 700-721: 138, p. 55-83: 141, p. 94-122 (1927, 1932, 1933).
Makroglou Α.: A block - by – block method for the numerical solution of Volterra delay integro - differential equations, Computing, 30, p. 49-62 (1983).
May, R. M. and Anderson, R.M.: Population biology of infectious diseases II, Nature 280, p. 455 - 461 (1979).
Mollison D.: Spatial contact models for ecological and epidemic spread, J. Roy. Statist. Soc. B, 39, p. 283-326 (1977).
Soper, Η. E.: Interpretation of periodicity in disease prevalence, J. Roy. Statist. Soc. B, 92, p. 34-73 (1929).
Wilson, L. O. and Burke, Μ. H.: The epidemic curve, Proc. Nat. Acad. Sci., 28, p. 361-366 (1924).
Most read articles by the same author(s)