Journal Article

Seasonally varying epidemics with and without latent period: a comparative simulation study

I. A. Moneim

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 24, issue 1, pages 1-15
Published in print March 2007 | ISSN: 1477-8599
Published online March 2007 | e-ISSN: 1477-8602 | DOI:
Seasonally varying epidemics with and without latent period: a comparative simulation study

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  • Applied Mathematics
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This paper studies two classes of epidemic models. These models are the standard SIR and SEIR models with time-varying periodic contact rate. The importance of the latent period is our target. When the latent period can be ignored and when it must be taken into account are the main points of our simulation. The comparison of the simulation results of our two models shows that the latent period is affecting the pattern of the dynamics of the disease. This paper addresses how model predictions are affected by the assumed form of the seasonally varying transmission rate and whether or not a latent class is included. Moreover, for some infectious diseases, using latent period leads to appearance or disappearance of some periodic solutions for the same parameter set. A key parameter for our models is the basic reproductive number R0. We have simulated our models for a set of values of parameters insuring that R0 > 1, which represent the endemic case (Greenhalgh & Moneim, 2003; Moneim & Greenhalgh, 2005a,b). Different patterns have been obtained for each of the SIR or SEIR; these patterns are representing the filtered results of the long-term behaviour of the endemic periodic solution for a range of amplitude parameter values of the periodic contact rate. So it is too important to determine which type of model SIR or SEIR is more likely to describe the actual nature of the dynamics of each disease.

Keywords: simulation; SIR; SEIR; Poincaré section; filter; bifurcation; periodicity; epidemics.

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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