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Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
agricultural and biological sciences
Growth rate and basic reproduction number for population models with a simple periodic factor
Mathematical Biosciences, Volume 210, No. 2, Year 2007
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Description
For continuous-time population models with a periodic factor which is sinusoidal, both the growth rate and the basic reproduction number are shown to be the largest roots of simple equations involving continued fractions. As an example, we reconsider an SEIS model with a fixed latent period, an exponentially distributed infectious period and a sinusoidal contact rate studied in Williams and Dye [B.G. Williams, C. Dye, Infectious disease persistence when transmission varies seasonally, Math. Biosci. 145 (1997) 77]. We show that apart from a few exceptional parameter values, the epidemic threshold depends not only on the mean contact rate, but also on the amplitude of fluctuations. © 2007 Elsevier Inc. All rights reserved.
Authors & Co-Authors
Bacaër, Nicolas
France, Bondy
Ird Centre D'ile-de-france
Ouifki, R.
South Africa, Stellenbosch
Stellenbosch University
Statistics
Citations: 105
Authors: 2
Affiliations: 2
Identifiers
Doi:
10.1016/j.mbs.2007.07.005
ISSN:
00255564
Study Design
Cross Sectional Study