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Issue Math. Model. Nat. Phenom.
Volume 3, Number 7, 2008
Special issue dedicated to Glenn Webb
Page(s) 180 - 193
DOI 10.1051/mmnp:2008049
Published online 23 October 2008

Math. Model. Nat. Phenom. Vol. 3, No. 7, 2008, pp. 180-193
DOI: 10.1051/mmnp:2008049

Analysis of a Model with Multiple Infectious Stages and Arbitrarily Distributed Stage Durations

Y. Yang, D. Xu and Z. Feng

Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA

zfeng@math.purdue.edu

Published online: 23 October 2008

Abstract
Infectious diseases may have multiple infectious stages with very different epidemiological attributes, including infectivity and disease progression. These stages are often assumed to have exponentially distributed durations in epidemiological models. However, models that use the exponential distribution assumption (EDA) may generate biased and even misleading results in some cases. This discrepancy is particularly damaging if the models are employed to assist policy-makers in disease control and interventions. This paper studies a mathematical model that includes multiple infectious stages and general distributions for the stage durations (with the exponential distribution as a special case). Formulas for the control reproductive number, Rc, and the basic reproductive number, R0, are derived, which can be conveniently applied to models in which specific stage distributions are assumed. It is also shown that the disease dynamics are determined by the reproductive numbers.


Mathematics Subject Classification. 37N25, 92D30

Key words: epidemiological model -- disease stage distribution -- disease control





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