Recurrent outbreaks of childhood diseases revisited: The impact of isolation

Zhilan Feng; Horst Thieme

doi:10.1016/0025-5564(94)00069-C

Recurrent outbreaks of childhood diseases revisited: The impact of isolation

Zhilan Feng, Horst Thieme

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

120 Scopus citations

Abstract

The recurrent outbreaks of measles and other childhood diseases have previously been explained by an interaction of intrinsic epidemiologic forces generating dampened oscillations and of seasonal and/or stochastic excitation. We show that isolation (i.e., sick individuals stay at home and have a reduced infective impact) can create self-sustained oscillations provided that the number of per capita contacts is largely independent of the number of individuals present. This means that the bilinear mass action term for disease incidence is modified by dividing it by the number of nonisolated individuals.

Original language	English (US)
Pages (from-to)	93-130
Number of pages	38
Journal	Mathematical Biosciences
Volume	128
Issue number	1-2
DOIs	https://doi.org/10.1016/0025-5564(94)00069-C
State	Published - 1995

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
General Biochemistry, Genetics and Molecular Biology
General Immunology and Microbiology
General Agricultural and Biological Sciences
Applied Mathematics

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10.1016/0025-5564(94)00069-C

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title = "Recurrent outbreaks of childhood diseases revisited: The impact of isolation",

abstract = "The recurrent outbreaks of measles and other childhood diseases have previously been explained by an interaction of intrinsic epidemiologic forces generating dampened oscillations and of seasonal and/or stochastic excitation. We show that isolation (i.e., sick individuals stay at home and have a reduced infective impact) can create self-sustained oscillations provided that the number of per capita contacts is largely independent of the number of individuals present. This means that the bilinear mass action term for disease incidence is modified by dividing it by the number of nonisolated individuals.",

author = "Zhilan Feng and Horst Thieme",

note = "Funding Information: We thank Steue Baer for useful discussions and for his generous help with the numerical aspects of this work. We thank William M. Riuera for many helpful suggestions, Herb Hethcote for a ualuable discussion on incidence rates, and a careful anonymous referee for bringing us back on track in our application sections. Research was supported in whole (Z.F.) or in part (H.R.T.) by National Science Foundation grant 9101979.",

year = "1995",

doi = "10.1016/0025-5564(94)00069-C",

language = "English (US)",

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TY - JOUR

T1 - Recurrent outbreaks of childhood diseases revisited

T2 - The impact of isolation

AU - Feng, Zhilan

AU - Thieme, Horst

N1 - Funding Information: We thank Steue Baer for useful discussions and for his generous help with the numerical aspects of this work. We thank William M. Riuera for many helpful suggestions, Herb Hethcote for a ualuable discussion on incidence rates, and a careful anonymous referee for bringing us back on track in our application sections. Research was supported in whole (Z.F.) or in part (H.R.T.) by National Science Foundation grant 9101979.

PY - 1995

Y1 - 1995

N2 - The recurrent outbreaks of measles and other childhood diseases have previously been explained by an interaction of intrinsic epidemiologic forces generating dampened oscillations and of seasonal and/or stochastic excitation. We show that isolation (i.e., sick individuals stay at home and have a reduced infective impact) can create self-sustained oscillations provided that the number of per capita contacts is largely independent of the number of individuals present. This means that the bilinear mass action term for disease incidence is modified by dividing it by the number of nonisolated individuals.

AB - The recurrent outbreaks of measles and other childhood diseases have previously been explained by an interaction of intrinsic epidemiologic forces generating dampened oscillations and of seasonal and/or stochastic excitation. We show that isolation (i.e., sick individuals stay at home and have a reduced infective impact) can create self-sustained oscillations provided that the number of per capita contacts is largely independent of the number of individuals present. This means that the bilinear mass action term for disease incidence is modified by dividing it by the number of nonisolated individuals.

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JF - Mathematical Biosciences

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Recurrent outbreaks of childhood diseases revisited: The impact of isolation

Abstract

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