# The Basic Reproduction Number of an Infectious Disease in a Stable Population: The Impact of Population Growth Rate on the Eradication Threshold

Mathematical Modelling of Natural Phenomena (2008)

- Volume: 3, Issue: 7, page 194-228
- ISSN: 0973-5348

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topInaba, H., and Nishiura, H.. "The Basic Reproduction Number of an Infectious Disease in a Stable Population: The Impact of Population Growth Rate on the Eradication Threshold." Mathematical Modelling of Natural Phenomena 3.7 (2008): 194-228. <http://eudml.org/doc/222224>.

@article{Inaba2008,

abstract = {
Although age-related heterogeneity of infection has been addressed in various
epidemic models assuming a demographically stationary population, only a few studies have
explicitly dealt with age-specific patterns of transmission in growing or decreasing population.
To discuss the threshold principle realistically, the present study investigates an age-duration-structured SIR epidemic model assuming a stable host population, as the first scheme to
account for the non-stationality of the host population. The basic reproduction number R0
is derived using the next generation operator, permitting discussions over the well-known
invasion principles. The condition of endemic steady state is also characterized by using
the effective next generation operator. Subsequently, estimators of R0 are offered which can
explicitly account for non-zero population growth rate. Critical coverages of vaccination are
also shown, highlighting the threshold condition for a population with varying size. When
quantifying R0 using the force of infection estimated from serological data, it should be
remembered that the estimate increases as the population growth rate decreases. On the
contrary, given the same R0, critical coverage of vaccination in a growing population would be
higher than that of decreasing population. Our exercise implies that high mass vaccination
coverage at an early age would be needed to control childhood vaccine-preventable diseases
in developing countries.
},

author = {Inaba, H., Nishiura, H.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {epidemiological model; stable age distribution; threshold; basic reproduction number; SIR model},

language = {eng},

month = {10},

number = {7},

pages = {194-228},

publisher = {EDP Sciences},

title = {The Basic Reproduction Number of an Infectious Disease in a Stable Population: The Impact of Population Growth Rate on the Eradication Threshold},

url = {http://eudml.org/doc/222224},

volume = {3},

year = {2008},

}

TY - JOUR

AU - Inaba, H.

AU - Nishiura, H.

TI - The Basic Reproduction Number of an Infectious Disease in a Stable Population: The Impact of Population Growth Rate on the Eradication Threshold

JO - Mathematical Modelling of Natural Phenomena

DA - 2008/10//

PB - EDP Sciences

VL - 3

IS - 7

SP - 194

EP - 228

AB -
Although age-related heterogeneity of infection has been addressed in various
epidemic models assuming a demographically stationary population, only a few studies have
explicitly dealt with age-specific patterns of transmission in growing or decreasing population.
To discuss the threshold principle realistically, the present study investigates an age-duration-structured SIR epidemic model assuming a stable host population, as the first scheme to
account for the non-stationality of the host population. The basic reproduction number R0
is derived using the next generation operator, permitting discussions over the well-known
invasion principles. The condition of endemic steady state is also characterized by using
the effective next generation operator. Subsequently, estimators of R0 are offered which can
explicitly account for non-zero population growth rate. Critical coverages of vaccination are
also shown, highlighting the threshold condition for a population with varying size. When
quantifying R0 using the force of infection estimated from serological data, it should be
remembered that the estimate increases as the population growth rate decreases. On the
contrary, given the same R0, critical coverage of vaccination in a growing population would be
higher than that of decreasing population. Our exercise implies that high mass vaccination
coverage at an early age would be needed to control childhood vaccine-preventable diseases
in developing countries.

LA - eng

KW - epidemiological model; stable age distribution; threshold; basic reproduction number; SIR model

UR - http://eudml.org/doc/222224

ER -

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