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

Inaba, 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 -