The Basic Reproduction Number of an Infectious Disease in a Stable Populatio: The Impact of Population Growth Rate on the Eradication Threshold
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概要
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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-specfic patterns of transmission in growing or decreasing population. To discuss the threshold principl realistically,the present study investigates an age-duration-structuredSIR epidemic model assuminga 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 perator,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 date, 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.Although we here present only estimation formulae,the reader may refer to Inaba and Nisiura[11] for theoretical detail and numerical examples.
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