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© 1996 Oxford University Press

research-article

A Model of Long-Term Decline in the Transmissibility of an Infectious Disease: Implications for the Incidence of Hepatitis A

NIGEL J GAY

Immunisation Division, PHLS Communicable Disease Surveillance Centre 61 Colindale Avenue, London NW9 5EQ, UK.

BACKGROUND: The epidemiology of hepatitis A in countries across the world is changing due to improvements in hygiene and living conditions which reduce the transmissibility of the infection.

METHODS: A mathematical model Is formulated to describe the changes in incidence of a directiy transmitted infection produced by a long term decline in its transmissibility. The basic reproduction number, the parameter describing transmissibility, is considered as a function of time. The relationship between the basic reproduction number and the force of infection is derived.

RESULTS: Theoretical examples demonstrate that a decline in transmissibility results in an initial decline in the force of Infection, but that this may be followed by a substantial resurgence. Resurgences may be possible after several decades of declining incidence, and are most marked following a rapid decline.

CONCLUSIONS: Countries which have experienced a rapid decline in the incidence of hepatitis A may be at risk of a resurgence. More detailed mathematical models, informed with data from regular age-stratified serologlcal surveys, should provide the basis for decisions on vaccination policy.

Keywords hepatitis A, models, transmission, basic reproduction number, force of Infection

Revised 1 November 1995


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