title: A model of long-term decline in the transmissibility of an infectious disease: implications for the incidence of hepatitis A.
abstract: 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 directly 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 serological surveys, should provide the basis for decisions on vaccination policy.
authors.affiliation: Immunisation Division, PHLS Communicable Disease Surveillance Centre, London, UK.
authors.forename: N J
authors.initials: NJ
authors.lastname: Gay
mesh_terms: D017677:Age Distribution; D003140:Communicable Disease Control; D003661:Decision Support Techniques; D004196:Disease Outbreaks / Q000517:prevention & control; D004198:Disease Susceptibility; D005260:Female; D006506:Hepatitis A / Q000453:epidemiology* / Q000517:prevention & control / Q000635:transmission*; D006801:Humans; D007113:Immunity, Innate; D017589:Immunization Programs; D015994:Incidence; D008297:Male; D015233:Models, Statistical; D011157:Population Dynamics; D013997:Time Factors