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.