A Model with Age Dependence and an Open Population

Abstract

The models in the previous sections assumed a constant, closed total population or, from another point of view, birth, death, and migration were in exact balance. In this section a special case of a model of F. Hoppensteadt is described in which these factors are allowed to vary and a further complication is permitted in the model in that age dependent rates of exposure, virility, etc., are also allowed. In fact, two types of age dependence will be introduced, dependence on chronological age and on class age. The first of these allows the disease to selectively infect a particular age group while the second allows the important rate constants to vary with the length of time individuals have been in a given class; for example, allowing the probability of transmitting the disease to decrease when the individual has been infective for a long period of time. The pair (a,c) (chronological age, class age) will be referred to as the age of the individual.