Models for age structured populations with distributed maturation rates (Q1074525)

The authors consider the effect on differential maturation rates of crop pests in age structured populations involved with agricultural modelling. The approach is based on the McKendrick equation, \(u_ t+u_ a=-\mu (a,t)u\), where a relates to the age distribution, t is the physiological elapse time and \(\mu\) is the age specific death rate, together with suitable initial and boundary conditions. The solution is approximated using a hybrid method of lines although other methods are discussed. A more general model which involves a diffusion term is investigated using a modified Leslie matrix approach in order to extend the applicability of the model to populations whose members age at differing rates. Comparative results are given and discussed.