A novel method for basic reproduction ratio of a diffusive size-structured population model with delay

In this paper, we discuss a new size-structured population model with a delay in birth process. The focus is to discuss the existence and the uniqueness results along with basic reproduction ratio (R). The birth function h is not necessarily a Ricker type of function but expression of R obtained in this paper works for a more general function h. This analysis covers a larger class of models. The model is converted into an abstract form and then theory of semigroup is used to obtain the results. The basic reproduction number is constructed as spectral radius of the next generation operator. The form for basic reproduction ratio is very general and can be applied to other models as well. We also solve the model numerically to study the effect of delay on population distribution.