Abstract
In the work, we focus on designing and analyzing a simple mathematical model of epidemic outbreaks involving vaccination in a heterogeneous population composed of two age groups. The model is based on the framework of matrix population models. It is designed to include the fundamental phenomena of interest while also making it as explicit as possible for examination using methods of real function analysis. Our aim is to examine differences between separable and non-separable mixing and answer the question, how many vaccines are needed to achieve herd immunity. Additionally, we aim to gain a better understanding of some controversies in vaccination prioritization where a superficial view could lead to misconceptions and subsequent poor decisions.