Modeling COVID-19 transmission: effects of age structure and vaccination.

A mathematical model for COVID-19 dynamics is developed, incorporating age structure, disease progression, and vaccination. Addressing gaps in existing literature, the model integrates heterogeneous intercohort mixing for realistic disease transmission, with a primary focus on Pakistan and global applicability. Well-posedness is established via the abstract Cauchy problem framework. Threshold parameters and stability analysis identify conditions for disease persistence or eradication. An age-free sub-model gives additional insights. Numerical simulations using the finite differences method confirm analytical results. The study shows the crucial role of age structure and vaccination in controlling COVID-19. It provides a strong mathematical foundation for effective public health strategies.