An Age-Distributed Immuno-Epidemiological Model with Information-Based Vaccination Decision

An age-distributed immuno-epidemiological model with information-based vaccination proposed in this work represents a system of integro-differential equations with compartments for the numbers of susceptible individuals, infected individuals, vaccinated individuals, and recovered individuals. This model describes the influence of vaccination decisions on epidemic progression in different age groups. In a particular case of the model without age distribution, we determine the basic reproduction number and the final size of epidemic, that is, the limiting number of susceptible individuals at asymptotically large time. Moreover, we study the existence and uniqueness of a positive solution for the age-structured model. Numerical simulations show that the information-based vaccination acceptance can significantly influence the epidemic progression. Though the initial stage of epidemic progression is the same for all memory kernels, as the epidemic progresses and more information about the disease becomes available, further epidemic progression strongly depends on the memory effect. A short-range memory kernel appears to be more effective in restraining the epidemic outbreaks because it allows for more responsive and adaptive vaccination decisions based on the most recent information about the disease. Additionally, the simulation results suggest that relying on either a responsive vaccination approach or a highly effective vaccine alone may be insufficient to significantly reduce the epidemic size and prevent large outbreaks. Both factors are necessary to achieve substantial epidemic control. Moreover, the impacts of the age-dependent initial susceptible population and the age-dependent memory kernel are studied through numerical simulation of the age-dependent model.