  A new age-distributed immuno-epidemiological model with information-based
vaccine uptake suggested in this work represents a system of
integro-differential equations for the numbers of susceptible individuals,
infected individuals, vaccinated individuals and recovered individuals. This
model describes the influence of vaccination decision on epidemic progression
in different age groups. We prove the existence and uniqueness of a positive
solution using the fixed point theory. In a particular case of age-independent
model, we determine the final size of epidemic, that is, the limiting number of
susceptible individuals at asymptotically large time. Numerical simulations
show that the information-based vaccine 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. 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.
