  Vaccination is essential for the management of infectious diseases, many of
which continue to pose devastating public health and economic challenges across
the world. However, many vaccines are imperfect having only a partial
protective effect in decreasing disease transmission and/or favouring recovery
of infected individuals, and possibly exhibiting trade-off between these two
properties. Furthermore, population turnover, that is the rate at which
individuals enter and exit the population, is another key factor determining
the epidemiological dynamics. While these factors have yet been studied
separately, we investigate the interplay between the efficiency and property of
an imperfect vaccine and population turnover. We build a mathematical model
with frequency incidence rate, a recovered compartment, and an heterogeneous
host population with respect to vaccination. We first compute the basic
reproduction number $\mathcal{R}_0$ and study the global stability of the
equilibrium points. Using a sensitivity analysis, we then assess the most
influential parameters determining the total number of infected and
$\mathcal{R}_0$ over time. We derive analytically and numerically conditions
for the vaccination coverage and efficiency to achieve disease eradication
($\mathcal{R}_0 < 1$) assuming different intensity of the population turnover
(weak and strong), vaccine properties (transmission and/or recovery) and
trade-off between the latter. We show that the minimum vaccination coverage
increases with lower population turnover, decreases with higher vaccine
efficiency (transmission or recovery), and is increased/decreased by up to 15\%
depending on the trade-off between the vaccine properties. We conclude that the
coverage target for vaccination campaigns should be evaluated based on the
interplay between these factors.
