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Vaccination is essential for the management of infectious diseases, many ofwhich continue to pose devastating public health and economic challenges acrossthe world. However, many vaccines are imperfect having only a partialprotective effect in decreasing disease transmission and/or favouring recoveryof infected individuals, and possibly exhibiting trade-off between these twoproperties. Furthermore, population turnover, that is the rate at whichindividuals enter and exit the population, is another key factor determiningthe epidemiological dynamics. While these factors have yet been studiedseparately, we investigate the interplay between the efficiency and property ofan imperfect vaccine and population turnover. We build a mathematical modelwith frequency incidence rate, a recovered compartment, and an heterogeneoushost population with respect to vaccination. We first compute the basicreproduction number $\mathcal{R}_0$ and study the global stability of theequilibrium points. Using a sensitivity analysis, we then assess the mostinfluential parameters determining the total number of infected and$\mathcal{R}_0$ over time. We derive analytically and numerically conditionsfor 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) andtrade-off between the latter. We show that the minimum vaccination coverageincreases with lower population turnover, decreases with higher vaccineefficiency (transmission or recovery), and is increased/decreased by up to 15\%depending on the trade-off between the vaccine properties. We conclude that thecoverage target for vaccination campaigns should be evaluated based on theinterplay between these factors.

Impact of imperfect vaccine, vaccine trade-off and population turnover on infectious disease dynamics