Impact of Imperfect Vaccine, Vaccine Trade-Off and Population Turnover on Infectious Disease Dynamics

Abstract

Vaccination is an essential tool for the management of infectious diseases. 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 a trade-off between these two properties. Furthermore, the success of vaccination also depends on the population turnover, and the rate of entry to and exit from the population. We here investigate by means of a mathematical model the interplay between these factors to predict optimal vaccination strategies. We first compute the basic reproduction number and study the global stability of the equilibria. We then assess the most influential parameters determining the total number of infected over time using a sensitivity analysis. We derive conditions for the vaccination coverage and efficiency to achieve disease eradication, assuming different intensities of population turnover (weak and strong), vaccine properties (transmission and/or recovery) and the 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 vaccine trade-off. We conclude that the coverage target for vaccination campaigns should be evaluated based on the interplay between these factors.

Keywords

• imperfect vaccine
• vaccine trade-off
• population turnover
• mathematical model
• global stability
• sensibility analysis