A note on the impact of a behavioral side-effect of vaccine failure on the spread of a contagious disease

Vaccines do save lives; however, no vaccine provides complete immunity for all vaccinated individuals. Thus, some individuals remain susceptible to the contagious disease against which they were vaccinated. By relying on the supposed acquired immunity, these individuals can reduce the self-imposed prevention measures and, as a consequence, they can involuntarily promote the spread of the infection. Here, such individuals are taken into account in an epidemic model based on ordinary differential equations. Depending on the parameter values related to contagion and vaccine efficacy, a less responsible behavior post-vaccination can increase the basic reproduction number of the disease as compared to the case with no vaccine. This result is discussed by considering the current COVID-19 outbreak.