Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Modeling the individual vaccination decisions : a structural explanation

Last modified: 2014-03-31


Although optimal vaccination strategies to control the spread of epidemics have been studies for several decades, only recently the "vaccine scares" (term coined by Earn and Bauch in their seminal paper) have been addressed. These situations arise when individuals question the validity of the global (optimum) vaccination strategies because of costs or side-effects at the individual level.

We consider a SIR model to which we superpose an individual decision level (to vaccinate or not): each individual will make his/her own choices depending on the expected course of the epidemic and his estimation of the personal cost (including side-effects). The course of the epidemic will therefore be the aggregation of individual decisions realizing thus a feedback from the individual to the societal level and vice-versa. A first question is whether such an equilibrium exists.

Starting from existing models that do not treat with full generality the feedback between the decisions at the individual level and the overall epidemic propagation, we consider here some extensions to such models and prove the existence of an equilibrium. Such information can help explain when will individuals voluntarily vaccinate and when not. It is seen that the answer differs from the classical "vaccination region" / "non-vaccination region" partition encountered in a SIR model without the individual dynamics.


vaccination; optimal vaccination; vaccine scares; Mean Field Games