Dynamics of Vaccination with Local Information

 

OLIVIA WOOLLEY MEZA

NORTHWESTERN UNIVERSITY

 

A high enough vaccine coverage level can eradicate a disease from a population. However, if individuals believe there is any risk associated with the vaccine, vaccination decisions driven by rational self-interest can keep the overall vaccination below this level. If almost everyone in a population has chosen to vaccinate, an unvaccinated individual may believe that it's unlikely that they will come into contact with someone who is infected, and thus they will feel more comfortable choosing not to vaccinate. Prior work has shown that in a well-mixed population with perfect information, a population of self-interested decision makers will never eradicate the disease. We consider an epidemiological model in a finite population with underlying spatial structure where there is strategic vaccination constrained by bounded rationality and limited information. Agents base their vaccination decisions on an empirical, local measure of the probability that they will be infected. We investigate how the likelihood that a disease is eradicated from a population changes as the fraction of individuals in the population that interact directly and share information changes. We look at this behavior on two, very different, underlying spaces: a plane and an Erdos-Renyi random network. In both cases each individual has both a contact neighborhood, the group of others who can contact the individual, and an information neighborhood, the group of others who the individual can obtain information about, either through observation or communication. Although individuals are only at a direct risk from those in their contact neighborhood, they base their decision to vaccinate on the number of individuals that have been infected in their information neighborhood. Results show that with a finite size population and local dynamics, infection can be eradicated even when individuals make self-interested rational decisions. This general finding applies to both topologies but each exhibits very different and interesting behavior. We focus on the region where contagion dynamics happen within a small neighborhood and the decision to vaccinate happens frequently as does loss of immunity. We find that in the plane the disease is less likely to be eradicated as agents have information about a larger region of space. Meanwhile, in a random network eradication is especially hard in the region where agents have mid-sized information neighborhoods. We shed light on both of these non-trivial behaviors through simulations and analytical models.