Transmissible vaccines whose dissemination rates vary through time, with applications to wildlife.

Transmission is a potential property of live viral vaccines that remains largely unexploited but may lie within the realm of many engineering designs. While likely unacceptable for vaccines of humans, transmission may be highly desirable for vaccines of wildlife, both to protect natural populations and also to limit zoonotic transmissions into humans. Defying intuition, transmission alone does not guarantee that a vaccine will perform well: the benefit of transmission over no transmission depends on and increases with the basic reproductive number of the vaccine, R. The R of an infectious agent in a homogeneous population is typically considered to be a fixed number, but some evidence suggests that dissemination of transmissible vaccines may change through time. One obvious possibility is that transmission will be greater from hosts directly vaccinated than from hosts who acquire the vaccine passively, but other types of change might also accrue. Whenever transmission changes over time, the R estimated from directly vaccinated hosts will not reflect the vaccine's long term impact. As there is no theory on the consequences of changing transmission rates for a vaccine, we derive conditions for a transmissible vaccine with varying transmission rates to protect a population from pathogen invasion. Being the first in the transmission chain, the R from directly vaccinated hosts has a larger effect than those from later steps in the chain. This mathematical property reveals that a transmissible vaccine with low long term transmission may nonetheless realize a big impact if early transmission is high. Furthermore, there may be ways to artificially elevate early transmission, thereby achieving high herd immunity from transmission while ensuring that the vaccine will ultimately die out.