Abstract
Cross-species transfers of pathogens (zoonoses) cause some of the most virulent diseases, including anthrax, hantavirus and Q fever. Zoonotic infections occur when a pathogen moves from its reservoir host species into a secondary host species. Similarly, commensal infections often have a primary reservoir location within their hosts' bodies from which they rarely cause disease symptoms, but commensals such as Neisseria meningitidis cause severe disease when they cross into a different body compartment from their normal location. Both zoonotic and commensal infections cause either mild symptoms or severe disease, but rarely intermediate symptoms. We develop a mathematical model for studying three factors that affect the probability of severe disease: the size of the inoculum, the route of inoculation and the frequency of naturally occurring infections that do not cause symptoms but do induce protective immunity (vaccinating inoculations). With a single route of infection, increasing pathogen density causes inoculations to develop more often into disease rather than asymptomatic vaccinations that provide protective immunity. With two routes of infection, it may happen that a lower density of a pathogen or of a particular antigenic variant leads to a relatively higher frequency of disease-inducing versus vaccinating inoculations. This reversal occurs when one route of infection tends to vaccinate against relatively common pathogens but less often vaccinates against relatively rare pathogens, whereas the other route of infection is susceptible to disease-inducing inoculation even at relatively low pathogen density.