Interactions between frequency-dependent and vertical transmission in host-parasite systems.

We investigate host-pathogen dynamics and conditions for coexistence in two models incorporating frequency-dependent horizontal transmission in conjunction with vertical transmission. The first model combines frequency-dependent and uniparental vertical transmission, while the second addresses parasites transmitted vertically via both parents. For the first model, we ask how the addition of vertical transmission changes the coexistence criteria for parasites transmitted by a frequency-dependent horizontal route, and show that vertical transmission significantly broadens the conditions for parasite invasion. Host-parasite coexistence is further affected by the form of density-dependent host regulation. Numerical analyses demonstrate that within a host population, a parasite strain with horizontal frequency-dependent transmission can be driven to extinction by a parasite strain that is additionally transmitted vertically for a wide range of parameters. Although models of asexual host populations predict that vertical transmission alone cannot maintain a parasite over time, analysis of our second model shows that vertical transmission via both male and female parents can maintain a parasite at a stable equilibrium. These results correspond with the frequent co-occurrence of vertical with sexual transmission in nature and suggest that these transmission modes can lead to host-pathogen coexistence for a wide range of systems involving hosts with high reproductive rates.