The effects of vertical transmission on a spatially-structured host-parasite model

Vertical transmission of an infectious disease from parent to offspring is a common transmission route in many systems. Here we investigate the dynamics of a pathogen with both horizontal and vertical transmission within a spatially structured population. We introduce a lattice model with a pair approximation that includes both local and global transmission and reproduction. We find that vertical transmission can determine pathogen invasion and reduce the horizontal transmission rate required for invasion. When the majority of transmission and reproduction is local, vertical transmission can destabilise a host population to cause limit cycles. Given the advantages of a pathogen having both horizontal and vertical transmission routes, we extend the model to investigate the likelihood a mutant strain with both transmission modes will outcompete a resident strain with only horizontal transmission. When there is no trade-off the mutant always invades and when there is a trade-off with horizontal transmission, the mutant emerges when the cost to the horizontal transmission rate is not too large. Depending on how the mutant appears within the host population, it may have an initial advantage over the resident strain even if it cannot outcompete in the long-term. Our work demonstrates the potential importance of vertical transmission within host-pathogen dynamics.