Abstract / Summary
Abstract Vertical transmission of an infectious disease from parent to offspring is a common transmission route in many systems. However, the majority of vertical transmission modelling has assumed a well-mixed population, and we do not know how the spatial structure present in most real-world populations will impact the dynamics of these systems. Here we investigate how spatial structure affects the dynamics of a pathogen with both horizontal and vertical transmission. We introduce a lattice model with a pair approximation that includes both local and global transmission and reproduction. We find that vertical transmission’s ability to determine pathogen invasion is dependant on spatial structure. 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 of a mutant strain with both transmission modes outcompeting a resident strain with only horizontal transmission. In the absence of cost the mutant always invades. When there is a trade-off between vertical and 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 that the importance of vertical transmission within host-parasite dynamics is preserved when spatial structure is included.