The critical vaccination threshold to prevent the invasion of an infectious disease is a well-established function of the basic reproductive ratio, R0. However, in practice, vaccination response is often initiated in response to the detection of an outbreak; e.g. the response to the H1N1 flu epidemic, or reactive vaccination to livestock outbreaks such as FMD. In these settings, outbreak managers must distribute vaccination during the outbreak, and thus, managers are analogous to competitors for susceptible hosts. Outbreak control, however, is often limited by logistical constraints on distribution and total effort. We model the deployment of outbreak response as diffusion of effort outward from a central location. While disease transmission is often positively correlated with host density, control effectiveness may be negatively correlated, with longer delays to vaccination per unit effort in areas with high host density. We couple our vaccine distribution model to a spatially explicit, stochastic epidemic model to evaluate optimal distribution strategies as a function of disease transmission rate and population density.
Results/Conclusions
When the population is dense, disease may spread quickly. However, for a given unit of vaccination effort, it takes longer to reach complete vaccination coverage when there are many to vaccinate. When population density is low, infection is unlikely to spread and very little vaccination effort is needed to achieve local herd immunity; thus, the outbreak size is minimized when vaccination is rapidly deployed to the full population. At high population density, disease spread is accelerated and the time required to achieve high local vaccination coverage per unit effort increases. In this setting, rapid deployment to all areas becomes sub-optimal as vaccination effort is “spread thin” and it takes too long to achieve sufficient coverage to interrupt transmission. At slower deployment rates, vaccination effort is concentrated over a smaller area allowing local herd immunity to limit outbreak spread. Thus, areas far from the distribution center are indirectly protected. The optimal spatially constrained vaccination strategy can reduce total outbreak size by 20% compared to widespread regional vaccination. We show that the optimal vaccination deployment rate depends on the timeliness of outbreak detection and response; thus the cost savings of spatially constrained vaccination can be allocated to outbreak surveillance.