Estimate of the reproduction ratio from surveillance may be biased in spatially structured population before epidemics, a new analytical approach to redefine basic reproduction ratio.

At the early stage of an epidemic, the reproduction ratio estimates the potential for disease outbreak and spread, informing public health decisions, resource allocation, and control measures. However, estimating R0 based on local surveillance data often neglects spatial structure, leading to biased results. Similarly, using global measures like R_{ref} (radius of the next-generation matrix) overlooks local transmission heterogeneity. To address these issues, we propose a novel analytical approach that combines branching processes with a metapopulation model to define a new reproduction ratio, R_{outbreak}, which accounts for both local and network-wide dynamics. This method improves the accuracy of outbreak surveillance and predictions.

We apply our approach to a pre-emptive vaccination scenario in Italy for emerging pathogens like SARS-CoV-2, using a spatial contact network provided by meta. Our model demonstrates that locally-based R0 significantly underestimates outbreak risk, particularly in small cities. By incorporating spatial variability, R_{outbreak} offers a more reliable estimate of outbreak potential.

In conclusion, our model corrects biases in traditional reproductive ratio estimates in spatially structured populations and introduces a new reproduction ratio that better accounts for spatial dynamics.