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There are often multiple diseases with cross immunity competing forvaccination resources. Here we investigate the optimal vaccination program in atwo-layer Susceptible-Infected-Removed (SIR) model, where two diseases withcross immunity spread in the same population, and vaccines for both diseasesare available. We identify three scenarios of the optimal vaccination program,which prevents the outbreaks of both diseases at the minimum cost. Weanalytically derive a criterion to specify the optimal program based on thecosts for different vaccines.

Optimal vaccination program for two infectious diseases with cross immunity