Basic Reproduction Ratios for Almost Periodic Compartmental Epidemic Models

The theory of the basic reproduction ratio $R_{0}$ R 0 and its computation formulae for almost periodic compartmental epidemic models are established. It is shown that the disease-free almost periodic solution is stable if $R_{0}<1$ R 0 < 1 , and unstable if $R_{0}>1$ R 0 > 1 . We also apply the developed theory to a patchy model with almost periodic population dispersal and disease transmission coefficients to obtain a threshold type result for uniform persistence and global extinction of the disease.