Computation of the basic reproduction numbers for reaction-diffusion epidemic models

We consider a class of $ k $-dimensional reaction-diffusion epidemic models ($ k = 1, 2, \cdots $) that are developed from autonomous ODE systems. We present a computational approach for the calculation and analysis of their basic reproduction numbers. Particularly, we apply matrix theory to study the relationship between the basic reproduction numbers of the PDE models and those of their underlying ODE models. We show that the basic reproduction numbers are the same for these PDE models and their associated ODE models in several important scenarios. We additionally provide two numerical examples to verify our analytical results.