Computing the basic reproductive numbers for epidemiological models in nonhomogeneous environments

In this paper, we present a numerical method to calculate the basic reproductive number, commonly denoted as R0R0, for a class of compartmental epidemiological models in nonhomogeneous environments. We focus our attention on time-periodic models that incorporate seasonal variation and heterogeneity into disease dynamics. Our numerical algorithm is based on a procedure that efficiently transforms the operator eigenvalue problem into a matrix eigenvalue problem. In addition to time-periodic ODE models, the proposed computational approach can also be applied to spatially heterogeneous epidemic models represented by reaction–diffusion PDE systems. We present several examples to demonstrate the validity and application of this algorithm, and we compare the method with existing approaches for the calculation of R0R0.