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 R0, 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 R0. [ABSTRACT FROM AUTHOR]