A high resolution finite difference method for a model of structured susceptible-infected populations coupled with the environment

We develop a general model describing a structured susceptible-infected (SI) population coupled with the environment. This model applies to problems arising in ecology, epidemiology, and cell biology. The model consists of a system of quasilinear hyperbolic partial differential equations coupled with a system of nonlinear ordinary differential equations that represents the environment. We develop a second-order high resolution finite difference scheme to numerically solve the model. Convergence of this scheme to a weak solution with bounded total variation is proved. Numerical simulations are provided to demonstrate the high-resolution property of the scheme and an application to a multi-host wildlife disease model is explored.(c) 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1420-1458, 2017