Incorporating landscape heterogeneities in the spread of an epidemics in wildlife

One of the main difficulties in the modeling and numerical simulation of the spread of an infectious disease in wildlife resides in properly taking into account the heterogeneities of the landscape. Forests, plains and mountains present different levels of hospitality, while large interstates, lakes and major waterways can provide strong natural barriers to the epidemic spread. A canonical approach has been to discretize both population and geography into geopolitical units and consider the movement of individuals from unit to unit [4]. This approach, however, does not well represent the biological realities of animal movement, since animals do not move at the scale of geopolitical units. We combine a standard SEI epidemiological model with a diffusion process to account for movement as a continuous process across a continuous region [1]. This results in a system of parabolic reaction-diffusion equations with nonlinear reaction term. Landscape heterogeneities are accounted for by including in the computational domain the significant geographical features of the area. We discretize the resulting model in time by an IMEX scheme and in space by finite elements. To show the effectiveness of the method, we present numerical simulation for rabies epidemics among raccoons in New York State