We investigate the temporal and spatial evolution of the spread of an infectious disease by performing a long-wavelength analysis of a classical model for the geographic spread of a rabies epidemic in a population of foxes subject to idealized boundary conditions. We consider twodimensional and three-dimensional landscapes consisting of an infinite horizontal strip bounded by two walls a finite distance apart and a horizontal region bounded above and below by horizontal walls, respectively. A nonlinear partial differential evolution Equation for the leading order of infectives is derived. The Equation captures the space and time variations of the spread of the disease in the weakly super critical region.
Long Wavelength Analysis of a Model for the Geographic Spread of a Disease,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 9,
2, Article 2.
Available at: https://digitalcommons.pvamu.edu/aam/vol9/iss2/2