Raimund Bürger, Gerardo Chowell, Elvis Gavilán, Pep Mulet, Luis M. Villada:
Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents
The propagation of hantavirus infection in rodents is described by a spatio-temporal susceptible-exposed-infective-recovered (SEIR) compartmental model that distinguishes between male and female subpopulations [L.J.S. Allen, R.K. McCormack and C.B. Jonsson, Bull. Math. Biol. 68 (2006), 511–524]. Both subpopulations are assumed to differ in their movement with respect to local variations of the densities of their own and the opposite gender group. Three alternative models for the movement of the male individuals are examined. In particular, in some cases the movement is not only directed by the gradient of a density (as in the standard diffusive case), but also by a nonlocal convolution of density values as proposed, in another context, in [R.M. Colombo and E. Rossi, Commun. Math. Sci., 13 (2015), 369–400]. An efficient numerical method for the resulting convection-diffusion-reaction system of partial differential equations is proposed. This method involves techniques of weighted essentially non-oscillatory (WENO) reconstructions in combination with implicit-explicit Runge-Kutta (IMEX-RK) methods for time stepping. The numerical results exhibit significant differences in the spatial-temporal behavior predicted by the different models that give rise to future directions of research.