Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents

In this article we describe the transmission dynamics of hantavirus in rodents using 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 in the densities of their own and the opposite gender group. Three alternative models for the movement of the male individuals are examined. 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 non-local 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 demonstrate significant differences in the spatio-temporal behavior predicted by the different models, which suggest future research directions.