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

Abstract

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.

Well‐posedness and control in a hyperbolic–parabolic parasitoid–parasite system

“…Refer to Refs. 11–13 for alternative algorithms. The numerical domain is the rectangle and we let the parameters , and vanish outside the physical domain .…”

Implicit-Explicit Methods for a Convection-Diffusion-Reaction Model of the Propagation of Forest Fires

“…Explicit numerical schemes for (1) on a uniform Cartesian grid of meshwidth ∆x and time step ∆t are easy to implement but are associated with a Courant-Friedrichs-Lewy (CFL) stability condition [2] that imposes the proportionality ∆t ≈ ∆x 2 [3][4][5][6][7][8][9][10][11][12][13]. This restriction makes long-term simulations of ( 1)-( 3) on a uniform grid unacceptably slow.…”

Global dynamics of a stage-structured hantavirus infection model with seasonality

“…Mathematical models were also proposed in [1,2,4,5] to include diffusion of rodents to investigate influence of host movement on the transmission dynamics. More recently, a deterministic hantavirus epidemic model has been developed and analyzed in Wolf et al [17].…”