Qualitative properties of the finite difference solution of a space-time epidemic propagation model

Abstract. The compartmental models of disease propagation give only the number of the infected individuals but do not give any piece of information about the locations of them. One of the remedies can be to transform the system into an integro-differential equation. We give the known basic qualitative properties of this system: monotonicity, nonnegativity preservation and the formulation of epidemic waves. Then we construct a finite difference numerical scheme to the system and give conditions for the discrete equivalents of the qualitative properties of the continuous system. We give a sufficient condition that guarantees the nonnegativity and the monotonicity, and a condition that is sufficient to extinguish an epidemic wave. We demonstrate the results on numerical examples.