The asymptotic speed of propagation of the deterministic non-reducible n-type epidemic

Abstract

A model has been formulated in to describe the spatial spread of an epidemic involving n types of individuals, when triggered by the introduction of infectives from outside. Wave solutions for such a model have been investigated in and have been shown only to exist at certain speeds. This paper establishes that the asymptotic speed of propagation, as defined in Aronson and Weinberger, of such an epidemic is in fact c0, the minimum speed at which wave solutions exist. This extends the known result for the one-type and host-vector epidemics.

Asymptotic speeds of spread and traveling waves for monotone semiflows with applications

“…In [44,45], Weinberger proved the existence of asymptotic speeds of spread for a discrete-time recursion with a translation-invariant order-preserving operator. Radcliffe and Rass [29,30,31] studied traveling waves and asymptotic speeds of spread for a class of epidemic systems of integral equations (see also their book [32]). In [21,22], Lui also generalized the results in [45] to systems of recursions.…”

Spatial Dynamics of Some Evolution Systems in Biology

“…Integral and integrodifferential equations: [7], [19], [4], [27], [29], [117,118], [28], [130][131][132], [101][102][103][104]' [133], [95], [20], [81], and [148].…”

Asymptotic speed of propagation and traveling wave solutions for a lattice integral equation

“…The problem of traveling wave solutions has been widely investigated for reaction-diffusion equations ( [3,4,8,9,11,12] and [17]) and integral equations [13,14]. The concept of asymptotic speed of propagation was introduced by Aronson and Weinberger [1,15] for reaction-diffusion equations and applied by Aronson [2], Diekeman [5], Thieme [13], Thieme and Zhao [14], Radcliffe and Rass [10] to integrodifferential and integral equations, and by Weng, Huang and Wu [16] to a lattice differential equation. The extensive references could be found in Thieme and Zhao [14].…”