1991
DOI: 10.1016/0025-5564(91)90009-8
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Dependence of epidemic and population velocities on basic parameters

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Cited by 282 publications
(211 citation statements)
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“…Since the zero-steady state is unstable, the population projection matrix is bounded by its linearisation at zero (Condition II) and density dependence is local, the dynamics of the invasion are dominated by the wavefront [28,29]. For the mathematical analysis, though not the later simulations, we will assume this Linear Conjecture [29], which has been proved rigorously for a narrower class of problem (see Appendix A).…”
Section: Methods Outlinementioning
confidence: 99%
See 1 more Smart Citation
“…Since the zero-steady state is unstable, the population projection matrix is bounded by its linearisation at zero (Condition II) and density dependence is local, the dynamics of the invasion are dominated by the wavefront [28,29]. For the mathematical analysis, though not the later simulations, we will assume this Linear Conjecture [29], which has been proved rigorously for a narrower class of problem (see Appendix A).…”
Section: Methods Outlinementioning
confidence: 99%
“…This is often referred to as the Linear Conjecture [29], and allows us to approximate the IDE by its linearisation. For an homogeneous IDE, the growth rate f (u t (y), y) has no explicit y dependence, allowing us to write it as f (u t (y)).…”
Section: Introductionmentioning
confidence: 99%
“…In particular, the discrete nature of individuals is not modeled, and the diffusion operator instantaneously propagates infinitesimally low densities across any region. This may lead to some pathological behavior, such as the somewhat infamous atto-fox (Mollison 1991), where 10 218 of an infected fox causes a reinvasion of rabies. Reaction-diffusion equations furthermore do not always replicate the limiting behavior of an underlying stochastic spatial process, as pointed out by Durrett and Levin (1994), although the authors remark that this issue can sometimes be alleviated by correcting the reaction terms by deriving them directly from the stochastic process.…”
Section: Limitations Of Reaction-diffusion Approachesmentioning
confidence: 99%
“…In this section we estimate the minimum speed at which these waves could propagate (assuming that the travelling waves do exist). We assume that close to the invading front, the nonlinear differential equations describing the spread of a population have similar speeds as their linear approximation (see the approaches in Medlock & Kot (2003); Mollison (1991)). Therefore, we first calculate the linearised system (3.5) at the steady state (u * 1 , u * 2 , f * , c * ) = (0, 1, 0, p 2 /q).…”
Section: Speed Of Travelling Wavesmentioning
confidence: 99%