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Lin, Guojian; Hong, Yiguang

Travelling wave fronts in a vector disease model with delay. (English) Zbl 1167.35392

Appl. Math. Modelling 32, No. 12, 2831-2838 (2008).
Summary: In this paper, we study the diffusive vector disease model with delay. This problem with strong biological background has attracted much research attention. We focus on the existence of traveling wave fronts, and find that there is a moving zone for the transition from the disease-free state to the infective state. To complete the theoretical analysis, we employ the mathematical tools including the monotone iteration technique as well as the upper and lower solution method.

Cited in 7 Documents

MSC:

35K55 Nonlinear parabolic equations
92D30 Epidemiology
92C50 Medical applications (general)
34K13 Periodic solutions to functional-differential equations
35Q51 Soliton equations
35R10 Partial functional-differential equations

Keywords:

vector disease model; travelling wave front; monotone iteration technique; upper and lower solution
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References:

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