Existence of travelling fronts in a diffusive vector disease model with spatio-temporal delay

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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/192000

Title: Existence of travelling fronts in a diffusive vector disease model with spatio-temporal delay
Author(s): Peng, Yahong; Zhang, Tonghua; Tade, Moses O.
Abstract: In this paper, we study travelling front solutions of a vector disease model incorporating time delays and diffusion. Special attention is paid to the modelling of the time delays to incorporate the associated non-local spatial terms which account for the drift of individuals to their present positions from their possible positions at previous times. We shall show that such fronts exist for the weak generic delay kernel and sufficiently small delays by using geometric singular perturbation theory. Then, for the discrete-delay case, following Canosa's asymptotic analysis method, we give some information on travelling front solutions.
Publication type: Journal article
Source: Nonlinear Analysis: Real World Applications, Vol. 11, no. 4 (Aug 2010), pp. 2472-2478
Publication year: 2010
FOR Code(s): 0102 Applied Mathematics
Keyword(s): Asymptotic analysis; Delay; Non-local effect; Perturbation techniques; Reaction diffusion systems; Reactiondiffusion system; Time delay; Travelling front; Travelling fronts; Vector disease model; Vectors
Publisher: Elsevier
ISSN: 1468-1218
Publisher URL: http://dx.doi.org/10.1016/j.nonrwa.2009.08.004