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Travelling waves of a diffusive epidemic model with latency and relapse. (English) Zbl 1264.34167

Summary: An SEIR epidemic model with relapse and spatial diffusion is studied. By analyzing the corresponding characteristic equations, the local stability of each of the feasible steady states to this model is discussed. The existence of a travelling wave solution is established by using the technique of upper and lower solutions and Schauder’s fixed point theorem. Numerical simulations are carried out to illustrate the main results.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
92D30 Epidemiology
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[1] Philosophical transactions of the Royal Society of London B 310 (1145) pp 327– (1985) · doi:10.1098/rstb.1985.0123
[2] DOI: 10.1046/j.1365-2656.2000.00428.x · doi:10.1046/j.1365-2656.2000.00428.x
[3] (1999)
[4] (1994)
[5] Journal of the American Medical Association 259 (7) pp 1051– (1988) · doi:10.1001/jama.1988.03720070051034
[6] DOI: 10.3934/mbe.2007.4.205 · Zbl 1123.92018 · doi:10.3934/mbe.2007.4.205
[7] DOI: 10.1016/j.nonrwa.2010.06.001 · Zbl 1208.34125 · doi:10.1016/j.nonrwa.2010.06.001
[8] (2002)
[9] Nature 250 pp 276– (1974) · doi:10.1038/250276a0
[10] DOI: 10.1016/j.jtbi.2008.12.032 · Zbl 1405.92260 · doi:10.1016/j.jtbi.2008.12.032
[11] DOI: 10.1007/s10255-006-0300-0 · Zbl 1106.34037 · doi:10.1007/s10255-006-0300-0
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