SIAM Journal on Applied Mathematics
Synchronization of pulse-coupled biological oscillators
SIAM Journal on Applied Mathematics
SIAM Review
The Mathematics of Infectious Diseases
SIAM Review
Travelling fronts for the KPP equation with spatio-temporal delay
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Global stability for reaction-diffusion equations in biology
Computers & Mathematics with Applications
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Mathematical models are used to determine if infection wave fronts could occur by traveling geographically in a loop around a region or continent. These infection wave fronts arise by Hopf bifurcation for some spatial models for infectious disease transmission with distributed-contacts. Periodic traveling waves are shown to exist for the spatial analog of the SIRS endemic model, in which the temporary immunity is described by a delay, but they do not exist in a similar spatial SIRS endemic model without a delay. Specifically, we found that the ratio of the delay @w in the recovered class and the average infectious period 1/@c must be sufficiently large for Hopf bifurcation to occur.