Keywords: deterministic models; epidemiology; population models; nonlinear flows; chaos; bifurcation; periodic orbits; equilibrium states; reaction kinetics; biological oscillators; Belousov-Zhabotinskij; perturbations; singular perturbation techniques; reaction diffusion systems; oscillator waves; quasiwaves; non-interacting oscillators; small diffusions; interacting populations; spatial patterns; pattern formation; spatial spread of contagious diseases