Electromagnetic fields (EMFs) can increase free radicals, activate the stress response and alter enzyme reactions. Intracellular signalling is mediated by free radicals and enzyme kinetics is affected by radical pair recombination rates. The magnetic field component of an external EMF can delay the "recombination rate" of free radical pairs. Magnetic fields thus increase radical life-times in biological systems. Although measured in nanoseconds, this extra time increases the potential to do more damage. Melatonin regulates the body's sleep-wake cycle or circadian rhythm. The World Health Organization (WHO) has confirmed that prolonged alterations in sleep patterns suppress the body's ability to make melatonin. Considerable cancer rates have been attributed to the reduction of melatonin production as a result of jet lag and night shift work. In this study, changes in circadian rhythm and melatonin concentration are observed due to the external perturbation of chemical reaction rates. We further analyze the pineal melatonin rhythm and investigate the critical time delay or maturation time of radical pair recombination rates, exploring the impact of the mRNA degradation rate on the critical time delay. The results show that significant melatonin interruption and changes to the circadian rhythm occur due to the perturbation of chemical reaction rates, as also reported in previous studies. The results also show the influence of the mRNA degradation rate on the circadian rhythm's critical time delay or maturation time. The results support the hypothesis that exposure to weak EMFs via melatonin disruption can adversely affect human health.