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In this paper, we investigate the dynamic properties of an SIR epidemic model with saturated growth rate. Under the conditions of an arbitrary initial value, we prove that the system exists unique positive solution, and give the sufficient conditions caused by random environmental factors leading to the extinction of infectious diseases. Moreover, we verify the conditions for the persistence of infectious diseases in the mean sense. Finally, we provide the biology interpretation and some strategies to control the infectious diseases.

A sensitive DC magnetic field sensor is constructed by measuring the signal-to-noise ratio of an AC-modulated magnetic field at a particular frequency from an optical whispering gallery mode microcapillary resonator. The sensing element consists of an optical whispering gallery mode microcapillary resonator bonded to a magnetostrictive material that enables it to respond to external magnetic fields. A DC magnetic field sensitivity of 0.1703dB/Oe and a linear detection range from 4.8Oe to 65.7Oe are realized under an AC modulation field of 168.1kHz in the unshielded environment at room temperature. To our best knowledge, this sensitivity is about 2.3 times of the maximum sensitivity of other DC magnetic field sensors based on magnetic fluid or magnetostrictive material integrated fiber systems that use the dissipative sensing scheme. Furthermore, the sensor can operate at a stable temperature in the range of [-11∼45]°C, as long as the modulation frequency of the AC-modulation field is adjusted according to the ambient temperature. This sensor provides us with a novel DC magnetic field sensing scheme, which may play a role in industrial fields related to current and position detection in the future.

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