Frequency estimation of physical symptoms for peoples is the most direct way to analyze and predict infectious diseases. In Internet of medical Things (IoMT), it is efficient and convenient for users to report their physical symptoms to hospitals or disease prevention departments by various mobile devices. Unfortunately, it usually brings leakage risk of these symptoms since data receivers may be untrusted. As a strong metric for health privacy, local differential privacy (LDP) requires that

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... rs should perturb their symptoms to prevent the risk. However, the widely-used data structure called sketch for frequency estimation doesn't satisfy the specified requirement. In this paper, we firstly define the problem of frequency estimation of physical symptoms under LDP. Then, we propose four different protocols, i.e., CMS-LDP, FCS-LDP, CS-LDP and FAS-LDP to solve the above problem. Next, we demonstrate that the designed protocols satisfy LDP and unbiased estimation. We also present two approaches to implement the key component (i.e., universal hash functions) of protocols. Finally, we conduct experiments to evaluate four protocols on two real-world datasets, representing two different distributions of physical symptoms. The results show that CMS-LDP and CS-LDP have relatively optimal utility for frequency estimation of physical symptoms in IoMT.