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Background In this study, we aimed to quantify the contribution of different transmission routes of the Middle East respiratory syndrome (MERS) and determine its transmissibility. Methods Based on the natural history and transmission features of MERS in different countries, a susceptible-exposed-symptomatic-asymptomatic-recovered/death (SEIARD) model and a multi-route dynamic model (MMDM). The SEIARD model and MMDM were adopted to simulate MERS in South Korea and Saudi Arabia, respectively. Data on reported MERS cases in the two countries were obtained from the World Health Organization. Thereafter, the next generation matrix method was employed to derive the equation for the basic reproduction number ( R 0 ), and the model fitting procedure was adopted to calculate the R 0 values corresponding to these different countries. Results In South Korea, ‘Person-to-Person’ transmission was identified as the main mode of MERS transmission in healthcare settings, while in Saudi Arabia, in addition to ‘Person-to-Person’ transmission, ‘Host-to-Host’ and ‘Host-to-Person’ transmission also occurred under certain scenarios, with camels being the main host. Further, the fitting results showed that the SEIARD model and MMDM fitted the data well. The mean R 0 value was 8.59 (95% confidence interval [CI]: 0–28.02) for MERS in South Korea, and for MERS in Saudi Arabia, it was 1.15 and 1.02 (95% CI: 0.86–1.44) for the ‘Person-to-Person’ and ‘Camel-to-Camel’ transmission routes, respectively. Conclusions The SEIARD and MMDM model can be used to simulate the transmission of MERS in different countries. Additionally, in Saudi Arabia, the transmissibility of MERS was almost the same among hosts (camels) and humans.

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COVID-19, which broke out globally in 2019, is an infectious disease caused by a novel strain of coronavirus, and its spread is highly contagious and concealed. Environmental vectors play an important role in viral infection and transmission, which brings new difficulties and challenges to disease prevention and control. In this paper, a type of differential equation model is constructed according to the spreading functions and characteristics of exposed individuals and environmental vectors during the virus infection process. In the proposed model, five compartments were considered, namely, susceptible individuals, exposed individuals, infected individuals, recovered individuals, and environmental vectors (contaminated with free virus particles). In particular, the re-positive factor was taken into account (i.e., recovered individuals who have lost sufficient immune protection may still return to the exposed class). With the basic reproduction number R0 of the model, the global stability of the disease-free equilibrium and uniform persistence of the model were completely analyzed. Furthermore, sufficient conditions for the global stability of the endemic equilibrium of the model were also given. Finally, the effective predictability of the model was tested by fitting COVID-19 data from Japan and Italy.

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