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In this paper, a generalized fractional-order SEIR model is proposed, denoted by SEIQRP model, which divided the population into susceptible, exposed, infectious, quarantined, recovered and insusceptible individuals and has a basic guiding significance for the prediction of the possible outbreak of infectious diseases like the coronavirus disease in 2019 (COVID-19) and other insect diseases in the future. Firstly, some qualitative properties of the model are analyzed. The basic reproduction number R 0 is derived. When R 0 < 1, the disease-free equilibrium point is unique and locally asymptotically stable. When R 0 > 1, the endemic equilibrium point is also unique. Furthermore, some conditions are established to ensure the local asymptotic stability of disease-free and endemic equilibrium points. The trend of COVID-19 spread in the USA is predicted. Considering the influence of the individual behavior and government mitigation measurement, a modified SEIQRP model is proposed, defined as SEIQRPD model, which is divided the population into susceptible, exposed, infectious, quaran

Background SARS-CoV-2 has been identified in the fecal matter of COVID-19 patients. However, sewage transmission has never been shown. In April 2020, a COVID-19 outbreak occurred in a densely populated community in Guangzhou, China. We investigated this outbreak to identify the mode of transmission. Method A home quarantined order was issued in the community. We collected throat swab samples from the residents and environmental samples from the surfaces inside and around the houses, and conducted RT-PCR testing and genome sequencing. We defined a case as a resident in this community with a positive RT-PCR test, with or without symptoms. We conducted a retrospective cohort study of all residents living in the same buildings as the cases to identify exposure risk factors. Result We found eight cases (four couples) in this community of 2888 residents (attack rate=2.8/1000), with onset during April 5–21, 2020. During their incubation periods, Cases 1-2 frequented market T with an ongoing outbreak. Cases 3-8 never visited market T during incubation period, lived in separate buildings from, and never interacted with, Cases 1-2. Retrospective cohort study showed that working as cleaners or waste picker (RR=13, 95% CIexact: 2.3-180), not changing to clean shoes after returning home (RR=7.4, 95% CIexact: 1.8-34), collating and cleaning dirty shoes after returning home (RR=6.3, 95% CIexact: 1.4-30) were significant exposure risk factors. Of 63 samples collected from street-sewage puddles and sewage-pipe surfaces, 19% tested positive for SARS-CoV-2. Of 50 environmental samples taken from cases’ apartments, 24% tested positive. Viral genome sequencing showed that the viruses identified from the squat toilet and shoe-bottom dirt inside the apartment of Cases 1-2 were homologous with those from Cases 3-8 and those identified from sewage samples. The sewage pipe leading from the apartment of Cases 1-2 to the drainage had a large hole above ground. Rainfalls after the onset of Cases 1-2 flooded the streets. Conclusion Our investigation has for the first time pointed to the possibility that SARS-CoV-2 might spread by sewage. This finding highlighted the importance of sewage management, especially in densely-populated places with poor hygiene and sanitation measures, such as urban slums and other low-income communities in developing countries.

In the end of 2019, a new type of coronavirus first appeared in Wuhan. Through the real-data of COVID-19 from January 23 to March 18, 2020, this paper proposes a fractional SEIHDR model based on the coupling effect of inter-city networks. At the same time, the proposed model considers the mortality rates (exposure, infection and hospitalization) and the infectivity of individuals during the incubation period. By applying the least squares method and predictioncorrection method, the proposed system is fitted and predicted based on the real-data from January 23 to March 18 − m where m represents predict days. Compared with the integer system, the non-network fractional model has been verified and can better fit the data of Beijing, Shanghai, Wuhan and Huanggang. Compared with the no-network case, results show that the proposed system with inter-city network may not be able to better describe the spread of disease in China due to the lock and isolation measures, but this may have a significant impact on countries that has no closure measures. Meanwhile, the proposed model is more