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With the outbreaks of the COVID-19 epidemics in several provinces of China, government takes prevention and control measures to contain the epidemics. It is more difficult to make the long-term prediction of the sporadic COVID-19 epidemics than widespread ones in that the former cannot obey the laws of the infectious disease well like the latter. In this paper, we make long-term predictions including end time and final size, peak and peak time of current confirmed cases and the number of accumulative removed cases of the sporadic COVID-19 epidemics in different regions of China by a novel non-autonomous delayed SIR compartment model (S-susceptible, I-infected, R-removed). The key contribution of this paper is that under the rigorous containments, we find transmission rate   β  (  t  )   is approximately an exponential decreasing function with respect to time t, rather than a fixed constant. In addition, the removed rate   γ  (  t  )   is approximately a piecewise linear increasing function instead of a linear increasing function which is (at + b)heaviside (t-14). First, according to the few data in the early stage, i.e., roughly the first 7 days, issued by the National Health Commission of China and local Health Commissions, we can accurately estimate these parameters, i.e., transmission and removed rates of the model. Then, by them, we accurately predict the evolution of the COVID-19 there. On the basis of them to predict Category A of the sporadic COVID-19 epidemics since July 20th, 2021 in this summer. The results agree very well to the actual ones. It is also adopted to predict Category B   -  -  -   the tour group epidemics since October 17th, 2021 and Category C   -  -  -   other sporadic epidemics since October 27th, 2021. The results show that although our method is simple and the needed data are very few, the long-term prediction of the sporadic COVID-19 epidemics in China is quite effective. We can use this novel non-autonomous delayed SIR model to accurately predict its end time and final size, peak and peak time of current confirmed cases and the number of accumulative removed cases in China. This work can help governments and policy-makers make optimal prevention and control policies for all cities and provinces to contain the COVID-19 epidemics, and prepare well for the resumption of work, production and classes in advance to reduce the economic and social losses.

Long-term prediction of the sporadic COVID-19 epidemics induced by $$\delta$$-virus in China based on a novel non-autonomous delayed SIR model