Initially found in Hubei, Wuhan, and identified as a novel virus of the coronavirus family by the WHO, COVID-19 has spread worldwide at exponential speed, causing millions of deaths and public fear. Currently, the USA, India, Brazil, and other parts of the world are experiencing a secondary wave of COVID-19. However, the medical, mathematical, and pharmaceutical aspects of its transmission, incubation, and recovery processes are still unclear. The classical susceptible–infected–recovered model has limitations in describing the dynamic behavior of COVID-19. Hence, it is necessary to introduce a recursive, latent model to predict the number of future COVID-19 infection cases in the USA. In this article, a dynamic recursive and latent infection model (RLIM) based on the classical SEIR model is proposed to predict the number of COVID-19 infections. Given COVID-19 infection and recovery data for a certain period, the RLIM is able to fit current values and produce an optimal set of parameters with a minimum error rate according to actual reported numbers. With these optimal parameters assigned, the RLIM model then becomes able to produce predictions of infection numbers within a certain period. To locate the turning point of COVID-19 transmission, an initial value for the secondary infection rate is given to the RLIM algorithm for calculation. RLIM will then calculate the secondary infection rates of a continuous time series with an iterative search strategy to speed up the convergence of the prediction outcomes and minimize the maximum square errors. Compared with other forecast algorithms, RLIM is able to adapt the COVID-19 infection curve faster and more accurately and, more importantly, provides a way to identify the turning point in virus transmission by searching for the equilibrium between recoveries and new infections. Simulations of four US states show that with the secondary infection rate initially set to 0.5 within the selected latent period of 14 days, RLIM is able to minimize this value at 0.07 and reach an equilibrium condition. A successful forecast is generated using New York state’s COVID-19 transmission, in which a turning point is predicted to emerge on January 31, 2021. Supplementary Information The online version contains supplementary material available at 10.1007/s11071-021-06520-1.

Initially found at Hubei, Wuhan and identified as a novel virus of coronavirus family by WHO, COVID-19 has spread worldwide with an exponentially speed, causing millions of death and public fear. Currently, COVID19 has brought a secondary wave within U.S., India, Brazil and other parts of the world. However, its transmission, incubation, and recovery processes are still unclear from the medical, mathematical and pharmaceutical aspects. Classical Suspect-Infection-Recovery model has limitations to describe the dynamic behavior of COVID-19. Hence, it becomes necessary to introduce a recursive, latent model to predict the number of future COVID-19 infected cases in U.S. In this article, a dynamic model called RLIM based on classical SEIR model is proposed to predict the number of COVID-19 infections with a dynamic secondary infection rate ω in assumption. An intermediate state called SI is introduced between recovery and infection statues to record the number of secondary infected cases from a latent period of recovery. Compared with other models, RLIM fits historical recovery cases and utilizes them to predict future infections. Because RLIM utilizes multiple information sources, and provides error back propagation schematics, it is reasonable to assert that its predictions are more accurate and persuasive. Projections of four U.S. COVID19 states show that with the secondary infectious rate ω varies from 0.01 to 0.3 within a latent period of 14 days chosen, RLIM can predict the newly infected number from January 15 to February 15, 2021 with AFER lower to 14%. It also successfully estimates the turning point of New Yorks infections in January 2021, based on current data records.