The first case of coronavirus disease 2019 in Japan was reported on 15 January 2020 and the number of reported cases has increased day by day. The purpose of this study is to give a prediction of the epidemic peak for COVID-19 in Japan by using the real-time data from 15 January to 29 February 2020. Taking into account the uncertainty due to the incomplete identification of infective population, we apply the well-known SEIR compartmental model for the prediction. By using a least-square-based method with Poisson noise, we estimate that the basic reproduction number for the epidemic in Japan is R 0 = 2.6 (95%CI, 2.4-2.8) and the epidemic peak could possibly reach the early-middle summer. In addition, we obtain the following epidemiological insights: (1) the essential epidemic size is less likely to be affected by the rate of identification of the actual infective population;(2) the intervention has a positive effect on the delay of the epidemic peak; (3) intervention over a relatively long period is needed to effectively reduce the final epidemic size.
In this paper, we study a class of periodic SEIRS epidemic models and it is shown that the global dynamics is determined by the basic reproduction number R 0 which is defined through the spectral radius of a linear integral operator. If R 0 < 1, then the disease free periodic solution is globally asymptotically stable and if R 0 > 1, then the disease persists.Our results really improve the results in [T. Zhang, Z. Teng, On a nonautonomous SEIRS model in epidemiology Bull. Math. Biol. 69 (8) (2007) 2537-2559] for the periodic case. Moreover, from our results, we see that the eradication policy on the basis of the basic reproduction number of the time-averaged system may overestimate the infectious risk of the periodic disease. Numerical simulations which support our theoretical analysis are also given.
Background
The pandemic coronavirus disease 2019 (COVID-19) has spread and caused enormous and serious damages to many countries worldwide. One of the most typical interventions is the social distancing such as lockdown that would contribute to reduce the number of contacts among undiagnosed individuals. However, prolongation of the period of such a restrictive intervention could hugely affect the social and economic systems, and the outbreak will come back if the strong social distancing policy will end earlier due to the economic damage. Therefore, the social distancing policy should be followed by massive testing accompanied with quarantine to eradicate the infection.
Methods
In this paper, we construct a mathematical model and discuss the effect of massive testing with quarantine, which would be less likely to affect the social and economic systems, and its efficacy has been proved in South Korea, Taiwan, Vietnam and Hong Kong.
Results
By numerical calculation, we show that the control reproduction number is monotone decreasing and convex downward with respect to the testing rate, which implies that the improvement of the testing rate would highly contribute to reduce the epidemic size if the original testing rate is small. Moreover, we show that the recurrence of the COVID-19 epidemic in Japan could be possible after the lifting of the state of emergency if there is no massive testing and quarantine.
Conclusions
If we have entered into an explosive phase of the epidemic, the massive testing could be a strong tool to prevent the disease as long as the positively reacted individuals will be effectively quarantined, no matter whether the positive reaction is pseudo or not. Since total population could be seen as a superposition of smaller communities, we could understand how testing and quarantine policy might be powerful to control the disease.
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