Generalized logistic growth modeling of the COVID-19 outbreak in 29 provinces in China and in the rest of the world

Abstract

Background: the COVID-19 has been successfully contained in China but is spreading all over the world. We use phenomenological models to dissect the development of the epidemics in China and the impact of the drastic control measures both at the aggregate level and within each province.We use the experience from China to analyze the calibration results on Japan, South Korea, Iran, Italy and Europe, and make future scenario projections. Methods: we calibrate the logistic growth model, the generalized logistic growth model, the generalized growth model and the generalized Richards model to the reported number of infected cases from Jan. 19 to March 10 for the whole of China, 29 provinces in China, four severely affected countries and Europe as a whole. The different models provide upper and lower bounds of our scenario predictions. Results:We quantitatively document four phases of the outbreak in China with a detailed analysis on the heterogenous situations across provinces. Based on Chinese experience, we identify a high risk in Japan with estimated total confirmed cases as of March 25 being 1574 (95% CI: [880, 2372]), and 5669 (95% CI: [988, 11340]) by June. For South Korea, we expect the number of infected cases to approach the ceiling, 7928 (95% CI: [6341, 9754]), in 20 days. We estimate 0.15% (95% CI: [0.03%, 0.30%]) of Italian population to be infected in a positive scenario. We would expect 114867 people infected in Europe in 10 days, in a negative but probable scenario, corresponding to 0.015% European population. Conclusions:The extreme containment measures implemented by China were very effective with some instructive variations across provinces. For other countries, it is almost inevitable to see the continuation of the outbreak in the coming months. Japan and Italy are in serious situations with no short-term end to the outbreak to be expected. There is a significant risk concerning the upcoming July 2020 Summer Olympics in Tokyo. Iran's situation is highly uncertain with unclear and negative future scenarios, while South Korea is approaching the end of the outbreak. Both Europe and the USA are at early stages of the outbreak, posing significant health and economic risks to the world in absence of serious measures.

Modelling fatality curves of COVID-19 and the effectiveness of intervention strategies

“…where in the left-hand side we have explicitly denoted the dependence of the solution of the RGM on the four parameters, namely r, α, K, and t c . We note, however, that the RGM is not reliable in situations where the epidemic is in such an early stage that the available data is well below the estimated inflection point t c , i.e., when the epidemic is still in the so-called exponential growth regime (Wu et al, 2020). In this case, it is preferable to 3/11 All rights reserved.…”

“…use the so-called generalized growth model (Wu et al, 2020;Chowell, 2017), which is defined by the following ODE:…”

“…1, encouraged us to apply the model to other countries at earlier stages of the epidemic. Here, however, care must be taken when estimating the model parameters from small time series, since it is well known that the Richards model (Wang et al, 2012;Hsieh, 2009) and its variants (Wu et al, 2020) are susceptible to the problem of over fitting, owing to the redundancy of the parameters. This may lead, for example, to estimation of certain parameters that are outside of biologically or otherwise reasonable ranges.…”

“…In other words, for our purposes here we assume that the restrictions 0 < r < 1 and 0 < α < 1 are useful empirical criteria for the validity of the RGM. The unsuitability of the RGM is particularly evident when the available data does not encompass the inflection point t c (Wu et al, 2020), although as more data is accumulated the model is expected to become more accurate.…”

A Bayesian Logistic Growth Model for the Spread of COVID-19 in New York

“…The logistic growth model is frequently used in order to model the spread of viral diseases and of covid-19 in particular (e.g. Batista, 2020;Wu et al, 2020). The differential equation is given in (1):…”