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

Abstract

Started in Wuhan, China, the COVID-19 has been spreading all over the world. We calibrate the logistic growth model, the generalized logistic growth model, the generalized Richards model and the generalized growth model to the reported number of infected cases for the whole of China, 29 provinces in China, and 33 countries and regions that have been or are undergoing major outbreaks. We 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 quantitatively document four phases of the outbreak in China with a detailed analysis on the heterogeneous situations across provinces. The extreme containment measures implemented by China were very effective with some instructive variations across provinces. Borrowing from the experience of China, we made scenario projections on the development of the outbreak in other countries. We identified that outbreaks in 14 countries (mostly in western Europe) have ended, while resurgences of cases have been identified in several among them. The modeling results clearly show longer after-peak trajectories in western countries, in contrast to most provinces in China where the after-peak trajectory is characterized by a much faster decay. We identified three groups of countries in different level of outbreak progress, and provide informative implications for the current global pandemic.

Social, economic, and environmental factors influencing the basic reproduction number of COVID-19 across countries

“…T has been estimated to be between 4-8 days; here we use 5.8 days (40–42). To Estimate r, we fit the rate of change in cumulative cases of a logistic growth model, with parameters r (intrinsic growth rate) and K (theoretical epidemic size without intervention), to observe time series in daily confirmed cases (5,43). The logistic growth model is superior to fitting an exponential curve to early case numbers given that case numbers do plateau in reality.…”

Application of a Semi-Empirical Dynamic Model to Forecast the Propagation of the COVID-19 Epidemics in Spain

“…The behaviour of this function gives rise to the logistic function and the typical sigmoid shape of its cumulative distribution if r < 2, while it shows a chaotic behaviour if r > 3.56995 (see Figure 3). Other authors have studied the behaviour of this logistic function applied to the COVID-19 epidemics [26,27]. In order to compare with the values of the basic reproduction number in Table 2 the empirically determined values of the growth parameter r are shown for the same countries in Table 1.…”

COVID-19 outbreak in Mauritius: Logistic growth and SEIR modelling with quarantine and an effective reproduction number

“…The growth curve is S-shaped if N (0) < K /2. Several extensions of the Verhulst model have been proposed to address deviations from the symmetric shape of the logistic curve [15]. Epidemiologically, the logistic equation is an exact solution of the susceptible-infected-susceptible (SIS) compartmental model for the infected cases where it is assumed that individuals who recover become immediately susceptible again because the disease confers no immunity against reinfection [17].…”

“…The growth curve is S-shaped if (0) < /2. Several extensions of the Verhulst model have been proposed to address deviations from the symmetric shape of the logistic curve [15].…”

“…More sophisticated models such as agent-based models can work at the level of individuals [13]. Logistic growth models are simpler but have nevertheless been widely used to describe epidemics [14, 15]. All these models have helped in informing and shaping policy decisions on effective responses to the SARS-CoV-2 virus.…”