Outbreak dynamics of COVID-19 in China and the United States

Abstract

On March 11, 2020, the World Health Organization declared the coronavirus disease 2019, COVID-19, a global pandemic. In an unprecedented collective effort, massive amounts of data are now being collected worldwide to estimate the immediate and long-term impact of this pandemic on the health system and the global economy. However, the precise timeline of the disease, its transmissibility, and the effect of mitigation strategies remain incompletely understood. Here we integrate a global network model with a local epidemic SEIR model to quantify the outbreak dynamics of COVID-19 in China and the United States. For the outbreak in China, in n = 30 provinces, we found a latent period of 2.56 ± 0.72 days, a contact period of 1.47 ± 0.32 days, and an infectious period of 17.82 ± 2.95 days. We postulate that the latent and infectious periods are disease-specific, whereas the contact period is behavior-specific and can vary between different provinces, states, or countries. For the early stages of the outbreak in the United States, in n = 50 states, we adopted the disease-specific values from China and found a contact period of 3.38 ± 0.69 days. Our network model predicts that-without the massive political mitigation strategies that are in place todaythe United States would have faced a basic reproduction number of 5.30 ± 0.95 and a nationwide peak of the outbreak on May 10, 2020 with 3 million infections. Our results demonstrate how mathematical modeling can help estimate outbreak dynamics and provide decision guidelines for successful outbreak control. We anticipate that our model will become a valuable tool to estimate the potential of vaccination and quantify the effect of relaxing political measures including total lockdown, shelter in place, and travel restrictions for low-risk subgroups of the population or for the population as a whole.

Outbreak dynamics of COVID-19 in Europe and the effect of travel restrictions

“…We model the spreading of COVID-19 through a mobility network of passenger air travel, which we represent as a weighted undirected graph G with N nodes and E edges (Peirlinck et al 2020). The N ¼ 27 nodes represent the countries of the European Union, the E ¼ 172 edges the most traveled connections between them.…”

“…From these data, we map out the temporal evolution of the infectious group I as the difference between the confirmed cases minus the recovered cases and deaths. To simulate the country-specific epidemiology of COVID-19 with the SEIR model, we utilize these data to identify the basic reproduction number R 0 ¼ C=B using the latent and infectious periods A ¼ 1=a ¼ 2:56 days and C ¼ 1=c ¼ 17:82 days, which we had previously identified for the COVID-19 outbreak in N ¼ 30 Chinese provinces (Peirlinck et al 2020), since the current European data are not yet complete for the identification of all three parameters. In addition to the basic reproduction number R 0 ¼ C=B, which is a direct measure of the contact period B ¼ 1=b, we also identify the initial community spread q ¼ E 0 =I 0 that defines the initial exposed population E 0 (Maier and Brockmann 2020), and the affected population g ¼ N Ã =N that defines the fraction of the epidemic subpopulation N Ã relative to the total population N (Eurostat, 2020).…”

“…Altogether we identify three parameters for 27 countries, the basic reproduction number R 0 ¼ C=B, the initial community spread q ¼ E 0 =I 0 , and the affected population g ¼ N Ã =N using the Levenberg-Marquardt method of least squares. For the indentified parameters, we compare two COVID-19 outbreak scenarios: outbreak dynamics with the current travel restrictions, a mobility coefficient of # ¼ 0:00, and a country-specific outbreak on day d 0 , the day at which 0.001% of the population is reported as infected; and outbreak dynamics without travel restrictions, with a mobility coefficient of # ¼ 0:43 (Peirlinck et al 2020), and a European outbreak on day d 0 in Italy, the first country in which 0.001% of the population is reported as infected. Figure 1 shows the basic reproduction number R 0 ¼ C=B, the initial community spread q ¼ E 0 =I 0 , and the affected population g ¼ N Ã =N across all 27 countries of the European Union.…”

“…As such, it provides valuable insight into the transmissibility of an infectious agent (Fang et al 2020). Here we leave this parameter free and identify it independently for each country in the European Union (Peirlinck et al 2020).…”

The reproduction number of COVID-19 and its correlation with public health interventions

“…The constant reproduction number in Figure 1, left, nicely captures the exponential increase at the early stages of the outbreak, but fails to "bend the curve" before herd immunity occurs. Nonetheless, several recent studies have successfully used an SEIR model with a constant reproduction number to model the outbreak dynamics of COVID-19 in China [35] and in Europe [28] by explicitly reducing the total population N to an affected population N * = η N. The scaling coefficient η = N * /N is essentially a fitting parameter that indirectly quantifies the level of confinement [3]. For example, when averaged over 30 Chinese provinces, the mean affected population was η = 5.19 · 10 −5 ± 2.23 ± 10 −4 , suggesting that the effect of COVID-19 was confined to only a very small fraction of the total population [35].…”