Post by Admin on Mar 19, 2020 4:38:59 GMT
Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV2)
Ruiyun Li1,*, Sen Pei2,*,†, Bin Chen3,*, Yimeng Song4, Tao Zhang5, Wan Yang6, Jeffrey Shaman2,†
Science 16 Mar 2020:
eabb3221
DOI: 10.1126/science.abb3221
Abstract
Estimation of the prevalence and contagiousness of undocumented novel coronavirus (SARS-CoV2) infections is critical for understanding the overall prevalence and pandemic potential of this disease. Here we use observations of reported infection within China, in conjunction with mobility data, a networked dynamic metapopulation model and Bayesian inference, to infer critical epidemiological characteristics associated with SARS-CoV2, including the fraction of undocumented infections and their contagiousness. We estimate 86% of all infections were undocumented (95% CI: [82%–90%]) prior to 23 January 2020 travel restrictions. Per person, the transmission rate of undocumented infections was 55% of documented infections ([46%–62%]), yet, due to their greater numbers, undocumented infections were the infection source for 79% of documented cases. These findings explain the rapid geographic spread of SARS-CoV2 and indicate containment of this virus will be particularly challenging.
The novel coronavirus that emerged in Wuhan, China (SARS-CoV2) at the end of 2019 quickly spread to all Chinese provinces and, as of 1 March 2020, to 58 other countries (1, 2). Efforts to contain the virus are ongoing; however, given the many uncertainties regarding pathogen transmissibility and virulence, the effectiveness of these efforts is unknown.
The fraction of undocumented but infectious cases is a critical epidemiological characteristic that modulates the pandemic potential of an emergent respiratory virus (3–6). These undocumented infections often experience mild, limited or no symptoms and hence go unrecognized, and, depending on their contagiousness and numbers, can expose a far greater portion of the population to virus than would otherwise occur. Here, to assess the full epidemic potential of SARS-CoV2, we use a model-inference framework to estimate the contagiousness and proportion of undocumented infections in China during the weeks before and after the shutdown of travel in and out of Wuhan.
We developed a mathematical model that simulates the spatiotemporal dynamics of infections among 375 Chinese cities (see supplementary materials). In the model, we divided infections into two classes: (i) documented infected individuals with symptoms severe enough to be confirmed, i.e., observed infections; and (ii) undocumented infected individuals. These two classes of infection have separate rates of transmission: β, the transmission rate due to documented infected individuals; and μβ, the transmission rate due to undocumented individuals, which is β reduced by a factor μ.
Spatial spread of SARS-CoV2 across cities is captured by the daily number of people traveling from city j to city i and a multiplicative factor. Specifically, daily numbers of travelers between 375 Chinese cities during the Spring Festival period (“Chunyun”) were derived from human mobility data collected by the Tencent Location-based Service during the 2018 Chunyun period (1 February–12 March 2018) (7). Chunyun is a period of 40 days—15 days before and 25 days after the Lunar New Year—during which there are high rates of travel within China. To estimate human mobility during the 2020 Chunyun period, which began 10 January, we aligned the 2018 Tencent data based on relative timing to the Spring Festival. For example, we used mobility data from 1 February 2018 to represent human movement on 10 January 2020, as these days were similarly distant from the Lunar New Year. During the 2018 Chunyun, a total of 1.73 billion travel events were captured in the Tencent data; whereas 2.97 billion trips are reported (7). To compensate for underreporting and reconcile these two numbers, a travel multiplicative factor, θ, which is greater than 1, is included (see supplementary materials).
To infer SARS-CoV2 transmission dynamics during the early stage of the outbreak, we simulated observations during 10–23 January 2020 (i.e., the period before the initiation of travel restrictions, fig. S1) using an iterated filter-ensemble adjustment Kalman filter (IF-EAKF) framework (8–10). With this combined model-inference system, we estimated the trajectories of four model state variables (Si, Ei, Iri, Iui: the susceptible, exposed, documented infected, and undocumented infected sub-populations in city i) for each of the 375 cities, while simultaneously inferring six model parameters (Z, D, μ, β, α, θ: the average latent period, the average duration of infection, the transmission reduction factor for undocumented infections, the transmission rate for documented infections; the fraction of documented infections, and the travel multiplicative factor).
Fig. 1 Best-fit model and sensitivity analysis.
Details of model initialization, including the initial seeding of exposed and undocumented infections, are provided in the supplementary materials. To account for delays in infection confirmation, we also defined a time-to-event observation model using a Gamma distribution (see supplementary materials). Specifically, for each new case in group Iri, a reporting delay td (in days) was generated from a Gamma distribution with a mean value of Td. In fitting both synthetic and the observed outbreaks, we performed simulations with the model-inference system using different fixed values of Td (6 days ≤ Td ≤ 10 days) and different maximum seeding, Seedmax (1500 ≤ Seedmax ≤ 2500) (see supplementary materials, fig. S2). The best fitting model-inference posterior was identified by log-likelihood.
We first tested the model-inference framework versus alternate model forms and using synthetic outbreaks generated by the model in free simulation. These tests verified the ability of the model-inference framework to accurately estimate all six target model parameters simultaneously (see supplementary methods and figs. S3 to S14). Indeed, the system could identify a variety of parameter combinations and distinguish outbreaks generated with high α and low μ from low α and high μ. This parameter identifiability is facilitated by the assimilation of observed case data from multiple (375) cities into the model-inference system and the incorporation of human movement in the mathematical model structure (see supplementary methods and figs. S15 and S16).
We next applied the model-inference framework to the observed outbreak before the travel restrictions of 23 January—a total of 801 documented cases throughout China, as reported by 8 February 2020 (1). Figure 1, A to C, shows simulations of reported cases generated using the best-fitting model parameter estimates. The distribution of these stochastic simulations captures the range of observed cases well. In addition, the best-fitting model captures the spread of infections with the novel coronavirus (COVID-19) to other cities in China (fig. S17). Our median estimate of the effective reproductive number, Re—equivalent to the basic reproductive number (R0) at the beginning of the epidemic—is 2.38 (95% CI: 2.04−2.77), indicating a high capacity for sustained transmission of COVID-19 (Table 1 and Fig. 1D). This finding aligns with other recent estimates of the reproductive number for this time period (6, 11–15). In addition, the median estimates for the latent and infectious periods are approximately 3.69 and 3.48 days, respectively. We also find that, during 10–23 January, only 14% (95% CI: 10–18%) of total infections in China were reported. This estimate reveals a very high rate of undocumented infections: 86%. This finding is independently corroborated by the infection rate among foreign nationals evacuated from Wuhan (see supplementary materials). These undocumented infections are estimated to have been half as contagious per individual as reported infections (μ = 0.55; 95% CI: 0.46–0.62). Other model fittings made using alternate values of Td and Seedmax or different distributional assumptions produced similar parameter estimates (figs. S18 to S22), as did estimations made using an alternate model structure with separate average infection periods for undocumented and documented infections (see supplementary methods, table S1). Further sensitivity testing indicated that α and μ are uniquely identifiable given the model structure and abundance of observations utilized (see supplementary methods and Fig. 1, E and F). In particular, Fig. 1F shows that the highest log-likelihood fittings are centered in the 95% CI estimates for α and μ and drop off with distance from the best fitting solution (α= 0.14 and μ = 0.55).
Using the best-fitting model (Table 1 and Fig. 1), we estimated 13,118 (95% CI: 2,974–23,435) total new COVID-19 infections (documented and undocumented combined) during 10–23 January in Wuhan city. Further, 86.2% (95% CI: 81.5%–89.8%) of all infections were infected from undocumented cases. Nationwide, the total number of infections during 10–23 January was 16,829 (95% CI: 3,797–30,271) with 86.2% (95% CI: 81.6%–89.8%) infected by undocumented cases.
Ruiyun Li1,*, Sen Pei2,*,†, Bin Chen3,*, Yimeng Song4, Tao Zhang5, Wan Yang6, Jeffrey Shaman2,†
Science 16 Mar 2020:
eabb3221
DOI: 10.1126/science.abb3221
Abstract
Estimation of the prevalence and contagiousness of undocumented novel coronavirus (SARS-CoV2) infections is critical for understanding the overall prevalence and pandemic potential of this disease. Here we use observations of reported infection within China, in conjunction with mobility data, a networked dynamic metapopulation model and Bayesian inference, to infer critical epidemiological characteristics associated with SARS-CoV2, including the fraction of undocumented infections and their contagiousness. We estimate 86% of all infections were undocumented (95% CI: [82%–90%]) prior to 23 January 2020 travel restrictions. Per person, the transmission rate of undocumented infections was 55% of documented infections ([46%–62%]), yet, due to their greater numbers, undocumented infections were the infection source for 79% of documented cases. These findings explain the rapid geographic spread of SARS-CoV2 and indicate containment of this virus will be particularly challenging.
The novel coronavirus that emerged in Wuhan, China (SARS-CoV2) at the end of 2019 quickly spread to all Chinese provinces and, as of 1 March 2020, to 58 other countries (1, 2). Efforts to contain the virus are ongoing; however, given the many uncertainties regarding pathogen transmissibility and virulence, the effectiveness of these efforts is unknown.
The fraction of undocumented but infectious cases is a critical epidemiological characteristic that modulates the pandemic potential of an emergent respiratory virus (3–6). These undocumented infections often experience mild, limited or no symptoms and hence go unrecognized, and, depending on their contagiousness and numbers, can expose a far greater portion of the population to virus than would otherwise occur. Here, to assess the full epidemic potential of SARS-CoV2, we use a model-inference framework to estimate the contagiousness and proportion of undocumented infections in China during the weeks before and after the shutdown of travel in and out of Wuhan.
We developed a mathematical model that simulates the spatiotemporal dynamics of infections among 375 Chinese cities (see supplementary materials). In the model, we divided infections into two classes: (i) documented infected individuals with symptoms severe enough to be confirmed, i.e., observed infections; and (ii) undocumented infected individuals. These two classes of infection have separate rates of transmission: β, the transmission rate due to documented infected individuals; and μβ, the transmission rate due to undocumented individuals, which is β reduced by a factor μ.
Spatial spread of SARS-CoV2 across cities is captured by the daily number of people traveling from city j to city i and a multiplicative factor. Specifically, daily numbers of travelers between 375 Chinese cities during the Spring Festival period (“Chunyun”) were derived from human mobility data collected by the Tencent Location-based Service during the 2018 Chunyun period (1 February–12 March 2018) (7). Chunyun is a period of 40 days—15 days before and 25 days after the Lunar New Year—during which there are high rates of travel within China. To estimate human mobility during the 2020 Chunyun period, which began 10 January, we aligned the 2018 Tencent data based on relative timing to the Spring Festival. For example, we used mobility data from 1 February 2018 to represent human movement on 10 January 2020, as these days were similarly distant from the Lunar New Year. During the 2018 Chunyun, a total of 1.73 billion travel events were captured in the Tencent data; whereas 2.97 billion trips are reported (7). To compensate for underreporting and reconcile these two numbers, a travel multiplicative factor, θ, which is greater than 1, is included (see supplementary materials).
To infer SARS-CoV2 transmission dynamics during the early stage of the outbreak, we simulated observations during 10–23 January 2020 (i.e., the period before the initiation of travel restrictions, fig. S1) using an iterated filter-ensemble adjustment Kalman filter (IF-EAKF) framework (8–10). With this combined model-inference system, we estimated the trajectories of four model state variables (Si, Ei, Iri, Iui: the susceptible, exposed, documented infected, and undocumented infected sub-populations in city i) for each of the 375 cities, while simultaneously inferring six model parameters (Z, D, μ, β, α, θ: the average latent period, the average duration of infection, the transmission reduction factor for undocumented infections, the transmission rate for documented infections; the fraction of documented infections, and the travel multiplicative factor).
Fig. 1 Best-fit model and sensitivity analysis.
Details of model initialization, including the initial seeding of exposed and undocumented infections, are provided in the supplementary materials. To account for delays in infection confirmation, we also defined a time-to-event observation model using a Gamma distribution (see supplementary materials). Specifically, for each new case in group Iri, a reporting delay td (in days) was generated from a Gamma distribution with a mean value of Td. In fitting both synthetic and the observed outbreaks, we performed simulations with the model-inference system using different fixed values of Td (6 days ≤ Td ≤ 10 days) and different maximum seeding, Seedmax (1500 ≤ Seedmax ≤ 2500) (see supplementary materials, fig. S2). The best fitting model-inference posterior was identified by log-likelihood.
We first tested the model-inference framework versus alternate model forms and using synthetic outbreaks generated by the model in free simulation. These tests verified the ability of the model-inference framework to accurately estimate all six target model parameters simultaneously (see supplementary methods and figs. S3 to S14). Indeed, the system could identify a variety of parameter combinations and distinguish outbreaks generated with high α and low μ from low α and high μ. This parameter identifiability is facilitated by the assimilation of observed case data from multiple (375) cities into the model-inference system and the incorporation of human movement in the mathematical model structure (see supplementary methods and figs. S15 and S16).
We next applied the model-inference framework to the observed outbreak before the travel restrictions of 23 January—a total of 801 documented cases throughout China, as reported by 8 February 2020 (1). Figure 1, A to C, shows simulations of reported cases generated using the best-fitting model parameter estimates. The distribution of these stochastic simulations captures the range of observed cases well. In addition, the best-fitting model captures the spread of infections with the novel coronavirus (COVID-19) to other cities in China (fig. S17). Our median estimate of the effective reproductive number, Re—equivalent to the basic reproductive number (R0) at the beginning of the epidemic—is 2.38 (95% CI: 2.04−2.77), indicating a high capacity for sustained transmission of COVID-19 (Table 1 and Fig. 1D). This finding aligns with other recent estimates of the reproductive number for this time period (6, 11–15). In addition, the median estimates for the latent and infectious periods are approximately 3.69 and 3.48 days, respectively. We also find that, during 10–23 January, only 14% (95% CI: 10–18%) of total infections in China were reported. This estimate reveals a very high rate of undocumented infections: 86%. This finding is independently corroborated by the infection rate among foreign nationals evacuated from Wuhan (see supplementary materials). These undocumented infections are estimated to have been half as contagious per individual as reported infections (μ = 0.55; 95% CI: 0.46–0.62). Other model fittings made using alternate values of Td and Seedmax or different distributional assumptions produced similar parameter estimates (figs. S18 to S22), as did estimations made using an alternate model structure with separate average infection periods for undocumented and documented infections (see supplementary methods, table S1). Further sensitivity testing indicated that α and μ are uniquely identifiable given the model structure and abundance of observations utilized (see supplementary methods and Fig. 1, E and F). In particular, Fig. 1F shows that the highest log-likelihood fittings are centered in the 95% CI estimates for α and μ and drop off with distance from the best fitting solution (α= 0.14 and μ = 0.55).
Using the best-fitting model (Table 1 and Fig. 1), we estimated 13,118 (95% CI: 2,974–23,435) total new COVID-19 infections (documented and undocumented combined) during 10–23 January in Wuhan city. Further, 86.2% (95% CI: 81.5%–89.8%) of all infections were infected from undocumented cases. Nationwide, the total number of infections during 10–23 January was 16,829 (95% CI: 3,797–30,271) with 86.2% (95% CI: 81.6%–89.8%) infected by undocumented cases.