Mathematical models provide a quantitative framework with which scientists can assess hypotheses on the potential underlying mechanisms that explain patterns in observed data at different spatial and ...temporal scales, generate estimates of key kinetic parameters, assess the impact of interventions, optimize the impact of control strategies, and generate forecasts. We review and illustrate a simple data assimilation framework for calibrating mathematical models based on ordinary differential equation models using time series data describing the temporal progression of case counts relating, for instance, to population growth or infectious disease transmission dynamics. In contrast to Bayesian estimation approaches that always raise the question of how to set priors for the parameters, this frequentist approach relies on modeling the error structure in the data. We discuss issues related to parameter identifiability, uncertainty quantification and propagation as well as model performance and forecasts along examples based on phenomenological and mechanistic models parameterized using simulated and real datasets.
Since December 2019, when the first case of coronavirus disease (COVID-19) was identified in the city of Wuhan in the Hubei Province of China, the epidemic has generated tens of thousands of cases ...throughout China. As of February 28, 2020, the cumulative number of reported deaths in China was 2,858. We estimated the time-delay adjusted risk for death from COVID-19 in Wuhan, as well as for China excluding Wuhan, to assess the severity of the epidemic in the country. Our estimates of the risk for death in Wuhan reached values as high as 12% in the epicenter of the epidemic and ≈1% in other, more mildly affected areas. The elevated death risk estimates are probably associated with a breakdown of the healthcare system, indicating that enhanced public health interventions, including social distancing and movement restrictions, should be implemented to bring the COVID-19 epidemic under control.
On 5 February 2020, in Yokohama, Japan, a cruise ship hosting 3,711 people underwent a 2-week quarantine after a former passenger was found with COVID-19 post-disembarking. As at 20 February, 634 ...persons on board tested positive for the causative virus. We conducted statistical modelling to derive the delay-adjusted asymptomatic proportion of infections, along with the infections' timeline. The estimated asymptomatic proportion was 17.9% (95% credible interval (CrI): 15.5-20.2%). Most infections occurred before the quarantine start.
On March 13, 2020, President Donald Trump declared a national emergency to combat the spread of COVID-19 in the USA, which led to a range of social distancing interventions across the country, ...including closures of schools, bars, cinemas, and restaurants, cancellation of large public gatherings, including cultural and sporting events, and discouraging gatherings of more than 50 people. ...an increasing number of businesses and companies have asked their employees to work remotely. During the influenza 2009 A/H1N1 pandemic, the implementation of social distancing interventions, including nationwide school closures and cancellation of public gatherings, was associated with a 30% reduction in the transmission rate.10 However, it increased after the mandatory school suspension resumed and before summer vacation started.10 Given the uncertainties surrounding the extent of the COVID-19 pandemic across the country, efforts to sustain online learning and remote working in combination with enhanced infection control measures in health-care settings and nursing homes could aid in mitigating the spread of the virus and gaining control of the epidemic's chains of transmission. Perhaps the most reasonable scenario ahead of us is that the transmission rate will decline during the next few months, partly driven by social distancing measures, a scenario that is reminiscent of the influenza 2009 A/H1N1 pandemic.10 Close monitoring of the transmission potential of the virus on the basis of reliable and publicly available data in near real-time will be key to short-term forecasts and sound public health decisions.
The complex and unprecedented Ebola epidemic ongoing in West Africa has highlighted the need to review the epidemiological characteristics of Ebola Virus Disease (EVD) as well as our current ...understanding of the transmission dynamics and the effect of control interventions against Ebola transmission. Here we review key epidemiological data from past Ebola outbreaks and carry out a comparative review of mathematical models of the spread and control of Ebola in the context of past outbreaks and the ongoing epidemic in West Africa. We show that mathematical modeling offers useful insights into the risk of a major epidemic of EVD and the assessment of the impact of basic public health measures on disease spread. We also discuss the critical need to collect detailed epidemiological data in real-time during the course of an ongoing epidemic, carry out further studies to estimate the effectiveness of interventions during past outbreaks and the ongoing epidemic, and develop large-scale modeling studies to study the spread and control of viral hemorrhagic fevers in the context of the highly heterogeneous economic reality of African countries.
•COVID-19 caused 6284 cases and 42 deaths in South Korea as of March 6, 2020.•The mean reproduction number Rt of COVID-19 in Korea was estimated at 1.5.•The crude case fatality rate is higher among ...males and increases with age.•Sustained disease transmission of COVID-19 in the region is suggested.•Our estimates support the implementation of social distancing measures in Korea.
Since the first case of 2019 novel coronavirus (COVID-19) identified on Jan 20, 2020, in South Korea, the number of cases rapidly increased, resulting in 6284 cases including 42 deaths as of Mar 6, 2020. To examine the growth rate of the outbreak, we present the first study to report the reproduction number of COVID-19 in South Korea.
The daily confirmed cases of COVID-19 in South Korea were extracted from publicly available sources. By using the empirical reporting delay distribution and simulating the generalized growth model, we estimated the effective reproduction number based on the discretized probability distribution of the generation interval.
We identified four major clusters and estimated the reproduction number at 1.5 (95% CI: 1.4–1.6). In addition, the intrinsic growth rate was estimated at 0.6 (95% CI: 0.6, 0.7), and the scaling of growth parameter was estimated at 0.8 (95% CI: 0.7, 0.8), indicating sub-exponential growth dynamics of COVID-19. The crude case fatality rate is higher among males (1.1%) compared to females (0.4%) and increases with older age.
Our results indicate an early sustained transmission of COVID-19 in South Korea and support the implementation of social distancing measures to rapidly control the outbreak.
COVID-19 vaccines have been authorized in multiple countries, and more are under rapid development. Careful design of a vaccine prioritization strategy across sociodemographic groups is a crucial ...public policy challenge given that 1) vaccine supply will be constrained for the first several months of the vaccination campaign, 2) there are stark differences in transmission and severity of impacts from severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) across groups, and 3) SARS-CoV-2 differs markedly from previous pandemic viruses. We assess the optimal allocation of a limited vaccine supply in the United States across groups differentiated by age and essential worker status, which constrains opportunities for social distancing. We model transmission dynamics using a compartmental model parameterized to capture current understanding of the epidemiological characteristics of COVID-19, including key sources of group heterogeneity (susceptibility, severity, and contact rates). We investigate three alternative policy objectives (minimizing infections, years of life lost, or deaths) and model a dynamic strategy that evolves with the population epidemiological status. We find that this temporal flexibility contributes substantially to public health goals. Older essential workers are typically targeted first. However, depending on the objective, younger essential workers are prioritized to control spread or seniors to directly control mortality. When the objective is minimizing deaths, relative to an untargeted approach, prioritization averts deaths on a range between 20,000 (when nonpharmaceutical interventions are strong) and 300,000 (when these interventions are weak). We illustrate how optimal prioritization is sensitive to several factors, most notably, vaccine effectiveness and supply, rate of transmission, and the magnitude of initial infections.
Simple phenomenological growth models can be useful for estimating transmission parameters and forecasting epidemic trajectories. However, most existing phenomenological growth models only support ...single-peak outbreak dynamics whereas real epidemics often display more complex transmission trajectories.
We develop and apply a novel sub-epidemic modeling framework that supports a diversity of epidemic trajectories including stable incidence patterns with sustained or damped oscillations to better understand and forecast epidemic outbreaks. We describe how to forecast an epidemic based on the premise that the observed coarse-scale incidence can be decomposed into overlapping sub-epidemics at finer scales. We evaluate our modeling framework using three outbreak datasets: Severe Acute Respiratory Syndrome (SARS) in Singapore, plague in Madagascar, and the ongoing Ebola outbreak in the Democratic Republic of Congo (DRC) and four performance metrics.
The sub-epidemic wave model outperforms simpler growth models in short-term forecasts based on performance metrics that account for the uncertainty of the predictions namely the mean interval score (MIS) and the coverage of the 95% prediction interval. For example, we demonstrate how the sub-epidemic wave model successfully captures the 2-peak pattern of the SARS outbreak in Singapore. Moreover, in short-term sequential forecasts, the sub-epidemic model was able to forecast the second surge in case incidence for this outbreak, which was not possible using the simple growth models. Furthermore, our findings support the view that the national incidence curve of the Ebola epidemic in DRC follows a stable incidence pattern with periodic behavior that can be decomposed into overlapping sub-epidemics.
Our findings highlight how overlapping sub-epidemics can capture complex epidemic dynamics, including oscillatory behavior in the trajectory of the epidemic wave. This observation has significant implications for interpreting apparent noise in incidence data where the oscillations could be dismissed as a result of overdispersion, rather than an intrinsic part of the epidemic dynamics. Unless the oscillations are appropriately modeled, they could also give a false positive, or negative, impression of the impact from public health interventions. These preliminary results using sub-epidemic models can help guide future efforts to better understand the heterogenous spatial and social factors shaping sub-epidemic patterns for other infectious diseases.
There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. ...The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014–2015 Ebola epidemic in West Africa.
•We review recent progress on characterizing early epidemic growth patterns.•We survey mathematical approaches for modeling early epidemic growth.•The standard SIR model can incorporate flexible early epidemic growth profiles.
Since the first cluster of cases was identified in Wuhan City, China, in December 2019, coronavirus disease 2019 (COVID-19) rapidly spreads globally. Scientists have made strides in estimating key ...transmission and epidemiological parameters. In particular, accumulating evidence points to a substantial fraction of asymptomatic or subclinical infections, which influences our understanding of the transmission potential and severity of this emerging disease. In this study, we derive estimates of the transmissibility and virulence of COVID-19 in Wuhan City, China, by reconstructing the underlying transmission dynamics using multiple data sources.
We employ statistical methods and publicly available epidemiological datasets to jointly derive estimates of transmissibility and severity associated with the novel coronavirus. For this purpose, the daily series of laboratory-confirmed COVID-19 cases and deaths in Wuhan City together with epidemiological data of Japanese repatriated from Wuhan City on board government-chartered flights were integrated into our analysis.
Our posterior estimates of basic reproduction number (R) in Wuhan City, China, in 2019-2020 reached values at 3.49 (95% CrI 3.39-3.62) with a mean serial interval of 6.0 days, and the enhanced public health intervention after January 23 in 2020 was associated with a significantly reduced R at 0.84 (95% CrI 0.81-0.88), with the total number of infections (i.e., cumulative infections) estimated at 1,906,634 (95% CrI 1,373,500-2,651,124) in Wuhan City, elevating the overall proportion of infected individuals to 19.1% (95% CrI 13.5-26.6%). We also estimated the most recent crude infection fatality ratio (IFR) and time-delay adjusted IFR at 0.04% (95% CrI 0.03-0.06%) and 0.12% (95% CrI 0.08-0.17%), respectively, estimates that are substantially smaller than the crude CFR estimated at 4.06%.
We have estimated key epidemiological parameters of the transmissibility and virulence of COVID-19 in Wuhan, China, during January-February 2020 using an ecological modeling approach that is suitable to infer epidemiological parameters with quantified uncertainty from partial observations collected by surveillance systems. Our estimate of time-delay adjusted IFR falls in the range of the median IFR estimates based on multiple serological studies conducted in several areas of the world.
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