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Mapping 2019-nCoV
Mapping 2019-nCoV
Update January 26
Update January 26
Lancet Inf Dis Article
Lancet Article
public health

Update January 31: Modeling the Spreading Risk of 2019-nCoV

By Lauren Gardner, January 31, 2020

Collaborators

This work is being led by Lauren Gardner at Johns Hopkins University CSSE, in collaboration with Aleksa Zlojutro and David Rey at rCITI at UNSW Sydney, and Ensheng Dong at JHU CSSE. At JHU, we have previously developed an interactive dashboard mapping the outbreak in real-time, and written a blog.

Model Implementation

This work builds on our previous analysis posted on January 26. We implemented a previously published model that integrates both outbreak dynamics and outbreak control into a decision-support tool for mitigating infectious disease pandemics at the onset of an outbreak through border control to evaluate the 2019-nCoV epidemic. A stochastic metapopulation epidemic simulation tool is used to simulate global outbreak dynamics, and the border control mechanism considered is passenger screening upon arrival at airports (entry screening), which is used to identify infected or at-risk individuals. A detailed description of the model is provided at the end of this section.

Our metapopulation model is based on a global network of local, city-level, populations connected by edges representing passenger air travel between cities. At each node of the network, we locally model outbreak dynamics using a discrete-time Susceptible-Exposed-Infected-Recovered (SEIR) compartmental model. IATA monthly passenger travel volumes for all travel routes connecting airport pairs (including stopovers) is used to construct the weighted edges. The SEIR parameters are defined based on a 5-day incubation period, which aligns with an estimated incubation period of 5.2 days in a recent NEJM publication. The effective contact rate in our model corresponds to a reproductive number of 2, which aligns with an estimate from Imperial College London, reporting a  range between 1.5 and 3.5, and the recent NEJM publication, which estimated an average R0 of 2.2. We set the recovery period to five days. We assume initial cases of 2019-nCoV are only present in Wuhan, and no border control is accounted for. The model results presented are based on an average of 250 runs.

Results

The results presented in this analysis are based on the 100 total cases of 2019-nCoV reported outside of mainland China on January 29. Specifically, we estimate the expected number of cases in mainland China at the end of January, as well as the global distribution of the infected travelers.  

We believe the actual number of 2019-nCoV cases in mainland China are likely much higher than that reported to date. Specifically, we estimate there to be around 58,000 cumulative cases of 2019-nCoV in mainland China by the end of January (as of January 31, the reported cases is close to 12,000). This estimate is in line with our previous analysis on January 25, which estimated the proportion of reported to estimated cases to be close to 10%.  It is likely that part of this discrepancy is due to reporting delays. However, the substantially larger number of estimated cases suggest a majority of the cases may be mild (or asymptomatic), do not require seeking medical care, and thus are not reported. Furthermore, based on this analysis, we believe the outbreak began in November, and there were already hundreds of human cases of 2019-nCoV in Wuhan in early December. The estimated verses confirmed cases during January are presented in Figure 1.

Figure 1. Estimated vs. Reported Cases of 2019-nCoV cases globally.

In addition to inferring the current outbreak size, the model provides the expected number of (the 100) imported cases arriving at each airport globally (based on final travel destinations of travelers). By aggregating this over all airports in a country/region we can estimate the total number of imported cases in each country/region. The country level importation risk is illustrated in the map in Figure 2, with the darker shades equating to higher importation risk, and the red outline indicating the set of countries reporting cases as of January 31. 

Figure 2. Heatmap of Countries/regions with highest risk of imported 2019-nCoV cases, January 31

Figure 3 below reveals how our estimated number of imported cases arriving in each country/region compared with the actual number of reported 2019-nCoV cases in each country. The simulation results align with the number of air travel reported cases outside of mainland China during the emerging stage of the epidemic. As of January 31, 24 countries excluding mainland China have reported at least one travel related case, with the list of affected countries consistent with our ranking.  Some of the reported cases (represented by the orange bars) were locally acquired in their respective country/region (e.g., U.S., Germany, Japan, Vietnam), which partially explains the discrepancy with our travel related risk estimates.

Figure 3. List of Countries/regions with estimated number of imported cases vs. reported number of 2019-nCoV cases (as of Jan 31) . 

We further present the results at the airport level (based on their final travel destination), to identify the set of cities outside mainland China at highest risk of an outbreak. Figure 4 illustrates the set of cities within the U.S. at greatest risk of 2019-nCoV based on the expected number of arriving infected travelers at airports in the city, and the red outlines highlight the states that have already reported cases.  The set of at-risk airports outside mainland China are illustrated in Figures 5, with the primary risk posed to southeast Asia. Only a subset of U.S. airports are listed in the top 100 globally. These results are consistent with our previous analysis on January 25.  While many of these cities have already reported cases, they should be prepared for additional cases to be reported over the coming days, both in travelers whom departed Wuhan before the travel ban was implemented on January 23, and possibly through human to human transmission from infected travelers who arrived previously.

Figure 4. Map of highest risk U.S. cities based on likelihood of 2019-nCoV arriving travelers

Figure 5. Map of the airports at highest risk of 2019-nCoV arriving travelers outside mainland China.

Limitations

There are multiple modeling assumptions and limitations that should be noted regarding these estimates.

  • There is still uncertainty about the transmission of 2019-nCoV. The parameters for the reproductive number and incubation period chosen for this analysis align with the best estimates to date. There is less known about the duration of the recovery period, which may be longer than the five days specified in this analysis. More data will help us finer tune our estimates.
  • Transmission of infection from asymptomatic individuals during the incubation period, as was recently confirmed, is not considered in this analysis. It is therefore likely the number of reported cases outside of China will increase in the coming days, especially in those cities identified to be at highest risk in this analysis. 
  • The model only accounts for passenger air travel, and excludes mobility within and between cities via other modes of transport. Therefore, the spreading risk between regions connected via alternatives modes of travel is underestimated. This is most applicable to spread within China, which we are underestimating.
  • The SEIR parameters used to model the outbreak within each city are deterministic. However, the spread of infected travelers moving between cities is modeled stochastically.
  • Arrival passenger screening at airports and the complete air travel ban implemented in Wuhan on January 23 are not accounted for in this analysis. We are therefore likely overestimating the number of cases exported out of Wuhan during the last few days of our simulation. However, this is unlikely to impact the relative ranking of the destinations.
  • No local control mechanisms (prophylaxtics, vaccines, school closures, quarantine efforts) within cities are accounted for. Thus, the R0 is assumed to be constant over time, and across all locations. It is likely R0 is highly variable between locations, and lower than it was at the start of the outbreak, due to changes in individual’s behavior. Additionally, some higher R0 estimates based on the early stages of the outbreak are likely an overestimate at this point in time. For this same reason we may be overestimating the growth of the outbreak over the last week, and therefore overestimating total cases.
  • We are using 2015 Travel data, because that is the most recent complete (airport-to-airport) data we had available in the lab.

References:

Zlojutro, A, Rey, D and L Gardner*. (2019) “Optimizing border control policies for global outbreak mitigation”. Scientific Reports 9:2216. DOI https://doi.org/10.1038/s41598-019-38665-w (Open Source link) https://rdcu.be/bniOs

Many outpatient facilities with expensive resources, such as infusion and imaging centers, experience surge in their patient arrival at times and are under-utilization at other times. This pattern results in patient safety concerns, patient and staff dissatisfaction, and limitation in growth, among others. Scheduling practices is found to be one of the main contributors to this problem.

We developed a real-time scheduling framework to address the problem, specifically for infusion clinics. The algorithm assumes no knowledge of future appointments and does not change past appointments. Operational constraints are taken into account, and the algorithm can offer multiple choices to patients.

We generalize this framework to a new scheduling model and analyze its performance through competitive ratio. The resource utilization of the real-time algorithm is compared with an optimal algorithm, which knows the entire future. It can be proved that the competitive ratio of the scheduling algorithm is between 3/2 and 5/3 of an optimal algorithm.

This work was performed with the MIT/MGH Collaboration.

In many healthcare services, care is provided continuously, however, the care providers, e.g., doctors and nurses, work in shifts that are discrete. Hence, hand-offs between care providers is inevitable. Hand-offs are generally thought to effect patient care, although it is often hard to quantify the effects due to reverse causal effects between patients’ duration of stay and the number of hand-off events. We use a natural randomized control experiment, induced by physicians’ schedules, in teaching general medicine teams. We employ statistical tools to show that between the two randomly assigned groups of patients, a subset who experiences hand-off experience a different length of stay compared to the other group.

This work was performed with the MIT/MGH Collaboration.

Primary care is an important piece in the healthcare system that affects the downstream medical care of patients heavily. There are specific challenges in primary care as healthcare shifts from fee-for-service to population health management and medical home, focuses on cost savings and integrates quality measures. We consider the primary care unit at a large academic center that is facing similar challenges. In this work we focus on the imbalance in workload, which is a growing regulatory burden and directly concerns any staff in primary care. It can result in missed opportunities to deliver better patient care or providing a good work-environment for the physicians and the staff. We consider the primary care unit at the large academic center and focus on their challenge in balancing staff time with quality of care through a redesign of their system. We employ optimization models to reschedule providers’ sessions to improve the patient flow, and through that, a more balanced work-level for the support staff. 

This work was performed with the MIT/MGH Collaboration.

Perioperative services are one of the vital components of hospitals and any disruption in their operations can leave a downstream effect in the rest of the hospital. A large body of evidence links inefficiencies in perioperative throughput with adverse clinical outcomes. A regular delay in the operating room (OR), may lead to overcrowding in post-surgical units, and consequently, more overnight patients in the hospital. Conversely, an underutilization of OR is not only a waste of an expensive and high-demand resource, but it also means that other services who have a demand are not able to utilize OR. This mismatch in demand and utilization may, in turn, lead to hold-ups in the OR and cause further downstream utilization. We investigate the utilization of operating rooms by each service. The null hypothesis of this work is that the predicted utilization of the OR, i.e., the current block schedule, matches completely with the actual utilization of the service. We test this hypothesis for different utilization definitions, including physical and operational utilization and reject the null hypothesis. We further analyze why a mismatch may exist and how to optimize the schedule to improve patient flow in the hospital.

A set of female individuals with the above criteria were considered. Further demographic and diet considerations (in order to select similar patients) led to selecting 11 different individuals’ one day of intake as the initial dataset for the model. In another setting, we only considered people that have consumed a reasonable amount of sodium and water. We consider these two nutrients as the main constraints in the DASH diet. 



In order to compare different potential data and their performance with the model, we used different data groups from the NHANES database. A group of middle-aged women with certain similar characteristics and a group of people with certain attributes in their diets. In the first group, we did not consider how the individual’s daily diet is reflecting on the constraints that the forward problem had and we relied on their own personal answer to questions regarding hypertension and also how prone they thought they were to type-2 diabetes. The result was a sparse set of variables and an inconclusive optimal solution in regards to the preferences. In the second group, we tried to obtain sub-optimal data. We prioritized the maximum sodium intake constraint and the water intake constraints as our main and most important constraints.