Case studies and reports
- Paper: Characterizing the spread of CoViD-19, D. Karlen, July 13, 2020.
- introduces the pypm framework and describes methods to define comparitive statistics with weak model dependence and estimate their uncertainties
- Presentation: Characterizing the spread of CoViD-19, D. Karlen, June 22, 2020.
- presentation at the CAIMS-PIMS Coronavirus Modelling Conference
Click on the titles below to see detailed results from the studies.
November 25, 2020: BC by health region
The BC government makes available the number of cases each day, divided into sex, age, and health region. The data differs somewhat from that used in the Canada-wide studies, possibly due to corrections in the dates assigned to each positive case.
The province saw COVID-19 growth in all regions, in October, with the strongest growth in the two Vancouver health regons. At the beginning of November, new restrictions came into force in Vancouver, and the data now shows a decline in cases - with more data, the daily growth (decline) will be better estimated.
November 25, 2020: 9 provinces
This is an update of the previous provincial analysis, now using data from March 1 - November 24.
To characterize the observed case histories, it is necessary to include the following transitory effects:
- changes to transmission rate: most notably starting in mid-March. For most provinces this is described sufficiently by a single transition
- outbreaks: in Alberta and Saskatchewan large outbreaks have occured. These are accounted for by injecting batches of new infections, sufficient to account for the effect observed in the case data
- reporting anomalies: Quebec released a large number of cases due to a backlog, and BC reported a change in test reporting policy on April 21. These are accounted for by injecting batches of additional positive test results.
The agreement between the model and the provincial case data is good, considering the relatively small number of parameters used. Click on the link above to see the results.
November 22, 2020: USA by state
This is a analysis that uses data on hospitalizations recently made available by the US HHS. Prior to this analysis, hospitalization data from the Covid Tracking Project has been used.
November 15, 2020: USA by state
This is the latest analysis prepared for the COVID-19 Forecast Hub, in coordination with the US CDC.
Most states are showing rapid growth in cases and hospitalizations. A summary of total US cases and deaths is shown along with a forecast that assumes no change to current practice.
Click on the above image to see a time lapse animation of how COVID-19 spread through the USA. The colors indicate the fraction of the population in each state who are contagious. The scale is logrithmic: a difference of 1 unit corresponds to a factor of 10 in the contagious fraction. The above still image is the snapshot for November 15.
October 5, 2020: California by age
California provides daily case, hospitalization, and death data by age group. This provides useful data to study how to model a non-homogenous population.
June 25, 2020: 13 German states
This study was used to demonstrate the methods to characterize the spread of CoViD-19 in the paper shown at the top of this page. Data from 13 states that reported at lease 2000 cases by the end of June 2020 were included. This is an excellent sample for confirming the statistical treatment, since all the states were subject to the same public health measures and testing policies. For more information about the findings, please refer to the paper.
June 24, 2020: Brazil states
An initial study of Brazil data: fitting to death data only.
Possible future studies
Reporting noise, due to the process by which reports are collected, greatly affect the variation seen in daily case numbers. These have strong negative correlation between neighboring days (as missed reports and included in the subsequent day’s reports). A simple model for reporting noise is included in
pyPM.ca, with a single parameter. Tests of the reporting noise model will be shown.
Negative binomial parameter: It is common to not treat infections as independent events (which would lead to treating the number of cases on a day as an outcome of a Poisson random variable). Instead, it is common to use a negative binomial distribution. The choice of the single additional parameter is studied.
Projections for growth resulting from relaxation of social distancing. Choose some modified transmission rates, show the expectations, and consider how much time is required to detect changes for a given significance.
Consider the effect of contact tracing (included in reference model 2.)