Coronavirus projection models

The impact of Covid-19 on our lives has been profound and unprecedented both socially and economically. As more countries implement implement social distancing, now a  one-third of the world’s population is in lockdown grinding economies of countries to halt and presenting the most serious threat to the world economy since Great Depression.  The cost on human lives is even more immense ; around 1.2 million people have been tested positive worldwide with more than 10 countries reporting more than 1000 deaths while in total 67,249 lives have been lost as of April 5th. The healthcare infrastructure of countries in Europe and in US are getting stretched to the limits and will soon cause a surge in death rates in coming weeks as the new cases exceeds the present hospitalization capacity in the countries. In these dark and uncertain times, the one glimmer of positive trend is that data and statistical models are now in focus as governments like the White House in US and UK are using them to make decisions on policy measures. However as always with models we need to be cautious in relying on a single number since the models are not snapshots of the future but are projecting a wide range of possibilities dependent on the extent and pace of the future social and policy actions and we need to be aware of these limitations inherent in the models.

On March 31st, the White House offered details of the models used to predict that around 200,000 lives could be lost in the US. The White House co-coordinator Dr. Deborah Brix mentioned that the figure came from combining projections from a model built by the Imperial College London published on March 16th with other models from leading epidemiology teams around the world. The projections from the paper from Imperial College by noted epidemiologist Neil Ferguson aligns with the upper bound of the graph below and predicts that there will be around 2.2 million deaths in average in US. Another paper published by the Institute for Health Metrics and Evaluation (IHME) projects total deaths averaging around 81,000 and aligns with the lower bound of the graph below.  The middle range is between 100,000 to 240,000 deaths in the US and is the basis for the 200,000 deaths being projected by the White House however we need to take caution in using a single number as it is the average of a wide range of projections.

The projections of model built by IHME estimate 81,000 deaths in a base case over next 4 months and the projections are updated daily on their website as new data becomes available but have certain technical and policy assumptions and the key one’s are the following with more details in their published paper;

  • most state level social distancing announced by the states in the US remain in effect until first week of Aug
  • social distancing measure are being  vigorously enforced and are fully complied 
  • excess demand for health system resources will be addressed based on new policy measures
  • in terms of technical specification, model assumes that the death rate at each location (state) follows a Gaussian error distribution which is parametrized with 3 parameters which are location-specific (i) ultimate level or maximum death level in each location dependent on weeks since social distancing was implemented (ii) speed of reaching inflection point when death rate is maximum and (iii) time at which rate of death is maximum

In contrast, the model used by Imperial College assumes a Gamma distribution to model variability in severity of  individual infectiousness and fits the data from Wuhan, China and from Italy to come up with a baseline of 2.4 new infections for each positive case (with a range of 2 to 2.6). Without any intervention, the model projects that 81% of the US population will be affected and deaths will be on average around 2.2 million and will peak after 3 months. Other assumptions in the model which account for variability in projections include;

  • infection in each country grows at an exponential growth rate with doubling time of 5 days
  • two-thirds of the cases are identifiable (symptomatic) and rest do not show symptoms (asymptomatic)
  • symptomatic cases are 50% more infectious

The outlook remains grim for the next few months and in these times we are all looking for a simple answer and a precise confirmation however the reality is that there is a range of outcomes with probabilities dependent on how strict are the social distancing norms and how fast are effective policy measures being implemented to address the healthcare infrastructure shortages. The next few weeks will show us whether we will hit the average projections by flattening the curve or not?

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