Actuarial pricing, capital modelling and reserving

Pricing Squad


Issue 34 -- April 2020

Welcome back to Pricing Squad

Pricing Squad is the newsletter for fellow pricing practitioners and actuaries in general insurance.

Today's issue is about COVID-19.


Keeping calm about COVID-19

Cases reported

You should probably pay no attention to the reported number of Corona cases. It depends more on the number of tests administered than on the actual number of people who have had the virus. Because many infected people go untested, the error in the reported number of cases is enormous. Garbage in garbage out.

Deaths reported

The reported number of COVID-19 deaths is the upper bound, not an unbiased estimate. All people, and especially the elderly, have multiple viruses in their bodies but death will always be attributed to COVID-19 as long as one of them is COVID-19.

Putting that aside, Corona / COVID-19 death toll in Italy reached 10k last night (28th March 2020).

For comparison, here are influenza related deaths in Italy and England in recent winter seasons (mid October - mid April):

SeasonItalyEngland
2013/147,027
2014/1520,25925,143
2015/1615,8019,459
2016/1724,98115,167

So Corona so far has not even matched a normal flu season in Italy.

Total annual number of deaths in Italy from all causes is approx. 400k.

What's next for Italy

Epidemics explode initially when there are many people available to be infected. Then the growth plateaus. Finally the growth slows down as there are few new uninfected people in the population.

For mathematical minds, virus saturation is 0 < f(x) < L. The differential equation is df(x)/dx = f(x)(1-f(x)). The solution is a logistic function f(x) = L/(1+exp(-k(x-x0)).

It seems that Italy has reached a plateau of the daily death toll increase so we now probably have enough data to estimate the parameters of the Italian saturation function. Below is my take on it.

L = final death toll = 15,480 (approx).

References:

  • Aldo Rosano et. al., "Investigating the impact of influenza on excess mortality in all ages in Italy during recent seasons (2013/14–2016/17 seasons)"
  • Public Health England, "Surveillance of influenza and other respiratory viruses in the UK Winter 2018 to 2019"


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