Generic probabilistic modelling and non-homogeneity issues for the UK epidemic of COVID-19

Anatoly Zhigljavsky; Jack Noonan

We assume that the person becomes infected τ days after catching the virus, where τ has Poisson distribution with mean of 1 week. To model the time to recover (or die) we use Erlang distribution with shape parameter k = 3 and rate parameter λ = 1/7 so that the mean of the distribution is k/λ = 1/σ = 21 (in simulations, we discretise the numbers to their nearest integers). This implies that we assume that the average longevity of the period of time while the infected person is contagious is 21 days, in line with the current knowledge, see e.g. [7, 8, 9] . Standard deviation of the chosen Erlang distribution is approximately 12, which is rather large and reflects the uncertainty we currently have about the period of time a person needs to recover (or die) from COVID-19. An increase in 1/σ would prolong the epidemic and smaller values of 1/σ would make it to cause people to be contagious for less time. The use of Erlang distribution is standard for modelling similar events in reliability and queuing theories, which have much in common with epidemiology. We have considered the sensitivity of the model in this study with respect to the choice of parameters λ and σ but more has to be done in cooperation with epidemiologists. As there are currently many outbreaks epidemics, new knowledge about the distribution of the period of infection by COVID-19 can emerge soon.