Mechanistic-statistical SIR modelling for early estimation of the actual number of cases and mortality rate from COVID-19

Lionel Roques; Etienne Klein; Julien Papaix; Samuel Soubeyrand

with S the susceptible population, I the infected population, R the recovered population (immune individuals) and N = S + I + R the total population, supposed to be constant. The parameter α is the infection rate (to be estimated) and 1/β is the mean time until an infected becomes recovered. Based on the results in [12] , the median period of viral shedding is 20 days, but the infectiousness tends to decay before the end of this period: the results in [13] show that infectiousness starts from 2.5 days before symptom onset and declines within 7 days of illness onset. Based on these observations we assume here that 1/β = 10 days. The initial conditions are S(t 0 ) = N −1, I(t 0 ) = 1 and R(t 0 ) = 0, where N = 67 10 6 corresponds to the population size. The SIR model is started at some time t = t 0 , which will be estimated and should approach the date of introduction of the virus in France (this point is shortly discussed at the end of this paper). The ODE system (1) is solved thanks to a standard numerical algorithm, using Matlab ® ode45 solver.