There are at least three errors in the manuscript, they are as follows:

- In the “Models with time-varying parameters” paragraph after equation (4), for the sentences

“εⁱ(t) describe the clustering of the population [39,40] but can also describe a reduction in the population due to voluntary avoidance behavior or social distancing. However due to the absence of structural identifiability properties [41, 42] it should be very difficult to estimate simultaneously both β(t) and εⁱ(t).”

“εⁱ(t)” must be replaced by “ε_i(t)” in accordance with the rest of the manuscript. Then these sentences become:

“ε_i(t) describe the clustering of the population [39,40] but can also describe a reduction in the population due to voluntary avoidance behavior or social distancing. However due to the absence of structural identifiability properties [41, 42] it should be very difficult to estimate simultaneously both β(t) and ε_i(t).”

- In the Fig 3 caption the equation of β(t) must be read as:

“β(t) = β₀.(1 + β₁ sin(2πt/365+2πϕ) + β₂ sin(2πt/(3 365)+2πϕ) + β₃ sin(2πt/(0.5 365)+2πϕ))

and not:

“β(t) = β₀.(1 + β₁ sin(2πt/365+2πϕ) + β₂ sin(2πt/(3 365)+2πϕ)) + β₃ sin(2πt/(0.5 365)+2πϕ))

- In the “SIRS model” paragraph after equation (5), the sentence

“Initially non-informative priors were used for the volatility σ, the reporting rate ρ and the initial conditions γ(0) by β(0) but to reduce problems linked to practical non-identifiability materialized by correlation between some estimates, informative priors were used for ρ (see S1 Fig).”

must be replaced (as in the uncorrected proofs) by:

“Initially non-informative priors were used for the volatility σ, the reporting rate ρ and the initial conditions (S(0), I(0), β(0)) to reduce problems linked to practical non-identifiability materialized by correlation between some estimates, informative priors were used for ρ (see S1 Fig).”