Table 1 Parameters used in the model for the State of São Paulo and Brazil

\(\beta (t)\)

Potentially infective contact rate

Fitted (changes over time)

\(p_{E}\)

Infectivity of exposed individuals

0.4^a

0.4^a

\(p_{I}\)

Infectivity of symptomatic individuals

1.0^a

1.0^a

\(p_{A}\)

Infectivity of asymptomatic individuals

1/3^a

1/3^a

\(p_{H}\)

Infectivity of hospitalized individuals

0.01^a

0.01^a

\(p_{G}\)

Infectivity of ICU patients

0.01^a

0.01^a

\(\mu\)

Natural mortality rate (life expectancy of 70 years)

3.91 × 10^–5 days^{−1 a}

3.91 × 10^–5 days^{−1 a}

\(\delta_{I}\)

Rate of evolution from exposed to infected

1/2 day^{−1 a}

1/2 day^{−1 a}

\(\delta_{A}\)

Rate of evolution from exposed to asymptomatic

0.874 day^{−1 b}

0.366 day^{−1 b}

\(\gamma_{I}\)

Rate of recovery from infected

1/3 day^{−1 a}

1/3 day^{−1 a}

\(\gamma_{A}\)

Rate of recovery from asymptomatic

1/14 day^{−1 a}

1/14 day^{−1 a}

\(\gamma_{H}\)

Rate of recovery from hospitalized

1/10 day^{−1 a}

1/10 day^{−1 a}

\(\gamma_{G}\)

Rate of recovery from ICU

0.05 day^{−1 b}

0.0556 day^{−1 b}

\(\alpha_{I}\)

Disease-induced mortality rate for infected individuals

5 × 10^–4 day^{−1 a}

3 × 10^–4 day^{−1 a}

\(\alpha_{A}\)

Disease-induced mortality rate for asymptomatic individuals

0 ^a

0 ^a

\(\alpha_{H}\)

Disease-induced mortality rate for hospitalized individuals

10^–4 day^{−1 b}

5.56 × 10^–4 day^{−1 b}

\(\alpha_{G}\)

Disease-induced mortality rate for ICU patients

Fitted (changes over time)

\(\sigma_{H}\)

Hospitalization rate

0.12 day^{−1 b}

0.0518 day^{−1 b}

\(\sigma_{G}\)

ICU admission rate

Fitted (changes over time)

\(\nu\)

Vaccination rate

Variable (from 5 × 10^–3 days⁻¹ to 10^–1 days⁻¹)

\(q\)

Vaccination efficacy

Variable

\(w\)

Adherence to the vaccination campaign

Variable

\(K(t)\)

Notification ratio

Fitted (changes over time)

\(\Lambda (t)\)

Birth rate

Changes over time