Scenarios for the Spread of COVID-19 in Manaus, Northern Brazil

BITAR, SANDRO; STEINMETZ, WILHELM ALEXANDER

doi:10.1590/0001-3765202020200615

SANDRO BITAR

Departamento de Matemática, Universidade Federal do Amazonas, Av. General Rodrigo Octávio, 6200, 69080-900 Manaus, AM, Brazil

http://orcid.org/0000-0001-6971-2477

WILHELM ALEXANDER STEINMETZ

Departamento de Matemática, Universidade Federal do Amazonas, Av. General Rodrigo Octávio, 6200, 69080-900 Manaus, AM, Brazil

http://orcid.org/0000-0002-9314-4999

AUTHOR CONTRIBUTIONS

The two authors contributed equally to this work.

Figures (3)
Tables (4)

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Figure 1
Flow Chart.

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Figure 2
Controlling the contact rate – 120 days horizon.

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Figure 3
Controlling the isolation rate of infectious individuals – 120 days horizon.

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Model Parameters t t :: Time in days. \alpha α :: Rate of disease transmission (appropriate number of contacts per unit of time). \gamma γ :: Recovery rate of non-hospitalized individuals (refers to those who have recovered in some way without resorting to hospitals). \mu μ :: Natural mortality rate. \phi_1 ϕ 1 :: Mortality rate due to COVID-19. \phi_2 ϕ 2 :: Mortality rate due to COVID-19 for isolated individuals, e.g. those hospitalized. \rho ρ :: Recovery rate of isolated individuals. \eta η :: Isolation rate for infectious individuals. \Delta_1 Δ 1 :: Recruitment rate of new healthy individuals (involves birth rate). \Delta_2 Δ 2 :: Recruitment rate for new infectious individuals (people who arrive in Manaus and are infectious).

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Table I
Parameter Values.

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Table II
Social Distancing – number of cases (Day 0 = April 6^th, 2020).

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Table III
Collective Awareness – number of cases (Day 0 = April 6^th, 2020).

		Model Parameters
\(t\)	::	Time in days.
\(\alpha\)	::	Rate of disease transmission (appropriate number of contacts per unit of time).
\(\gamma\)	::	Recovery rate of non-hospitalized individuals (refers to those who have recovered in some way without resorting to hospitals).
\(\mu\)	::	Natural mortality rate.
\(\phi_1\)	::	Mortality rate due to COVID-19.
\(\phi_2\)	::	Mortality rate due to COVID-19 for isolated individuals, e.g. those hospitalized.
\(\rho\)	::	Recovery rate of isolated individuals.
\(\eta\)	::	Isolation rate for infectious individuals.
\(\Delta_1\)	::	Recruitment rate of new healthy individuals (involves birth rate).
\(\Delta_2\)	::	Recruitment rate for new infectious individuals (people who arrive in Manaus and are infectious).

Parameter	Value	Comments
\(\alpha\)	\(\zeta R_0 (\gamma+\mu)\)	We estimate \(R_0 = 3.7\), varying the parameter \(\zeta\) in the interval [0,1].
\(\mu\)	0.00445/365	Crude mortality rate in the State of Amazonas\(^{*}\)
\(\gamma\)	1/14.25	We estimate the average recovery time for non-hospitalized infectious patients at \(14.25\) days according to Chang et al. 2020CHANG D, MO G, YUAN X, TAO Y, PENG X, WANG F, XIE L, SHARMA L, CRUZ C & QIN E. 2020. Time Kinetics of Viral Clearance and Resolution of Symptoms in Novel Coronavirus Infection. Am J Respir Crit Care Med 201(9): doi:10.1164/rccm.202003-0524LE..
\(\phi_1\)	0.0034	see Worldometer 2020
\(\phi_2\)	(see text)
\(\rho\)	(see text)
\(\eta\)	0.14 \(\leq \eta \leq\) 1	This parameter is varied in the scenarios.
\(\Delta_1\)	0.002016/365	Crude natality rate in the State of Amazonas\(^{*}\)
\(\Delta_2\)	0	(see text)

Social Distancing
Horizon	None	Limited	Intermediate	Lockdown
15 days	25,00	17,000	9,000	5,000
30 days	> 50,000	> 50,000	30,000	9,000
60 days	> > 50,000	> > 50,000	> 50,000	26,000

Collective Awareness
Horizon	Basic	Intermediate	Raised
15 days	25,000	15,000	9,000
30 days	> 50,000	> 50,000	28,000
60 days	> > 50,000	> > 50,000	> 50,000

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Scenarios for the Spread of COVID-19 in Manaus, Northern Brazil

Abstract