The Sooner Strict Public Health Strategies are Applied the Lower the Peak of the Epidemic: the SARS-CoV-2 Case

VILLAVICENCIO-PULIDO, J. G.; BARRADAS, I.; SALDAÑA, F.; NILA LUÉVANO, C.

doi:10.5540/tcam.2023.024.03.00575

J. G. VILLAVICENCIO-PULIDO ^**Corresponding author: José Geiser Villavicencio Pulido - E-mail: j.villavicencio@correo.ler.uam.mx

Departamento de Ciencias Ambientales, Universidad Autónoma Metropolitana, Av. de las Garzas No. 10, C.P. 52005, Lerma de Villada, Estado de México, México - E-mail: j.villavicencio@correo.ler.uam.mx

https://orcid.org/0000-0003-1085-8556

I. BARRADAS

CIMAT. A.C., México - E-mail: barradas@cimat.mx

https://orcid.org/0000-0002-5973-9200

F. SALDAÑA

UNAM, México - E-mail: fernando.saldana@cimat.mx

https://orcid.org/0000-0003-0558-1169

C. NILA LUÉVANO

Independent researcher, México - E-mail: claudia.nila@gmail.com

https://orcid.org/0000-0002-9695-089X

*Corresponding author: José Geiser Villavicencio Pulido - E-mail: j.villavicencio@correo.ler.uam.mx

Variable	Variable description
S(t)	Susceptible individuals
S_c (t)	Cautious susceptible individuals
E(t)	Exposed/latent individuals
A(t)	Asymptomatic individuals
I(t)	Symptomatic individuals
D(t)	Diagnosed individuals being isolated and treated
R(t)	Recovered individuals
V(t)	SARS-CoV-2 in circulation in contaminated environments

Parameter	Parameter description
β _A	Asymptomatic infection rate
β _I	Symptomatic infection rate
β _V	Infection rate of hosts in a contaminated environment
σ	Transfer out rate of the exposed class
γ _A	Recovery rate of asymptomatic individuals
γ _I	Recovery rate of symptomatic individuals
µ	Induced-death rate of the disease
p	probability of one exposed individual becoming symptomatic
c ₁	Virus reproduction rate by asymptomatic individuals
c ₂	Virus reproduction rate by symptomatic individuals
µ _V	Natural mortality rate of virus circulating in the environment
α	Rate in which susceptible individuals become cautious susceptible individuals
θ	θ ∈ (0, 1) reduction factor of the infectious rate
d ₁	Diagnosis rate of exposed and asymptomatic individuals
d ₂	Diagnosis rate of symptomatic individuals
γ _D	Recovery rate of diagnosed individuals
m	Induced-death rate of virus due to cleaning measures in the environment
δ	δ ∈ (0, 1) fraction of susceptible individuals applying strict control strategies

Parameter	Value	Units	Source
σ	0.15325	day ⁻¹	¹1 J.A. Backer, D. Klinkenberg & J. Wallinga. Incubation period of 2019 novel coronavirus (2019-ncov) infections among travellers from wuhan, china. Euro Surveill, 25 (2020), 2000062.
γ _A	0.13978	day ⁻¹	²¹21 B. Tang, X. Wang, Q. Li, N.L. Bragazzi, S. Tang, Y. Xiao & J.W. J. Estimation of the Transmission Risk of the 2019-nCoV and Its Implication for Public Health Interventions. Journal of Clinical Medicine, 9 (2020).
γ _I	0.33029	day ⁻¹	²¹21 B. Tang, X. Wang, Q. Li, N.L. Bragazzi, S. Tang, Y. Xiao & J.W. J. Estimation of the Transmission Risk of the 2019-nCoV and Its Implication for Public Health Interventions. Journal of Clinical Medicine, 9 (2020).
γ _D	0.1162	day ⁻¹	²¹21 B. Tang, X. Wang, Q. Li, N.L. Bragazzi, S. Tang, Y. Xiao & J.W. J. Estimation of the Transmission Risk of the 2019-nCoV and Its Implication for Public Health Interventions. Journal of Clinical Medicine, 9 (2020).
µ	1.7826 × 10⁻⁵	day ⁻¹	²¹21 B. Tang, X. Wang, Q. Li, N.L. Bragazzi, S. Tang, Y. Xiao & J.W. J. Estimation of the Transmission Risk of the 2019-nCoV and Its Implication for Public Health Interventions. Journal of Clinical Medicine, 9 (2020).
p	0.868343	dimensionless	²¹21 B. Tang, X. Wang, Q. Li, N.L. Bragazzi, S. Tang, Y. Xiao & J.W. J. Estimation of the Transmission Risk of the 2019-nCoV and Its Implication for Public Health Interventions. Journal of Clinical Medicine, 9 (2020).
µ _V	1	day ⁻¹	¹²12 G. Kampf, D. Tpdt, S. Pfaender & E. Steinmann. Persistence of coronavirus on inanimate surfaces and its inactivation with biocidal agents. Journal of Hospital Infection, 104 (2020), 246-251.

Parameter	MAP estimate	Posterior mean	95% credible interval
β _A	0.0011449235	0.0011419836	(4.48 × 10⁻⁵ , 0.071054381)
β _I	0.020927934	0.107460168	(0.008764924, 0.290194056)
β _V	2.70 × 10⁻⁶	2.84 × 10⁻⁶	(2.63 × 10⁻⁶ , 2.92 × 10⁻⁶)
c ₁	0.000898382	0.00230416	(0.0001092413, 0.003184447)
c ₂	0.001474126	0.000821253	(0.000324343, 0.001658102)

	d ₁	d ₂	θ	m	δ
Case A)	[0.0,0.0505]	[0.0,0.505]	[0,0.5]	[0.0,1]	(0, 1)
Case B)	[0.0,0.0505]	[0.0,0.505]	[0.5,1]	[0.0,1]	(0, 1)
Case C)	[0.0,0.0505]	[0.0,0.505]	[0,0.5]	[0.0,10]	(0, 1)
Case D)	[0.0,0.0505]	[0.0,0.505]	[0.5,1]	[0.0,10]	(0, 1)
Case E)	[0.0,0.0505]	[0.0,0.505]	[0.8,1]	[0.0,0.156]	(0, 1)
Case F)	[0.0,0.2]	[0.0,0.505]	[0.8,1]	[0.0,0.156]	(0, 1)

\begin{array}{lcl} \dot{S} & = & - \frac{(β_{A} A + β_{I} I)}{N - D - δ S_{c}} S - β_{V} V S - α S, \\ \dot{S_{c}} & = & - \frac{(β_{A} A + β_{I} I)}{N - D - δ S_{c}} θ S_{c} - β_{V} θ V S_{c} + α S, \\ \dot{E} & = & \frac{(β_{A} A + β_{I} I)}{N - D - δ S_{c}} (S + θ S_{c}) + β_{V} V S + β_{V} θ V S_{c} - σ E - d_{1} E, \\ \dot{A} & = & (1 - p) σ E - d_{1} A - γ_{A} A, \\ \dot{I} & = & p σ E - d_{2} I - γ_{I} I - μ I, \\ \dot{D} & = & d_{1} (E + A) + d_{2} I - γ_{D} D - μ D, \\ \dot{R} & = & γ_{A} A + γ_{I} I + γ_{D} D, \\ \dot{V} & = & c_{1} A + c_{2} I - (μ_{V} + m) V . \end{array}

\begin{matrix} \begin{array}{l} \dot{S} & = & - \frac{β_{A} S A + β_{I} S I}{N} - β_{V} S V, \end{array} \\ \begin{array}{l} \dot{E} & = & \frac{β_{A} S A + β_{I} S I}{N} + β_{V} S V - σ E, \end{array} \\ \begin{array}{l} \dot{A} & = & (1 - p) σ E - γ_{A} A, \end{array} \\ \begin{array}{l} \dot{I} & = & p σ E - γ_{I} I - μ I, \end{array} \\ \begin{array}{l} \dot{R} & = & γ_{A} A + γ_{I} I, \end{array} \\ \begin{array}{l} \dot{V} & = & c_{1} A + c_{2} I - μ_{V} V . \end{array} \end{matrix}

\begin{array}{lcl} β_{A} & ~ & Γ (1, 10^{7}) \\ β_{I} & ~ & Γ (1, 10^{7}) \\ β_{V} & ~ & Γ (1, 10^{7}) \\ c_{1} & ~ & Γ (\frac{121}{24}, \frac{11}{24}) \\ c_{2} & ~ & Γ (\frac{121}{24}, \frac{11}{24}) \\ κ^{2} & ~ & Γ (1, 10^{2}) \end{array}

[1] *Corresponding author: José Geiser Villavicencio Pulido - E-mail: j.villavicencio@correo.ler.uam.mx

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The Sooner Strict Public Health Strategies are Applied the Lower the Peak of the Epidemic: the SARS-CoV-2 Case

ABSTRACT