Formulation and Solution of an Inverse Reliability Problem to Simulate the Dynamic Behavior of COVID-19 Pandemic

LOBATO, F. S.; PLATT, G. M.; LIBOTTE, G. B.; SILVA NETO, A. J.

doi:10.5540/tcam.2021.022.01.00091

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Articles • Trends Comput. Appl. Math. 22 (1) • Jan-Mar 2021 • https://doi.org/10.5540/tcam.2021.022.01.00091 copy

Formulation and Solution of an Inverse Reliability Problem to Simulate the Dynamic Behavior of COVID-19 Pandemic

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Different types of mathematical models have been used to predict the dynamic behavior of the novel coronavirus (COVID-19). Many of them involve the formulation and solution of inverse problems. This kind of problem is generally carried out by considering the model, the vector of design variables, and system parameters as deterministic values. In this contribution, a methodology based on a double loop iteration process and devoted to evaluate the influence of uncertainties on inverse problem is evaluated. The inner optimization loop is used to find the solution associated with the highest probability value, and the outer loop is the regular optimization loop used to determine the vector of design variables. For this task, we use an inverse reliability approach and Differential Evolution algorithm. For illustration purposes, the proposed methodology is applied to estimate the parameters of SIRD (Susceptible-Infectious-RecoveryDead) model associated with dynamic behavior of COVID-19 pandemic considering real data from China’s epidemic and uncertainties in the basic reproduction number (ℛ₀). The obtained results demonstrate, as expected, that the increase of reliability implies the increase of the objective function value.

Keywords:
inverse problem; reliability-based optimization; modeling; COVID-19

	Best	Average	Worst
β (Day⁻¹)	0.3686	0.3686	0.3686
γ (Day⁻¹)	2.3927×10⁻³	2.3924×10⁻³	2.3922×10⁻³
α (Day⁻¹)	7.5125×10⁻²	7.5124×10⁻²	7.5124×10⁻²
I _n0	2.7806×10⁻³	2.7806×10⁻³	2.7805×10⁻³
OF	0.8249	0.8249	0.8249

ℛ_0,ref	β(Day ⁻¹ )	γ(Day ⁻¹ )	α(Day ⁻¹ )	I _n0	OF
1	0.2649	1.8787×10⁻¹	7.7165×10⁻²	4.1938×10⁻³	17.2903
2	0.2253	3.5523×10⁻²	7.7164×10⁻²	2.1340×10⁻²	15.9483
3	0.2450	4.5079×10⁻³	7.6254×10⁻²	4.1302×10⁻³	9.5994
4	0.3193	2.6826×10⁻³	7.5835×10⁻²	2.8668×10⁻³	2.2746
5	0.3686	2.3927×10⁻³	7.5125×10⁻²	2.7806×10⁻³	0.8249

	Ω (Reliability), $cov = 0.05$ Normal			Ω (Reliability), $cov = 0.05$ LogNormal
	1 (84.14%)	2.5 (99.38%)	5 (99.99%)	1 (84.14%)	2.5 (99.38%)	5 (99.99%)
$μ_{β}^{*}$	0.3531	0.3189	0.2701	0.3531	0.3192	0.2717
$μ_{γ}^{*} \times 10^{3}$	2.4471	2.6955	3.6039	2.4470	2.6918	3.5374
$μ_{α}^{*} \times 10^{2}$	7.7165	7.7026	7.6974	7.7165	7.7023	7.6909
$I_{n 0} \times 10^{3}$	2.7272	2.8757	3.5146	2.7272	2.8732	3.4672
OF	0.9628	2.3019	6.6220	0.9624	2.2868	6.4338
	Ω (Reliability), $cov = 0.1$ Normal			Ω (Reliability), $cov = 0.1$ LogNormal
	1 (84.14%)	2.5 (99.38%)	5 (99.99%)	1 (84.14%)	2.5 (99.38%)	5 (99.99%)
$μ_{β}^{*}$	0.3299	0.2701	0.2265	0.3301	0.2718	0.2200
$μ_{γ}^{*} \times 10^{3}$	2.5911	3.6039	16.5553	2.5889	3.5335	12.2093
$μ_{α}^{*} \times 10^{2}$	7.7165	7.7165	7.7167	7.7162	7.7161	7.7159
$I_{n 0}^{*} \times 10^{3}$	2.8067	3.5146	12.5514	2.8052	3.4645	9.4883
OF	1.7090	6.6220	14.5111	1.6991	6.4181	14.1303

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[1] *Corresponding author: F. S. LOBATO - E-mail: fslobato@ufu.br