Identification of an Epidemiological Model to Simulate the COVID-19 Epidemic Using Robust Multiobjective Optimization and Stochastic Fractal Search

Traditionally, the identification of parameters in the formulation and solution of inverse problems considers that models, variables, and mathematical parameters are free of uncertainties. This aspect simplifies the estimation process, but does not consider the influence of relatively small changes in the design variables in terms of the objective function. In this work, the SIDR (Susceptible, Infected, Dead, and Recovered) model is used to simulate the dynamic behavior of the novel coronavirus disease (COVID-19), and its parameters are estimated by formulating a robust inverse problem, that is, considering the sensitivity of design variables. For this purpose, a robust multiobjective optimization problem is formulated, considering the minimization of uncertainties associated with the estimation process and the maximization of the robustness parameter. To solve this problem, the Multiobjective Stochastic Fractal Search algorithm is associated with the Effective Mean concept for the evaluation of robustness. The results obtained considering real data of the epidemic in China demonstrate that the evaluation of the sensitivity of the design variables can provide more reliable results.

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

Trends in Computational and Applied Mathematics ◽

10.5540/tcam.2021.022.01.00091 ◽

2021 ◽

Vol 22 (1) ◽

pp. 91-107

Author(s):

F. S. Lobato ◽

G. M. Platt ◽

G. B. Libotte ◽

A. J. Silva Neto

Keyword(s):

Dynamic Behavior ◽

Differential Evolution Algorithm ◽

Iteration Process ◽

Real Data ◽

The Novel ◽

Design Variables ◽

Different Types ◽

Evolution Algorithm ◽

Novel Coronavirus ◽

Optimization Loop

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-Recovery-Dead) 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.

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A penalty-guided fractal search algorithm for reliability–redundancy allocation problems with cold-standby strategy

Proceedings of the Institution of Mechanical Engineers Part O Journal of Risk and Reliability ◽

10.1177/1748006x19825707 ◽

2019 ◽

Vol 233 (5) ◽

pp. 775-790

Author(s):

Mohammad N Juybari ◽

Mostafa Abouei Ardakan ◽

Hamed Davari-Ardakani

Keyword(s):

System Reliability ◽

Optimization Problem ◽

Search Algorithm ◽

Population Based ◽

Benchmark Problems ◽

Redundancy Allocation ◽

Cold Standby ◽

System Reliability Optimization ◽

Stochastic Fractal Search Algorithm ◽

Stochastic Fractal Search

This article addresses the system reliability optimization problem as reliability–redundancy allocation problem, aiming to maximize the system reliability through a trade-off between redundancy levels and the reliability of the components. In this study, cold-standby strategy has been considered for the redundant components, and a population-based meta-heuristic algorithm, called stochastic fractal search, is applied to solve different benchmark problems. Using the proposed stochastic fractal search algorithm, all the benchmark problems are improved and new structures with higher reliability values have been found. The experimental results reveal the superiority of the proposed stochastic fractal search algorithm in terms of quality and robustness of the solutions in cold-standby redundancy case compared to all previous studies.

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Modeling and Forecasting of COVID-19 Spreading by Delayed Stochastic Differential Equations

Axioms ◽

10.3390/axioms10010018 ◽

2021 ◽

Vol 10 (1) ◽

pp. 18

Author(s):

Marouane Mahrouf ◽

Adnane Boukhouima ◽

Houssine Zine ◽

El Mehdi Lotfi ◽

Delfim F. M. Torres ◽

...

Keyword(s):

Real Data ◽

Economic Damage ◽

Population Parameter ◽

The Novel ◽

First Case ◽

Epidemiological Trend ◽

Modeling And Forecasting ◽

Novel Coronavirus ◽

Parameter Values ◽

Stochastic Time

The novel coronavirus disease (COVID-19) pneumonia has posed a great threat to the world recent months by causing many deaths and enormous economic damage worldwide. The first case of COVID-19 in Morocco was reported on 2 March 2020, and the number of reported cases has increased day by day. In this work, we extend the well-known SIR compartmental model to deterministic and stochastic time-delayed models in order to predict the epidemiological trend of COVID-19 in Morocco and to assess the potential role of multiple preventive measures and strategies imposed by Moroccan authorities. The main features of the work include the well-posedness of the models and conditions under which the COVID-19 may become extinct or persist in the population. Parameter values have been estimated from real data and numerical simulations are presented for forecasting the COVID-19 spreading as well as verification of theoretical results.

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