An analysis of a nonlinear susceptible-exposed-infected-quarantine-recovered pandemic model of a novel coronavirus with delay effect

Raza, Ali; Ahmadian, Ali; Rafiq, Muhammad; Salahshour, Soheil; Феррара, Массимилиано

doi:10.1016/j.rinp.2020.103771

Cited by 40 publications

(30 citation statements)

References 21 publications

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“…In line with the Grünwald-Letnikov formula, the solution form (33) of the fractional-order nonlinear equation has been obtained which can be considered as an equation regarding an unknown variable xðt N Þ. We choose the Newton algorithm to gain the value of xðt N Þ via equation (33) which is expressed as…”

Section: Numerical Results Of the Fractional-order Differentialmentioning

confidence: 99%

“…Nowadays, coronavirus is a pandemic that has become a concern for the whole world. Scholars at home and abroad predict [30], analyze [31,32], and intervene [33] the spread of the coronavirus according to the infectious disease models of coronavirus outbreak. It can be seen that the analysis of infectious diseases based on infectious disease models is of great significance for understanding the trend of infectious diseases, reducing the number of infections, and preventing recurrence.…”

Section: Introductionmentioning

confidence: 99%

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Parameter Estimation for the One-Term (Multiterm) Fractional-Order SEIAR Models of Norovirus Outbreak

Wang

Pan

2021

Advances in Mathematical Physics

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In the paper, we use the Caputo fractional derivative to consider general single-term and multiterm fractional-order SEIAR models for the outbreak of Norovirus. Then, the inverse problem about parameter estimation for these fractional-order SEIAR models of the Norovirus outbreak is studied firstly. To provide the numerical solution of the single-term (or multiterm) fractional-order nonlinear differential equation, the GMMP scheme and Newton method are introduced. Then, we make use of the modified hybrid Nelder-Mead simplex search and particle swarm optimization (MH-NMSS-PSO) algorithm to obtain the fractional orders and parameters for these fractional-order SEIAR models of Norovirus outbreak. To guarantee the correctness and effectiveness of the methods, the data of a 2007 Norovirus outbreak in a middle school in one city is used as the real data to solve the inverse problem of the parameter estimation. With the new parameters, all numerical studies illustrate that the numerical solutions fit very well with the real data, which reveals that the single-term and multiterm fractional-order SEIAR models of Norovirus outbreak all can predict the number of the infectious people accurately. And it also shows that the GMMP scheme and the MH-NMSS-PSO method are efficient and valid for estimating the parameters of the single-term (or multiterm) fractional-order nonlinear equations. Then, we research the impact of changes in each parameter on the amount of infected humans I t when the remaining parameters are unchanged. All results of numerical simulation reveal that the single-term and multiterm fractional-order SEIAR model of Norovirus can provide better results than other models. And we also study the effect of the isolation on different days. The conclusion is obtained that the earlier the isolation is taken, the less the infected people are. Hence, for a fractional-order application in the SEIAR model of Norovirus outbreak, we establish the effective parameter estimation methods.

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Section: Numerical Results Of the Fractional-order Differentialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Parameter Estimation for the One-Term (Multiterm) Fractional-Order SEIAR Models of Norovirus Outbreak

Wang

Pan

2021

Advances in Mathematical Physics

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“…SEIR is a classic transmission physical dynamics model, which can specifically simulate the spread of diseases among different groups. It is different from the traditional classic dynamics model and is added with new exposure mechanism [12] , so it is more suitable for the modeling and prediction of COVID-19 virus.…”

Section: Methodsmentioning

confidence: 99%

Prediction on transmission trajectory of COVID-19 based on particle swarm algorithm

Ding

Chen

Liu

et al. 2021

Pattern Recognition Letters

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This study aimed to predict the transmission trajectory of the 2019 Corona Virus Disease (COVID-19). The particle swarm optimization (PSO) algorithm was combined with the traditional susceptible exposed infected recovered (SEIR) infectious disease prediction model to propose a SEIR-PSO prediction model on the COVID-19. In addition, the domestic epidemic data from February 25, 2020 to March 20, 2020 in China were selected as the training set for analysis. The results showed that when the conversion rate, recovery rate, and mortality rate of the SEIR-PSO model were 1/5, 1/15, and 1/13, its predictive effect on the number of people diagnosed with COVID-19 was the closest to the real data; and the SEIR-PSO model showed a mean-square errors (MSE) value of 1304.35 and mean absolute error (MAE) value of 1069.18, showing the best prediction effect compared with the susceptible infectious susceptible (SIS) model and the SEIR model. In contrary to the standard particle swarm optimization (SPSO) and linear weighted particle swarm optimization (LPSO), which were two classical improved PSO algorithms, the reliability and diversity of the SEIR-PSO model were higher. In summary, the SEIR-PSO model showed excellent performance in predicting the time series of COVID-19 epidemic data, and showed reliable application value for the prevention and control of COVID-19 epidemic.

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“…For that purpose, low and high dimensional models are most recommendable to study and forecast pandemics as the previous one dealt with the minimal compartments and later with maximum parameters [42] . Several models on the COVID-19 have been published to provide the best information with high precision, as presented in [43] , [44] , [45] , [46] , [47] . This SIR model was chosen because it simulates the maximum number of COVID-19 patients and the time required to reach pandemic levels.…”

Section: Introductionmentioning

confidence: 99%

Non-standard computational analysis of the stochastic COVID-19 pandemic model: An application of computational biology

Noor

Raza

Arif

et al. 2022

Alexandria Engineering Journal

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The present study is conducted to analyse the computational dynamical analysis of the stochastic susceptible-infected-recovered pandemic model of the novel coronavirus. We adopted two ways for stochastic modelling like as transition probabilities and parametric perturbation techniques. We applied different and well-known computational methods like Euler Maruyama, stochastic Euler, and stochastic Runge Kutta to study the dynamics of the model mentioned above. Unfortunately, these computational methods do not restore the dynamical properties of the model like positivity, boundedness, consistency, and stability in the sense of biological reasoning, as desired. Then, for the given stochastic model, we developed a stochastic non-standard finite difference method. Following that, several theorems are presented to support the proposed method, which is shown to satisfy all of the model's dynamical properties. To that end, several simulations are presented to compare the proposed method's efficiency to that of existing stochastic methods.

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An analysis of a nonlinear susceptible-exposed-infected-quarantine-recovered pandemic model of a novel coronavirus with delay effect

Cited by 40 publications

References 21 publications

Parameter Estimation for the One-Term (Multiterm) Fractional-Order SEIAR Models of Norovirus Outbreak

Parameter Estimation for the One-Term (Multiterm) Fractional-Order SEIAR Models of Norovirus Outbreak

Prediction on transmission trajectory of COVID-19 based on particle swarm algorithm

Non-standard computational analysis of the stochastic COVID-19 pandemic model: An application of computational biology

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