Research

14 pages, 540 KiB

Open AccessArticle

The SQEIRP Mathematical Model for the COVID-19 Epidemic in Thailand

by Sowwanee Jitsinchayakul, Usa Wannasingha Humphries and Amir Khan

Axioms 2023, 12(1), 75; https://doi.org/10.3390/axioms12010075 - 11 Jan 2023

Cited by 4 | Viewed by 1684

The spread of COVID-19 started in late December 2019 and is still ongoing. Many countries around the world have faced an outbreak of COVID-19, including Thailand, which must keep an eye on the spread and find a way to deal with this extreme [...] Read more.

The spread of COVID-19 started in late December 2019 and is still ongoing. Many countries around the world have faced an outbreak of COVID-19, including Thailand, which must keep an eye on the spread and find a way to deal with this extreme outbreak. Of course, we are unable to determine the number of people who will contract this disease in the future. Therefore, if there is a tool that helps to predict the outbreak and the number of people infected, it will be able to find preventive measures in time. This paper aims to develop a mathematical model suitable for the lifestyle of the Thai population facing the COVID-19 situation. It has been established that after close contact with an infected person, a group of individuals will be quarantined and non-quarantined. If they contract COVID-19, they will enter the incubation period of the infection. The incubation period is divided into the quarantine class and the exposed class. Afterwards, both classes will move to the hospitalized infected class and the infected class, wherein the infected class is able to spread the disease to the surrounding environment. This study describes both classes in the SQEIRP model based on the population segmentation that was previously discussed. After that, the positive and bounded solutions of the model are examined, and we consider the equilibrium point, as well as the global stability of the disease-free point according to the Castillo-Chavez method. The SQEIRP model is then numerically analyzed using MATLAB software version R2022a. The cumulative percentage of hospitalized and non-hospitalized infections after 7 days after the commencement of the infection was determined to be 11 and 34 percent of the entire population, respectively. The Next-Generation Matrix approach was used to calculate the Basic Reproduction Numbers (

R_{0}

). The SQEIRP model’s

R_{0}

was 3.78, indicating that one infected individual can result in approximately three additional infections. The results of this SQEIRP model provide a preliminary guide to identifying trends in population dynamics in each class. Full article

(This article belongs to the Special Issue Mathematics of the COVID-19)

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16 pages, 464 KiB

Open AccessArticle

A New Emergency-Risk-Evaluation Approach under Spherical Fuzzy-Information Environments

by Kuei-Hu Chang

Axioms 2022, 11(9), 474; https://doi.org/10.3390/axioms11090474 - 16 Sep 2022

Cited by 7 | Viewed by 1267

Abstract

When major emergencies or accidents occur, risk evaluation and prediction are the most important means to reduce their impact. Typical risk evaluation uses the failure mode and effects analysis (FMEA) method for failure-risk ranking and control. However, when faced with severe special infectious [...] Read more.

When major emergencies or accidents occur, risk evaluation and prediction are the most important means to reduce their impact. Typical risk evaluation uses the failure mode and effects analysis (FMEA) method for failure-risk ranking and control. However, when faced with severe special infectious diseases such as COVID-19, there are many cognitive and information uncertainties that the FMEA method is unable to effectively handle. To effectively deal with the issue of risk evaluation when major emergencies or accidents occur, this paper integrated the risk-priority number and spherical fuzzy-sets methods to propose a novel emergency-risk-evaluation method. In the numerical verification, this paper applied the example of preventing secondary COVID-19 transmissions in hospitals to explain the calculation procedure and validity of the proposed new emergency-risk-evaluation approach. The calculation results were also compared with the typical RPN, fuzzy-set, and intuitionistic fuzzy-set methods. The calculation results showed that the proposed new emergency-risk-evaluation approach could effectively handle the cognitive and informational uncertainties of emergency-risk-evaluation issues during the COVID-19 pandemic. Full article

(This article belongs to the Special Issue Mathematics of the COVID-19)

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15 pages, 419 KiB

Open AccessArticle

A Fractional COVID-19 Model with Efficacy of Vaccination

by M. Nandhini, R. Lavanya and Juan J. Nieto

Axioms 2022, 11(9), 446; https://doi.org/10.3390/axioms11090446 - 31 Aug 2022

Cited by 3 | Viewed by 1167

Abstract

This paper develops a fractional-order model of COVID-19 with vaccination. The model is well designed by including both the efficacy and inefficacy of vaccinations in humans. Besides calculating the reproduction number, equilibrium points and the feasibility region are also determined. Stability analysis for [...] Read more.

This paper develops a fractional-order model of COVID-19 with vaccination. The model is well designed by including both the efficacy and inefficacy of vaccinations in humans. Besides calculating the reproduction number, equilibrium points and the feasibility region are also determined. Stability analysis for the proposed model around equilibrium points is discussed. Fixed-point theory is employed to identify the singularity of the solution. Adomian decomposition and Laplace integral transformation are combined to obtain the solution. We present the solutions graphically to analyze the contributions of the disease dynamics based on different values of the fractional order. This study seeks an in-depth understanding of COVID-19 transmission to improve health outcomes. Full article

(This article belongs to the Special Issue Mathematics of the COVID-19)

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29 pages, 8785 KiB

Open AccessArticle

Design of Type-3 Fuzzy Systems and Ensemble Neural Networks for COVID-19 Time Series Prediction Using a Firefly Algorithm

by Patricia Melin, Daniela Sánchez, Juan R. Castro and Oscar Castillo

Axioms 2022, 11(8), 410; https://doi.org/10.3390/axioms11080410 - 17 Aug 2022

Cited by 20 | Viewed by 1926

Abstract

In this work, information on COVID-19 confirmed cases is utilized as a dataset to perform time series predictions. We propose the design of ensemble neural networks (ENNs) and type-3 fuzzy inference systems (FISs) for predicting COVID-19 data. The answers for each ENN module [...] Read more.

In this work, information on COVID-19 confirmed cases is utilized as a dataset to perform time series predictions. We propose the design of ensemble neural networks (ENNs) and type-3 fuzzy inference systems (FISs) for predicting COVID-19 data. The answers for each ENN module are combined using weights provided by the type-3 FIS, in which the ENN is also designed using the firefly algorithm (FA) optimization technique. The proposed method, called ENNT3FL-FA, is applied to the COVID-19 data for confirmed cases from 12 countries. The COVID-19 data have shown to be a complex time series due to unstable behavior in certain periods of time. For example, it is unknown when a new wave will exist and how it will affect each country due to the increase in cases due to many factors. The proposed method seeks mainly to find the number of modules of the ENN and the best possible parameters, such as lower scale and lower lag of the type-3 FIS. Each module of the ENN produces an individual prediction. Each prediction error is an input for the type-3 FIS; moreover, outputs provide a weight for each prediction, and then the final prediction can be calculated. The type-3 fuzzy weighted average (FWA) integration method is compared with the type-2 FWA to verify its ability to predict future confirmed cases by using two data periods. The achieved results show how the proposed method allows better results for the real prediction of 20 future days for most of the countries used in this study, especially when the number of data points increases. In countries such as Germany, India, Italy, Mexico, Poland, Spain, the United Kingdom, and the United States of America, on average, the proposed ENNT3FL-FA achieves a better performance for the prediction of future days for both data points. The proposed method proves to be more stable with complex time series to predict future information such as the one utilized in this study. Intelligence techniques and their combination in the proposed method are recommended for time series with many data points. Full article

(This article belongs to the Special Issue Mathematics of the COVID-19)

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21 pages, 1188 KiB

Open AccessArticle

Stability Analysis of Delayed COVID-19 Models

by Mohamed A. Zaitri, Cristiana J. Silva and Delfim F. M. Torres

Axioms 2022, 11(8), 400; https://doi.org/10.3390/axioms11080400 - 13 Aug 2022

Cited by 4 | Viewed by 1418

Abstract

We analyze mathematical models for COVID-19 with discrete time delays and vaccination. Sufficient conditions for the local stability of the endemic and disease-free equilibrium points are proved for any positive time delay. The stability results are illustrated through numerical simulations performed in MATLAB. [...] Read more.

We analyze mathematical models for COVID-19 with discrete time delays and vaccination. Sufficient conditions for the local stability of the endemic and disease-free equilibrium points are proved for any positive time delay. The stability results are illustrated through numerical simulations performed in MATLAB. Full article

(This article belongs to the Special Issue Mathematics of the COVID-19)

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15 pages, 614 KiB

Open AccessArticle

Fractional Modelling and Optimal Control of COVID-19 Transmission in Portugal

by Silvério Rosa and Delfim F. M. Torres

Axioms 2022, 11(4), 170; https://doi.org/10.3390/axioms11040170 - 11 Apr 2022

Cited by 9 | Viewed by 2050

Abstract

A fractional-order compartmental model was recently used to describe real data of the first wave of the COVID-19 pandemic in Portugal [Chaos Solitons Fractals 144 (2021), Art. 110652]. Here, we modify that model in order to correct time dimensions and use it to [...] Read more.

A fractional-order compartmental model was recently used to describe real data of the first wave of the COVID-19 pandemic in Portugal [Chaos Solitons Fractals 144 (2021), Art. 110652]. Here, we modify that model in order to correct time dimensions and use it to investigate the third wave of COVID-19 that occurred in Portugal from December 2020 to February 2021, and that has surpassed all previous waves, both in number and consequences. A new fractional optimal control problem is then formulated and solved, with vaccination and preventive measures as controls. A cost-effectiveness analysis is carried out, and the obtained results are discussed. Full article

(This article belongs to the Special Issue Mathematics of the COVID-19)

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14 pages, 994 KiB

Open AccessArticle

A Discrete-Time Compartmental Epidemiological Model for COVID-19 with a Case Study for Portugal

by Sandra Vaz and Delfim F. M. Torres

Axioms 2021, 10(4), 314; https://doi.org/10.3390/axioms10040314 - 23 Nov 2021

Cited by 6 | Viewed by 1855

Abstract

Recently, a continuous-time compartmental mathematical model for the spread of the Coronavirus disease 2019 (COVID-19) was presented with Portugal as case study, from 2 March to 4 May 2020, and the local stability of the Disease Free Equilibrium (DFE) was analysed. Here, we [...] Read more.

Recently, a continuous-time compartmental mathematical model for the spread of the Coronavirus disease 2019 (COVID-19) was presented with Portugal as case study, from 2 March to 4 May 2020, and the local stability of the Disease Free Equilibrium (DFE) was analysed. Here, we propose an analogous discrete-time model and, using a suitable Lyapunov function, we prove the global stability of the DFE point. Using COVID-19 real data, we show, through numerical simulations, the consistence of the obtained theoretical results. Full article

(This article belongs to the Special Issue Mathematics of the COVID-19)

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17 pages, 2232 KiB

Open AccessArticle

Model Predictive Control of COVID-19 Pandemic with Social Isolation and Vaccination Policies in Thailand

by Jatuphorn Jankhonkhan and Wannika Sawangtong

Axioms 2021, 10(4), 274; https://doi.org/10.3390/axioms10040274 - 25 Oct 2021

Cited by 8 | Viewed by 2093

Abstract

This study concerns the COVID-19 pandemic in Thailand related to social isolation and vaccination policies. The behavior of disease spread is described by an epidemic model via a system of ordinary differential equations. The invariant region and equilibrium point of the model, as [...] Read more.

This study concerns the COVID-19 pandemic in Thailand related to social isolation and vaccination policies. The behavior of disease spread is described by an epidemic model via a system of ordinary differential equations. The invariant region and equilibrium point of the model, as well as the basic reproduction number, are also examined. Moreover, the model is fitted to real data for the second wave and the third wave of the pandemic in Thailand by a sum square error method in order to forecast the future spread of infectious diseases at each time. Furthermore, the model predictive control technique with quadratic programming is used to investigate the schedule of preventive measures over a time horizon. As a result, firstly, the plan results are proposed to solve the limitation of ICU capacity and increase the survival rate of patients. Secondly, the plan to control the outbreak without vaccination shows a strict policy that is difficult to do practically. Finally, the vaccination plan significantly prevents disease transmission, since the populations who get the vaccination have immunity against the virus. Moreover, the outbreak is controlled in 28 weeks. The results of a measurement strategy for preventing the disease are examined and compared with a control and without a control. Thus, the schedule over a time horizon can be suitably used for controlling. Full article

(This article belongs to the Special Issue Mathematics of the COVID-19)

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13 pages, 808 KiB

Open AccessArticle

How Containment Can Effectively Suppress the Outbreak of COVID-19: A Mathematical Modeling

by Bootan Rahman, Sarbaz H. A. Khoshnaw, Grace O. Agaba and Fahad Al Basir

Axioms 2021, 10(3), 204; https://doi.org/10.3390/axioms10030204 - 28 Aug 2021

Cited by 7 | Viewed by 1950

Abstract

In this paper, the aim is to capture the global pandemic of COVID-19 with parameters that consider the interactions among individuals by proposing a mathematical model. The introduction of a parsimonious model captures both the isolation of symptomatic infected individuals and population lockdown [...] Read more.

In this paper, the aim is to capture the global pandemic of COVID-19 with parameters that consider the interactions among individuals by proposing a mathematical model. The introduction of a parsimonious model captures both the isolation of symptomatic infected individuals and population lockdown practices in response to containment policies. Local stability and basic reproduction numbers are analyzed. Local sensitivity indices of the parameters of the proposed model are calculated, using the non-normalization, half-normalization, and full-normalization techniques. Numerical investigations show that the dynamics of the system depend on the model parameters. The infection transmission rate (as a function of the lockdown parameter) for both reported and unreported symptomatic infected peoples is a significant parameter in spreading the infection. A nationwide public lockdown decreases the number of infected cases and stops the pandemic’s peak from occurring. The results obtained from this study are beneficial worldwide for developing different COVID-19 management programs. Full article

(This article belongs to the Special Issue Mathematics of the COVID-19)

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13 pages, 711 KiB

Open AccessEditor’s ChoiceArticle

Mathematical Analysis of a Fractional COVID-19 Model Applied to Wuhan, Spain and Portugal

by Faïçal Ndaïrou and Delfim F. M. Torres

Axioms 2021, 10(3), 135; https://doi.org/10.3390/axioms10030135 - 27 Jun 2021

Cited by 17 | Viewed by 2989

Abstract

We propose a qualitative analysis of a recent fractional-order COVID-19 model. We start by showing that the model is mathematically and biologically well posed. Then, we give a proof on the global stability of the disease free equilibrium point. Finally, some numerical simulations [...] Read more.

We propose a qualitative analysis of a recent fractional-order COVID-19 model. We start by showing that the model is mathematically and biologically well posed. Then, we give a proof on the global stability of the disease free equilibrium point. Finally, some numerical simulations are performed to ensure stability and convergence of the disease free equilibrium point. Full article

(This article belongs to the Special Issue Mathematics of the COVID-19)

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23 pages, 2988 KiB

Open AccessArticle

New Procedures of a Fractional Order Model of Novel Coronavirus (COVID-19) Outbreak via Wavelets Method

by Maryamsadat Hedayati, Reza Ezzati and Samad Noeiaghdam

Axioms 2021, 10(2), 122; https://doi.org/10.3390/axioms10020122 - 16 Jun 2021

Cited by 19 | Viewed by 1901

Abstract

Coronaviruses are a group of RNA (ribonucleic acid) viruses with the capacity for rapid mutation and recombination. Coronaviruses are known to cause respiratory or intestinal infections in humans and animals. In this paper, a biologically compatible set of nonlinear fractional differential equations governing [...] Read more.

Coronaviruses are a group of RNA (ribonucleic acid) viruses with the capacity for rapid mutation and recombination. Coronaviruses are known to cause respiratory or intestinal infections in humans and animals. In this paper, a biologically compatible set of nonlinear fractional differential equations governing the outbreak of the novel coronavirus is suggested based on a model previously proposed in the literature. Then, this set is numerically solved utilizing two new methods employing sine–cosine and Bernoulli wavelets and their operational matrices. Moreover, the convergence of the solution is experimentally studied. Furthermore, the accuracy of the solution is proved via comparing the results with those obtained in previous research for the primary model. Furthermore, the computational costs are compared by measuring the CPU running time. Finally, the effects of the fractional orders on the outbreak of the COVID-19 are investigated. Full article

(This article belongs to the Special Issue Mathematics of the COVID-19)

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