Implementation of computationally efficient numerical approach to analyze a Covid-19 pandemic model

Butt, Azhar Iqbal Kashif; Rafiq, Muhammad; Ahmad, Waheed; Ahmad, Naeed

doi:10.1016/j.aej.2023.01.052

Cited by 19 publications

(23 citation statements)

References 65 publications

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“…A well‐designed mathematical model could help us in understanding the disease's transmission mechanism and it may be useful to study disease patterns for eradication of disease effectively. There exist several mathematical models [1–29] designed by researchers with different assumptions to study flow dynamics and to control of corona virus disease. In this section, we design a new mathematical model for the corona virus disease that will explain the disease transmission dynamics reliably.…”

Section: Covid‐19 Model Formulationmentioning

confidence: 99%

“…Moreover, d 1 , d 2 , d 3 indicate the death rate due to the COVID-19 disease for symptomatic, asymptomatic, and hospitalized individuals, respectively. The numerical values of the parameters involved in model (2) are listed in Table 1.…”

Section: Covid-19 Model Formulationmentioning

confidence: 99%

“…This section is devoted to present properties of the proposed model (2). First of all, we prove the most important property for an ODE or system of ODEs: the existence and uniqueness of the solution.…”

Section: Model Propertiesmentioning

confidence: 99%

“…Disease symptoms might occur as early as two days after closed contact or as delay as 14 days after exposure. Corona virus can originate a range of symptoms like fever, headache, body aches, cough, vomiting, diarrhea, trouble in breathing or shortness of breath, and sore throat [1, 2]. If the infection becomes more acute, the infected human may face pneumonia, kidney failure, respiratory syndrome, and even death due to infection.…”

Section: Introductionmentioning

confidence: 99%

“…The fatality rate of infectious disease can be decreased by using face masks, washing hands, avoiding social gatherings, and isolating infected individuals along with proper medication [3][4][5]. The people in the age group of 60 or more and the people of any age with severe health issues such as obesity, diabetes, and heart problems are at high risk of developing acute symptoms of corona virus [1][2][3][4][5]. The main reason of transmission of virus to others is due to the droplets ejected from the nose when a COVID-19 infected person coughs or sneezes.…”

Section: Introductionmentioning

confidence: 99%

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A new design and analysis of optimal control problems arising from COVID‐19 outbreak

Butt

Chamaleen

Imran

et al. 2023

Math Methods in App Sciences

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In this manuscript, we append the hospitalization, diagnosed and isolation compartments to the classic SEIR model to design a new COVID‐19 epidemic model. We further subdivide the isolation compartment into asymptomatic infected and symptomatic infected compartments. For validity of the purposed model, we prove the existence of a unique solution and prove the positivity and boundedness of the solution. To study disease dynamics, we compute equilibrium points and the reproduction number . We also investigate the local and global stabilities at both of the equilibrium points. Sensitivity analysis will be performed to observe the effect of transmission parameters on . For optimal control analysis, we design two different optimal control problems by taking different optimal control approaches. Firstly, we add an isolation compartment in the newly designed model, and secondly, three parameters describing non‐pharmaceutical behaviors such as educating people to take precautionary measures, providing intensive medical care with medication, and utilizing resources by government are added in the model. We set up optimality conditions by using Pontryagin's maximum principle and develop computing algorithms to solve the conditions numerically. At the end, numerical solutions will be displayed graphically with discussion.

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Section: Covid‐19 Model Formulationmentioning

confidence: 99%

Section: Covid-19 Model Formulationmentioning

confidence: 99%

Section: Model Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%