Qualitative Analysis of a Mathematical Model in the Time of COVID-19

Shah, Kamal; Abdeljawad, Thabet; Mahariq, İbrahim; Jarad, Fahd

doi:10.1155/2020/5098598

Cited by 96 publications

(62 citation statements)

References 32 publications

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“…Thus, it is meaningful to study the proposed TB model in feasible region . For the upcoming results, we suggest the readers some recent related results for the stabilities and numerical techniques given in [23][24][25][26][27][28][29].…”

Section: Lemma 22mentioning

confidence: 99%

Stability analysis of a dynamical model of tuberculosis with incomplete treatment

et al. 2020

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A simple deterministic epidemic model for tuberculosis is addressed in this article. The impact of effective contact rate, treatment rate, and incomplete treatment versus efficient treatment is investigated. We also analyze the asymptotic behavior, spread, and possible eradication of the TB infection. It is observed that the disease transmission dynamics is characterized by the basic reproduction ratio $\Re _{0}$ ℜ 0 ; if $\Re _{0}<1$ ℜ 0 < 1 , there is only a disease-free equilibrium which is both locally and globally asymptotically stable. Moreover, for $\Re _{0}>1$ ℜ 0 > 1 , a unique positive endemic equilibrium exists which is globally asymptotically stable. The global stability of the equilibria is shown via Lyapunov function. It is also obtained that incomplete treatment of TB causes increase in disease infection while efficient treatment results in a reduction in TB. Finally, for the estimated parameters, some numerical simulations are performed to verify the analytical results. These numerical results indicate that decrease in the effective contact rate λ and increase in the treatment rate γ play a significant role in the TB infection control.

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Section: Lemma 22mentioning

confidence: 99%

Stability analysis of a dynamical model of tuberculosis with incomplete treatment

et al. 2020

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“…added to the acronym SIR is the exposure compartment to make it SEIR. Other authors who adopted the SIR/SEIR model include [2][3][4][5][6][7]. Artificial intelligence and machine learning approach was equally used to model and forecast cases of COVID-19.…”

Section: The Sir and Seir Modelmentioning

confidence: 99%

Forecasting of New Cases of COVID-19 in Nigeria Using Autoregressive Fractionally Integrated Moving Average Models

Adesina

Onanaye

Okewole

et al. 2020

ARJOM

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The emergence of global pandemic known as COVID-19 has impacted significantly on human lives and measures have been taken by government all over the world to minimize the rate of spread of the virus, one of which is by enforcing lockdown. In this study, Autoregressive fractionally integrated moving average (ARFIMA) Models was used to model and forecast what the daily new cases of COVID-19 would have been ten days after the lockdown was eased in Nigeria and compare to the actual new cases for the period when the lockdown was eased. The proposed model ARFIMA model was compared with ARIMA (1, 0, 0), and ARIMA (1, 0, 1) and found to outperform the classical ARIMA models based on AIC and BIC values. The results show that the rate of spread of COVID-19 would have been significantly less if the strict lockdown had continued. ARFIMA model was further used to model what new cases of COVID-19 would be ten days ahead starting from 31st of August 2020. Therefore, this study recommends that government should further enforce measures to reduce the spread of the virus if business must continue as usual.

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“…Therefore, various numerical procedures (methods) have been constructed in literature to deal with such problems, see [54][55][56]. For classical and usual fractional derivatives, the numerical schemes have been framed, and on further slight modification they may be extended to the new nonlocal FODEs, see [57][58][59][60][61][62][63]. Therefore a fractional-type two-step AB method is applied to simulate the results via Matlab-16.…”

Section: Introductionmentioning

confidence: 99%

On modeling of coronavirus-19 disease under Mittag-Leffler power law

2020

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This paper investigates a new model on coronavirus-19 disease (COVID-19) with three compartments including susceptible, infected, and recovered class under Mittag-Leffler type derivative. The mentioned derivative has been introduced by Atangana, Baleanu, and Caputo abbreviated as $(\mathcal{ABC})$ ( ABC ) . Upon utilizing fixed point theory, we first prove the existence of at least one solution for the considered model and its uniqueness. Also, some results about stability of Ulam–Hyers type are also established. By applying a numerical technique called fractional Adams–Bashforth (AB) method, we develop a scheme for the approximate solutions to the considered model. Using some real available data, we perform the concerned numerical simulation corresponding to different values of fractional order.

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Qualitative Analysis of a Mathematical Model in the Time of COVID-19

Cited by 96 publications

References 32 publications

Stability analysis of a dynamical model of tuberculosis with incomplete treatment

Stability analysis of a dynamical model of tuberculosis with incomplete treatment

Forecasting of New Cases of COVID-19 in Nigeria Using Autoregressive Fractionally Integrated Moving Average Models

On modeling of coronavirus-19 disease under Mittag-Leffler power law

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