A fractional-order epidemic model with time-delay and nonlinear incidence rate

Rihan, Fathalla A.; Al‐Mdallal, Qasem M.; Alsakaji, Hebatallah J.; Hashish, A. H.

doi:10.1016/j.chaos.2019.05.039

Cited by 121 publications

(65 citation statements)

References 32 publications

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“…A more sophisticated model is also required to investigate the dynamics of COVID-19 with immune system in cells level [42]. Fractional derivatives can also be included in the model to consider long-run memory [43,44].…”

Section: Resultsmentioning

confidence: 99%

Stochastic SIRC epidemic model with time-delay for COVID-19

2020

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Environmental factors, such as humidity, precipitation, and temperature, have significant impacts on the spread of the new strain coronavirus COVID-19 to humans. In this paper, we use a stochastic epidemic SIRC model, with cross-immune class and time-delay in transmission terms, for the spread of COVID-19. We analyze the model and prove the existence and uniqueness of positive global solution. We deduce the basic reproduction number ${\mathcal{R}}_{0}^{s}$ R 0 s for the stochastic model which is smaller than ${\mathcal{R}}_{0}$ R 0 of the corresponding deterministic model. Sufficient conditions that guarantee the existence of a unique ergodic stationary distribution, using the stochastic Lyapunov function, and conditions for the extinction of the disease are obtained. Our findings show that white noise plays an important part in controlling the spread of the disease; When the white noise is relatively large, the infectious diseases will become extinct; Re-infection and periodic outbreaks can occur due to the existence of feedback time-delay (or memory) in the transmission terms.

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Section: Resultsmentioning

confidence: 99%

Stochastic SIRC epidemic model with time-delay for COVID-19

2020

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“…In general, the stability region of the system contains FDs, which is greatest when compared with the stability region of the system with integer-order derivatives (see, e.g., [56]). erefore, we investigate analytically the stability of the EPs E 0 and E * .…”

Section: Theoremmentioning

confidence: 99%

Fractional Optimal Control with Fish Consumption to Prevent the Risk of Coronary Heart Disease

et al. 2020

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According to the World Health Organization (WHO), Chronic Heart Disease (CHD) is one of the greatest defies currently confronting humankind which is sweeping the whole globe, with an expanding trend in developing countries. In this paper, a mathematical model (MM) was proposed to study the connection between fish consumption and CHD mortality in Egypt, by considering a system of ordinary differential equations (ODEs) involving time-fractional derivative (FD). We considered here the study on Egypt for the ease of obtaining real data, but the method and approach adopted here is not limited to Egypt only and can be applied to any country in the world with the information of the real data related to the subject of the study. Additionally, the control function which represents the metabolic and the behavioural risk factors of CHD that help to reduce the number of mortality due to CHD is incorporated in the proposed MM. A fractional optimal control problem (FOCP) with a proposed control is formulated and studied theoretically using the Pontryagin maximum principle, to minimize the susceptible population and also to decrease the mortality rate of CHD. Moreover, firstly we discussed the positivity and boundedness of solutions; then, the model equilibria are determined and their local stability analysis was investigated; furthermore, we use the improved forward-backward sweep method (FBSM) based on the predictor-corrector method (PCM) in order to obtain the solution of proposed FOCP. In addition, some numerical simulations were performed to show the effect of the proposed optimal control (OC) besides the impact of fish consumption on the mortality of CHD.

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“…They claimed that new strange behaviors of the attractors were not possible by only classical differentiations. In short, the study can be continued for the charming and effective role of fractional calculus in applied engineering problems, 20–31 but we include here recent attempt in categorically as epidemiology, 32–39 heat and mass transfer, 40–44 fluid mechanics, 45–47 nanofluids, 48–51 and electrical engineering 52–55 . Motivating by above discussion, our aim is to propose the controlling analysis and coexisting attractors provided by memristor through highly nonlinear for mathematical relationships of governing differential equations.…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of memristor through fractal‐fractional differential operators: A numerical study

Abro

Atangana

2020

Math Methods in App Sciences

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The newly generalized energy storage component, namely, memristor, which is a fundamental circuit element so called universal charge‐controlled mem‐element, is proposed for controlling the analysis and coexisting attractors. The governing differential equations of memristor are highly nonlinear for mathematical relationships. The mathematical model of memristor is established in terms of newly defined fractal‐fractional differential operators so called Atangana‐Baleanu, Caputo‐Fabrizio, and Caputo fractal‐fractional differential operator. A novel numerical approach is developed for the governing differential equations of memristor on the basis of Atangana‐Baleanu, Caputo‐Fabrizio, and Caputo fractal‐fractional differential operator. We discussed chaotic behavior of memristor under three criteria such as (i) varying fractal order, we fixed fractional order; (ii) varying fractional order, we fixed fractal order; and (ii) varying fractal and fractional orders simultaneously. Our investigated graphical illustrations and simulated results via MATLAB for the chaotic behaviors of memristor suggest that newly presented Atangana‐Baleanu, Caputo‐Fabrizio, and Caputo fractal‐fractional differential operators generate significant results as compared with classical approach.

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A fractional-order epidemic model with time-delay and nonlinear incidence rate

Cited by 121 publications

References 32 publications

Stochastic SIRC epidemic model with time-delay for COVID-19

Stochastic SIRC epidemic model with time-delay for COVID-19

Fractional Optimal Control with Fish Consumption to Prevent the Risk of Coronary Heart Disease

Mathematical analysis of memristor through fractal‐fractional differential operators: A numerical study

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