Predictor-Corrector Methods for Solving Continuous Casting Problem

Pieskä, J.; Laitinen, Erkki K.; Лапин, А. В.

doi:10.1007/3-540-26825-1_73

Cited by 2 publications

(7 citation statements)

References 5 publications

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“…The results are displayed in Figure 11. As for the case of the fractional model with mass incidence law (5), Figure 11 reveals that when the fractional order η decreases, the solutions of our fractional model (35) have different behaviors. The number of typhoid cases decreases and the peak is delayed when the fractional order decreases.…”

Section: Numerical Results Of the Fractional Model With Standard Incidence Lawmentioning

confidence: 88%

“…To simulate the new fractional model (35), we use the parameter values listed in Table 2. Note that the new typhoid model has been calibrated using real data from Mbandjock, Cameroon (see [5,6]).…”

Section: Numerical Results Of the Fractional Model With Standard Incidence Lawmentioning

confidence: 99%

“…The relative change is r = 1.83 × 10 −7 and the function tolerance is equal to 10 −6 . (35). Red bullets denote real data (see [5,6]).…”

Section: Numerical Results Of the Fractional Model With Standard Incidence Lawmentioning

confidence: 99%

“…One can cite, among others, the Implicit Quadrature method [24], the Approximate Mittag-Leffler method [33], the Predictor Corrector method [34], and the Adams-Bashforth-Moulton method [25]. The choice of the method depends on several factors, such as the amount of information treated [35] and the accuracy order [36]. The numerical scheme proposed in this work is constructed using the Adams-Bashforth-Moulton method.…”

Section: Numerical Scheme Of the Fractional Model And Its Stability Analysismentioning

confidence: 99%

“…For the new typhoid model (34) (resp. (35)), the disease-free equilibrium Q 0 is globally asymptotically stable if R c < 1 and unstable otherwise.…”

Section: Model Dynamics With the Standard Incidence Lawmentioning

confidence: 99%

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Fractional Dynamics of Typhoid Fever Transmission Models with Mass Vaccination Perspectives

2021

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In this work, we formulate and mathematically study integer and fractional models of typhoid fever transmission dynamics. The models include vaccination as a control measure. After recalling some preliminary results for the integer model (determination of the epidemiological threshold denoted by Rc, asymptotic stability of the equilibrium point without disease whenever Rc<1, the existence of an equilibrium point with disease whenever Rc>1), we replace the integer derivative with the Caputo derivative. We perform a stability analysis of the disease-free equilibrium and prove the existence and uniqueness of the solution of the fractional model using fixed point theory. We construct the numerical scheme and prove its stability. Simulation results show that when the fractional-order η decreases, the peak of infected humans is delayed. To reduce the proliferation of the disease, mass vaccination combined with environmental sanitation is recommended. We then extend the previous model by replacing the mass action incidences with standard incidences. We compute the corresponding epidemiological threshold denoted by Rc☆ and ensure the uniform stability of the disease-free equilibrium, for both new models, when Rc☆<1. A new calibration of the new model is conducted with real data of Mbandjock, Cameroon, to estimate Rc☆=1.4348. We finally perform several numerical simulations that permit us to conclude that such diseases can possibly be tackled through vaccination combined with environmental sanitation.

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Section: Numerical Results Of the Fractional Model With Standard Incidence Lawmentioning

confidence: 88%

Section: Numerical Results Of the Fractional Model With Standard Incidence Lawmentioning

confidence: 99%

“…The relative change is r = 1.83 × 10 −7 and the function tolerance is equal to 10 −6 . (35). Red bullets denote real data (see [5,6]).…”

Section: Numerical Results Of the Fractional Model With Standard Incidence Lawmentioning

confidence: 99%

Section: Numerical Scheme Of the Fractional Model And Its Stability Analysismentioning

confidence: 99%

“…For the new typhoid model (34) (resp. (35)), the disease-free equilibrium Q 0 is globally asymptotically stable if R c < 1 and unstable otherwise.…”

Section: Model Dynamics With the Standard Incidence Lawmentioning

confidence: 99%

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