A novel piece-wise approach to modeling interactions in a food web model

Cao, Yan; Alamri, Sagr; Rajhi, Ali A.; Anqi, Ali E.; Riaz, Muhammad Bilal; Elagan, S. K.; Jawa, Taghreed M.

doi:10.1016/j.rinp.2021.104951

Cited by 7 publications

(3 citation statements)

References 69 publications

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“…We shall now show the existence and uniqueness of the solution for the stochastic differential equation given in (19) based on Theorem 3. Let us first write the system (19) in a Volterra type of integrals for all t in ½t 2 , T:…”

Section: Proofmentioning

confidence: 99%

“…where t 2 ≤ t ≤ T, and the initial condition is given by Xðt We shall now show the existence and uniqueness of the solution for all t such that t ∈ ðt 2 , TÞ. Indeed, by referring to (19), we want to show the following items:…”

Section: Proofmentioning

confidence: 99%

“…Zeb et al [18] investigated a five-dimensional compartmental model of COVID-19 with the concept of piecewise derivative and integral operators combining the Caputo-Fabrizio, classical, and stochastic differential equations. A mathematical model representing an interaction in a food web is considered, and the concept of piecewise differential and integral operator is imposed for investigation in [19]. A mathematical model of the third wave of COVID-19 is developed and considered with the concept of piecewise differential and integral operators [2].…”

Section: Introductionmentioning

confidence: 99%

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On a Mathematical Model of Tumor‐Immune Interaction with a Piecewise Differential and Integral Operator

Rezapour

Deressa

Mukharlyamov

et al. 2022

Journal of Mathematics

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The representation of mathematical models via piecewise differential and integral operators for dynamic systems has this potential to capture cross-over behaviors such as a passage from deterministic to randomness which can be exhibited by different systems. A 3D mathematical model, similar to the prey-predator system, of tumor-immune interaction with piecewise differential and integral operators is developed and analyzed. Three different scenarios, namely, cross-overs from deterministic to randomness, the Mittag-Leffler law to randomness, and a cross-over behavior from fading memory to the power-law and a random process, are considered. The existence, uniqueness, positivity, and boundedness of the solutions of the systems are proved via the linear growth and Lipschitz conditions. The numerical approximations by Toufik, Atangana, and Araz are used for approximation of solutions and simulation of the piecewise models in different scenarios. From the nondimensionalized version of the 3D model representation, it is shown that the parameter values have an impact on the growth of tumor cells, and activating the proliferation of the resting cells has negatively affected the development of tumor cells. Moreover, the dynamics of tumor-immune interaction exhibited a cross-over behavior, and this behavior is exposed by the piecewise modeling approach used for the representations.

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Section: Proofmentioning

confidence: 99%

Section: Proofmentioning

confidence: 99%