Page 139 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 3 – Internet of Bio-Nano Things for health applications

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 3

4. CONCLUSION [5] X. Li, Y. Wang, Z. Xiang. Global existence and
boundedness in a 2D Keller–Segel–Stokes
In this paper, an extension of the Keller-Segel system with nonlinear diffusion and
equation has been established. It has taken rotational flux. Commun. Math. Sci., 14 (2016).
advantage of having a second-order differential
equation to establish a novel Bessel-Keller-Segel [6] Gerald Rosen, Navier-Stokes symmetry in the
equation by which, at a first instance, it would give phenomenological transport theory for
information about the electric behavior of bacteria bacterial chemotaxis, Phys, Rev. A 29, 5, May
and the possible implications of this in the social 1984.
behavior. This appears to be crucial in prospective [7] Estrada-Rodriguez, Gissell, Gimperlein,
nanonetworks. Therefore, the electrodynamics of HeikoPainter, Kevin. (2017). Fractional Patlak-
an electrically charged bacteria aggregation has -Keller--Segel Equations for Chemotactic
been derived through closed-form equations. Superdiffusion. SIAM Journal on Applied
Interestingly, the shape of the curve of derived Mathematics. 78. 10.1137/17M1142867.
current exhibits a kind of discharge. Although a
tentative interpretation in terms of social [8] T. Xiang, “How strong a logistic damping can
disruption because social behavior of the bacteria prevent blow-up for the minimal Keller-
population is assumed, simulations and Segel chemotaxis system?,” J. Math. Anal.
experimental studies should be done to corroborate Appl. 459, 1172–1200 (2018).
the theory of this paper. The assumptions made https://doi.org/10.1016/j.jmaa.2017.11.022.
throughout this paper have served to minimize the [9] Fournier, N., & Jourdain, B. (2015). Stochastic
mathematical load that involves a second-order particle approximation of the Keller-Segel
differential equation. Indeed the resulting curves equation and two-dimensional generalization
have kept a close relationship with well-known of Bessel processes. Annals of Applied
electrodynamics. Probability, 27, 2807-2861.
In future work, some well-known families of [10] T. Black. Sublinear signal production in a two-
bacteria and their data will be employed to explore dimensional Keller–Segel–Stokes system
the possible similarities with the present proposal. Nonlinear Anal. Real World Appl., 31 (2016),
pp. 593-609.

[11] Huber Nieto-Chaupis, Macrophage-Like
REFERENCES Nanorobots To Anticipate Bacterial Dynamics,
[1] E. F. Keller and L. A. Segel, Model for 2019 IEEE 9th Annual Computing and
chemotaxis, J. Theor. Biol. 30 (1971) 225234. Communication Workshop and Conference
(CCWC) Year: 2019, Conference Paper.
[2] Michael Vilkhovoy, Mason Minot and Jeffrey D.
Varner, Effective Dynamic Models of [12] J. D. Jackson, Classical Electrodynamics, 3rd
Metabolic Networks, IEEE Life Sciences Edition, Chap-I BoundaryValue Problems in
Letters, Volume: 2, Issue: 4, 2016. Electrostatics: I. Wiley 1998.

[3] Bige D. Unluturk, Sasitharan, [13] Wolfram Mathematica, www.wolfram.com.
Balasubramaniam, Ian F. Akyildiz, The Impact [14] Gosztolai, A., Barahona, M. Cellular memory
of Social Behavior on the Attenuation and enhances bacterial chemotactic navigation in
Delay of Bacterial Nanonetworks, IEEE rugged environments. Commun Phys 3, 47
Transactions on NanoBioscience, Year: 2016 (2020). https://doi.org/10.1038/s42005-
Volume: 15, Issue: 8. 020-0312-8.
[4] I. F. Akyildiz, The internet of Bio-Nano things,
IEEE Communications Magazine Year: 2015,
Volume: 53, Issue: 3, Pages: 32 - 40.

© International Telecommunication Union, 2021 127