Global Existence of a Virus Infection Model with Saturated Chemotaxis

Ruijing Li

doi:doi:10.11648/j.ijssam.20210602.12

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Global Existence of a Virus Infection Model with Saturated Chemotaxis

Ruijing Li

Published in International Journal of Systems Science and Applied Mathematics (Volume 6, Issue 2)

Received: 26 April 2021 Accepted: 11 May 2021 Published: 27 May 2021

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Abstract

In this paper, a virus infection model with saturated chemotaxis is formulated and analyzed, where the chemotactic sensitivity for chemotactic movements of the cells is described. This model contains three state variables namely the population density of uninfected cells, the population density of infected cells and the concentration of virus particles, respectively. By virtue of regularized approximation technique and fixed point theorem, the local solvability of the regularized system corresponding to the original system is established. Then by extracting a suitable sequence along which the respective approximate solutions approach a limit in convenient topologies, with addition of Gagliardo-Nirenberg interpolation inequality as well as L^p-estimate techniques, we show that the original system describing the virus infection model exists at least one global weak solution. To illustrate the application of our theoretical results, an optimal control problem of the epidemic system is considered, where the admissible control domain is assumed to be a bounded closed convex subset. With the help of Aubin compactness theorem and lower semicontinuous of the cost functional, the existence of the optimal pair is proved. Our results generalize and improve partial previously known ones, and moreover, we first prove that the optimal control problem has at least one optimal pair.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 6, Issue 2)
DOI	10.11648/j.ijssam.20210602.12
Page(s)	40-54
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Virus Infection, Global Existence, Chemotaxis, Optimal Control

References

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Ruijing Li. (2021). Global Existence of a Virus Infection Model with Saturated Chemotaxis. International Journal of Systems Science and Applied Mathematics, 6(2), 40-54. https://doi.org/10.11648/j.ijssam.20210602.12

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ACS Style

Ruijing Li. Global Existence of a Virus Infection Model with Saturated Chemotaxis. Int. J. Syst. Sci. Appl. Math. 2021, 6(2), 40-54. doi: 10.11648/j.ijssam.20210602.12

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Ruijing Li. Global Existence of a Virus Infection Model with Saturated Chemotaxis. Int J Syst Sci Appl Math. 2021;6(2):40-54. doi: 10.11648/j.ijssam.20210602.12

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@article{10.11648/j.ijssam.20210602.12,
  author = {Ruijing Li},
  title = {Global Existence of a Virus Infection Model with Saturated Chemotaxis},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {6},
  number = {2},
  pages = {40-54},
  doi = {10.11648/j.ijssam.20210602.12},
  url = {https://doi.org/10.11648/j.ijssam.20210602.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20210602.12},
  abstract = {In this paper, a virus infection model with saturated chemotaxis is formulated and analyzed, where the chemotactic sensitivity for chemotactic movements of the cells is described. This model contains three state variables namely the population density of uninfected cells, the population density of infected cells and the concentration of virus particles, respectively. By virtue of regularized approximation technique and fixed point theorem, the local solvability of the regularized system corresponding to the original system is established. Then by extracting a suitable sequence along which the respective approximate solutions approach a limit in convenient topologies, with addition of Gagliardo-Nirenberg interpolation inequality as well as Lp-estimate techniques, we show that the original system describing the virus infection model exists at least one global weak solution. To illustrate the application of our theoretical results, an optimal control problem of the epidemic system is considered, where the admissible control domain is assumed to be a bounded closed convex subset. With the help of Aubin compactness theorem and lower semicontinuous of the cost functional, the existence of the optimal pair is proved. Our results generalize and improve partial previously known ones, and moreover, we first prove that the optimal control problem has at least one optimal pair.},
 year = {2021}
}

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TY  - JOUR
T1  - Global Existence of a Virus Infection Model with Saturated Chemotaxis
AU  - Ruijing Li
Y1  - 2021/05/27
PY  - 2021
N1  - https://doi.org/10.11648/j.ijssam.20210602.12
DO  - 10.11648/j.ijssam.20210602.12
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 40
EP  - 54
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20210602.12
AB  - In this paper, a virus infection model with saturated chemotaxis is formulated and analyzed, where the chemotactic sensitivity for chemotactic movements of the cells is described. This model contains three state variables namely the population density of uninfected cells, the population density of infected cells and the concentration of virus particles, respectively. By virtue of regularized approximation technique and fixed point theorem, the local solvability of the regularized system corresponding to the original system is established. Then by extracting a suitable sequence along which the respective approximate solutions approach a limit in convenient topologies, with addition of Gagliardo-Nirenberg interpolation inequality as well as Lp-estimate techniques, we show that the original system describing the virus infection model exists at least one global weak solution. To illustrate the application of our theoretical results, an optimal control problem of the epidemic system is considered, where the admissible control domain is assumed to be a bounded closed convex subset. With the help of Aubin compactness theorem and lower semicontinuous of the cost functional, the existence of the optimal pair is proved. Our results generalize and improve partial previously known ones, and moreover, we first prove that the optimal control problem has at least one optimal pair.
VL  - 6
IS  - 2
ER  -

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Author Information

Ruijing Li

School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou, China

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Plain Text BibTeX RIS

APA Style

Ruijing Li. (2021). Global Existence of a Virus Infection Model with Saturated Chemotaxis. International Journal of Systems Science and Applied Mathematics, 6(2), 40-54. https://doi.org/10.11648/j.ijssam.20210602.12

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ACS Style

Ruijing Li. Global Existence of a Virus Infection Model with Saturated Chemotaxis. Int. J. Syst. Sci. Appl. Math. 2021, 6(2), 40-54. doi: 10.11648/j.ijssam.20210602.12

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AMA Style

Ruijing Li. Global Existence of a Virus Infection Model with Saturated Chemotaxis. Int J Syst Sci Appl Math. 2021;6(2):40-54. doi: 10.11648/j.ijssam.20210602.12

Copy | Download

@article{10.11648/j.ijssam.20210602.12,
  author = {Ruijing Li},
  title = {Global Existence of a Virus Infection Model with Saturated Chemotaxis},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {6},
  number = {2},
  pages = {40-54},
  doi = {10.11648/j.ijssam.20210602.12},
  url = {https://doi.org/10.11648/j.ijssam.20210602.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20210602.12},
  abstract = {In this paper, a virus infection model with saturated chemotaxis is formulated and analyzed, where the chemotactic sensitivity for chemotactic movements of the cells is described. This model contains three state variables namely the population density of uninfected cells, the population density of infected cells and the concentration of virus particles, respectively. By virtue of regularized approximation technique and fixed point theorem, the local solvability of the regularized system corresponding to the original system is established. Then by extracting a suitable sequence along which the respective approximate solutions approach a limit in convenient topologies, with addition of Gagliardo-Nirenberg interpolation inequality as well as Lp-estimate techniques, we show that the original system describing the virus infection model exists at least one global weak solution. To illustrate the application of our theoretical results, an optimal control problem of the epidemic system is considered, where the admissible control domain is assumed to be a bounded closed convex subset. With the help of Aubin compactness theorem and lower semicontinuous of the cost functional, the existence of the optimal pair is proved. Our results generalize and improve partial previously known ones, and moreover, we first prove that the optimal control problem has at least one optimal pair.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Global Existence of a Virus Infection Model with Saturated Chemotaxis
AU  - Ruijing Li
Y1  - 2021/05/27
PY  - 2021
N1  - https://doi.org/10.11648/j.ijssam.20210602.12
DO  - 10.11648/j.ijssam.20210602.12
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 40
EP  - 54
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20210602.12
AB  - In this paper, a virus infection model with saturated chemotaxis is formulated and analyzed, where the chemotactic sensitivity for chemotactic movements of the cells is described. This model contains three state variables namely the population density of uninfected cells, the population density of infected cells and the concentration of virus particles, respectively. By virtue of regularized approximation technique and fixed point theorem, the local solvability of the regularized system corresponding to the original system is established. Then by extracting a suitable sequence along which the respective approximate solutions approach a limit in convenient topologies, with addition of Gagliardo-Nirenberg interpolation inequality as well as Lp-estimate techniques, we show that the original system describing the virus infection model exists at least one global weak solution. To illustrate the application of our theoretical results, an optimal control problem of the epidemic system is considered, where the admissible control domain is assumed to be a bounded closed convex subset. With the help of Aubin compactness theorem and lower semicontinuous of the cost functional, the existence of the optimal pair is proved. Our results generalize and improve partial previously known ones, and moreover, we first prove that the optimal control problem has at least one optimal pair.
VL  - 6
IS  - 2
ER  -

Copy | Download