Intracellular Virus Dynamics A Study of The Converting from The Deterministic Model to its Stochastic Counterpart

Asmahan M. A.  Billiwa; Abdalsalam B. H.  Aldaikh

doi:10.54172/kt3kdf94

Authors

Asmahan M. A. Billiwa Department of Mathematics, Faculty of Science, University of Omar Al-Mukhtar, Libya Author
Abdalsalam B. H. Aldaikh Department of Mathematics, Faculty of Science, University of Omar Al-Mukhtar, Libya Author

DOI:

https://doi.org/10.54172/kt3kdf94

Keywords:

Intracellular Virus Movement Model, Stochastic Model, Covariance Matrix, Diffusion Matrix

Abstract

By examining both deterministic and stochastic models, the intracellular viral movement model explores the complex dynamics of the interaction of viruses with host cells. Since such movement is not deterministic but rather random, the main goal of this study is to build a stochastic model corresponding to the deterministic one, that describes the movement of viruses and their intracellular interactions in a more realistic way. The model helps explain how viruses are produced and reproduce by analyzing the mechanisms that generate and deplete structural proteins and viral nucleic acids, and by examining the effect of the viral template, the findings may help improve methods for treating and preventing viral infections by shedding light on structural proteins and viral DNA. The deterministic and stochastic systems were solved numerically and represented using MATAB tools, to gain deeper insights.

References

Allen, L. J. (2010). An introduction to stochastic processes with applications to biology. CRC press.

Chou, C.-S., & Friedman, A. (2015). Introduction to Mathematical Biology.

Dimitrov, D. S. J. N. R. M. (2004). Virus entry: molecular mechanisms and biomedical applications. 2(2), 109-122.

Forterre, P. J. O. H. U., Sem Monogr. (2017). The origin, nature and definition of viruses (and life): new concepts and controversies. 31, 15-26.

Gelderblom, H. R. J. M. M. t. e. (1996). Structure and classification of viruses.

Harley, J. (2002). L. and Prescott, M.“Laboratory Exercises in Microbiology Fifth Edition”. In: McGraw-Hill Companies. New York.

Miao, H., Hollenbaugh, J. A., Zand, M. S., Holden-Wiltse, J., Mosmann, T. R., Perelson, A. S.,…Topham, D. J. J. J. o. v. (2010). Quantifying the early immune response and adaptive immune response kinetics in mice infected with influenza A virus. 84(13), 6687-6698.

Modrow, S., Falke, D., Truyen, U., & Schätzl, H. J. M. V. (2013). Viruses: definition, structure, classification. 17.

Srivastava, R., You, L., Summers, J., & Yin, J. J. J. o. t. b. (2002). Stochastic vs. deterministic modeling of intracellular viral kinetics. 218(3), 309-321.

Varanda, C., Félix, M. d. R., Campos, M. D., & Materatski, P. J. V. (2021). An overview of the application of viruses to biotechnology. 13(10), 2073.