Semi-analytical solutions for the delayed and diffusive viral infection model with logistic growth

Volume 12, Issue 9, pp 589--601 http://dx.doi.org/10.22436/jnsa.012.09.04

Publication Date: May 03, 2019 Submission Date: January 11, 2019 Revision Date: April 03, 2019 Accteptance Date: April 07, 2019

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Authors

H. Y. Alfifi - Department of Basic Sciences, College of Education, Imam Abdulrahman Bin Faisal University, Dammam, Saudi Arabia.

Abstract

In the one-dimensional reaction-diffusion domain of this study, semi-analytical solutions are used for a delayed viral infection system with logistic growth. Through an ordinary differential equations system, the Galerkin technique is believed to estimate the prevailing partial differential equations. In addition, Hopf bifurcation maps are constructed. The effect of diffusion coefficient stricture and delay on the model is comprehensively investigated, and the outcomes demonstrate that diffusion and delay can stabilize or destabilize the system. We found that, as the delay parameter values rise, the values of the Hopf bifurcations for growth and the rates of viral death are augmented, whereas the rate of production is decreased. For the growth, production, and death rates strictures, there is determination of an asymptotically unstable region and a stable region. Illustrations of the unstable and stable limit cycles, as well as the Hopf bifurcation points, are found to prove the formerly revealed outcomes in the Hopf bifurcation map. The results of the semi-analytical solutions and numerical assessments revealed that the semi-analytical solutions are highly effective.

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Keywords

• Reaction-diffusion
• delay
• Hopf bifurcations
• viral infection
• semi-analytical solutions
• limit cycle

MSC

•  35K57
•  34C05
•  34K18
•  34-XX
•  35-XX

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