The ACE2 receptor protein-mediated SARS-CoV-2 infection: dynamic properties of a novel delayed stochastic system

Kai Zhang; Xinzhu Meng; Abdullah Khames Alzahrani; Kai Zhang; Xinzhu Meng; Abdullah Khames Alzahrani

doi:10.3934/math.2024394

AIMS Mathematics

2024, Volume 9, Issue 4: 8104-8133. doi: 10.3934/math.2024394

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Research article

The ACE2 receptor protein-mediated SARS-CoV-2 infection: dynamic properties of a novel delayed stochastic system

1.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
2.
Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Received: 05 January 2024 Revised: 17 February 2024 Accepted: 18 February 2024 Published: 26 February 2024
MSC : 37H10, 60H10

We investigated the dynamic effect of stochastic environmental fluctuations on the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus infection system with time delay and mediations by the angiotensin-converting enzyme 2 (ACE2) receptor protein. First, we discussed the existence and uniqueness of global positive solutions as well as the stochastic ultimate boundedness of the stochastic SARS-CoV-2 model. Second, the asymptotic properties of stochastic time-delay system were investigated by constructing a number of appropriate Lyapunov functions and applying differential inequality techniques. These properties indicated a positive relationship between the strength of oscillations and the intensity of environmental fluctuations, and this launched the properties of a deterministic system. When the random disturbance was relatively large, the disease went extinct. When the random disturbance was relatively small and $ R_0 < 1 $, the disease could become extinct. Conversely, when the random disturbance was smaller and $ R_0 > 1 $, then it would oscillate around the disease enduring equilibrium. At last, a series of numerical simulations were carried out to show how the SARS-CoV-2 system was affected by the intensity of environmental fluctuations and time delay.
- stochastic environmental fluctuations,
- SARS-CoV-2 system,
- Lyapunov functional,
- time delay,
- asymptotic properties
Citation: Kai Zhang, Xinzhu Meng, Abdullah Khames Alzahrani. The ACE2 receptor protein-mediated SARS-CoV-2 infection: dynamic properties of a novel delayed stochastic system[J]. AIMS Mathematics, 2024, 9(4): 8104-8133. doi: 10.3934/math.2024394

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Abstract

We investigated the dynamic effect of stochastic environmental fluctuations on the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus infection system with time delay and mediations by the angiotensin-converting enzyme 2 (ACE2) receptor protein. First, we discussed the existence and uniqueness of global positive solutions as well as the stochastic ultimate boundedness of the stochastic SARS-CoV-2 model. Second, the asymptotic properties of stochastic time-delay system were investigated by constructing a number of appropriate Lyapunov functions and applying differential inequality techniques. These properties indicated a positive relationship between the strength of oscillations and the intensity of environmental fluctuations, and this launched the properties of a deterministic system. When the random disturbance was relatively large, the disease went extinct. When the random disturbance was relatively small and $ R_0 < 1 $, the disease could become extinct. Conversely, when the random disturbance was smaller and $ R_0 > 1 $, then it would oscillate around the disease enduring equilibrium. At last, a series of numerical simulations were carried out to show how the SARS-CoV-2 system was affected by the intensity of environmental fluctuations and time delay.

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