Minimal Wave Speed for a Nonlocal Viral Infection Dynamical Model
Abstract
:1. Introduction
- , , , J is compactly supported and for all .
2. Traveling Wave Solutions
2.1. The Existence of Traveling Fronts for
- If , the equation admits two positive roots and satisfying , for , for , and
- If , then , and for all
- If , then for all
2.2. The Existence of a Traveling Front with Wave Speed
2.3. The Nonexistence of Traveling Fronts for
3. Discussion of Results
- Choose an appropriate spatial domain and then discretize it. We take the domain to be . The discretization step size is , which results in 5001 ordinary differential equations. Under our specified parameters and initial values, the viruses are always away from the boundaries of the domain during our simulation.
- Let be the time step. We use the ode45 function in Matlab to solve the ordinary differential equations for numerical simulation.
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Ren, X.; Liu, L.; Zhang, T.; Liu, X. Minimal Wave Speed for a Nonlocal Viral Infection Dynamical Model. Fractal Fract. 2024, 8, 135. https://doi.org/10.3390/fractalfract8030135
Ren X, Liu L, Zhang T, Liu X. Minimal Wave Speed for a Nonlocal Viral Infection Dynamical Model. Fractal and Fractional. 2024; 8(3):135. https://doi.org/10.3390/fractalfract8030135
Chicago/Turabian StyleRen, Xinzhi, Lili Liu, Tianran Zhang, and Xianning Liu. 2024. "Minimal Wave Speed for a Nonlocal Viral Infection Dynamical Model" Fractal and Fractional 8, no. 3: 135. https://doi.org/10.3390/fractalfract8030135