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Numerical approximation of basic reproduction number for an age‐structured HIV infection model with both virus‐to‐cell and cell‐to‐cell transmissions.
- Source :
-
Mathematical Methods in the Applied Sciences . 11/30/2021, Vol. 44 Issue 17, p12851-12859. 9p. - Publication Year :
- 2021
-
Abstract
- The basic reproduction number (R0) often cannot be explicitly computed when dealing with continuously age‐structured epidemic models. In this paper, we numerically compute R0 of a PDE model for a human immunodeficiency virus (HIV) infection, defined as the spectral radius of a next‐generation operator. Since R0 cannot be analytically obtained, on the one hand, we discretize the linearized PDE model into a system of linear ODEs (Euler method), and on the other hand, we discretize the eigenvalue problem (pseudo‐spectral method). In both cases, we approximate R0 by the largest eigenvalue R0, n of a next‐generation matrix, and we show the convergence of R0, n to R0 as the discretization index n increases to infinity. Finally, we present several tests to check/compare the accuracy of both numerical methods. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01704214
- Volume :
- 44
- Issue :
- 17
- Database :
- Academic Search Index
- Journal :
- Mathematical Methods in the Applied Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 153434179
- Full Text :
- https://doi.org/10.1002/mma.7586