Numerical approximation of basic reproduction number for an
age-structured HIV infection model with both virus-to-cell and
In general, the basic reproduction number (R0) cannot be explicitly
calculated for HIV(Human Immunodeficiency Virus) infection model with
age-structured in a infinite dimensional spaces. To find R0, we need to
transform the HIV model into a finite-dimensional space. In this paper,
we are absorbed in numerical approximation of R0, which is the
non-negative dominant eigenvalues of the positive irreducible matrices
whose spectrum radius is defined as the next generation matrix. The
linear operators generated by infected population are discretized into
ordinary differential equations in a finite n-dimensional space. Thus,
the abstract problem is transformed to find the positive dominant
eigenvalues of the next generation matrix, we obtain a threshold R_0,n.
Based on the spectral approximation theory, we show that R_0,n →R0 as n
→+∞. Finally, by virtue of a numerical simulation, we demonstrate the
results of the theorem.