@Article{cmes.2025.067397,
AUTHOR = {Benjamin Wacker, Jan Christian Schlüter},
TITLE = {A Time-Continuous Model for an Untreated HIV-Infection and a Novel Non-Standard Finite-Difference-Method for Its Discretization},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {144},
YEAR = {2025},
NUMBER = {2},
PAGES = {2191--2229},
URL = {http://www.techscience.com/CMES/v144n2/63711},
ISSN = {1526-1506},
ABSTRACT = {In this work, we re-investigate a classical mathematical model of untreated HIV infection suggested by Kirschner and introduce a novel non-standard finite-difference method for its numerical solution. As our first contribution, we establish non-negativity, boundedness of some solution components, existence globally in time, and uniqueness on a time interval  for an arbitrary  for the time-continuous problem which extends known results of Kirschner’s model in the literature. As our second analytical result, we establish different equilibrium states and examine their stability properties in the time-continuous setting or discuss some numerical tools to evaluate this question. Our third contribution is the formulation of a non-standard finite-difference method which preserves non-negativity, boundedness of some time-discrete solution components, equilibria, and their stabilities. As our final theoretical result, we prove linear convergence of our non-standard finite-difference-formulation towards the time-continuous solution. Conclusively, we present numerical examples to illustrate our theoretical findings.},
DOI = {10.32604/cmes.2025.067397}
}