Numerical analysis demonstrates that discontinuous Galerkin schemes preserve threshold stability in age-structured tuberculosis models, highlighting reliable epidemic predictions.
This paper investigates the numerical threshold stability of an age-structured tuberculosis (TB) transmission model. The age domain is discretized using discontinuous Galerkin (DG) methods, yielding a semi-discrete numerical system. To ensure biological relevance, we rigorously analyze the positivity and boundedness of the numerical solutions. Additionally, by examining the existence of equilibria states, we introduce a numerical basic reproduction number [Formula: see text], which is shown to converge to the analytical basic reproduction number [Formula: see text]. Our results demonstrate that the proposed numerical threshold [Formula: see text] effectively characterizes the stability of the system. Furthermore, we extend this framework to a fully discrete scheme constructed via the linearly implicit Euler method, proving that analogous stability properties hold. Finally, numerical experiments validate the theoretical findings and illustrate the accuracy and robustness of the proposed methods.
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Yang et al. (2026) studied this question.
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