The numerical approximation to a stochastic age-structured HIV/AIDS model with nonlinear incidence rates. (English) Zbl 1492.92109
Summary: In this paper, a stochastic age-structured HIV/AIDS model with nonlinear incidence rates is proposed. It is of great importance to develop efficient numerical approximation methods to solve this HIV/AIDS model since most stochastic partial differential equations (SPDEs) cannot be solved analytically. From the perspective of biological significance, the exact solution of the HIV/AIDS model must be nonnegative and bounded. Then a modified explicit Euler-Maruyama (EM) scheme is constructed based on a projection operator. The EM scheme could preserves the nonnegativity of the numerical solutions and also make the numerical solutions not outside the domain of the exact solutions. The convergence results between the numerical solutions and the exact solutions are analyzed, and some numerical examples are given to verify our theoretical results.
MSC:
| 92D30 | Epidemiology |
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 65C20 | Probabilistic models, generic numerical methods in probability and statistics |
Keywords:
stochastic age-structured HIV/AIDS model; explicit Euler-Maruyama scheme; projection operator; convergenceReferences:
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