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28 April 2023 Analysis of a multi-state HIV transmission model based on differential dynamical system
Shuyuan Chen
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Proceedings Volume 12610, Third International Conference on Artificial Intelligence and Computer Engineering (ICAICE 2022); 126104M (2023) https://doi.org/10.1117/12.2671263
Event: Third International Conference on Artificial Intelligence and Computer Engineering (ICAICE 2022), 2022, Wuhan, China
Abstract
In this paper, a multi-state AIDS model is developed and used to analysis the potential impact of a non-complete vaccine immunization. The model is a nonlinear ODE system, also a differential dynamical system. In this paper, we divide AIDS into multiple-state and construct ODE for the change in the number of people in each stage. The main point of this paper is to proof that the transmission of AIDS in the population is stable under vaccine immunization. The form of stability under different conditions is also given. Firstly, our article describes the parameters and builds the model, then verifies the well-definition and positive invariance of the model. Next, the concept of basic reproduction number ℛ0 is introduced from the next generation matrix. Importantly, in order to verify the disease-free equilibrium of the model, we use the Lyapunov function to proof globally asymptotically stable of the ODE system. In the proof, we know: the system is globally asymptotically stable when ℛ0 ≤ 1. In addition, when ℛ0 ⪆ 1, the system has a unique endemic equilibrium solution, i.e. locally stable. Finally, after the proof, we conclude: (1) If we can keep the ℛ0 ≤ 1, AIDS will die out when time tends to infinity. (2) If ℛ0 ⪆ 1, the infected population would exist in the population at a constant rate for a long time, that is, the proportion of the infected population tends to 1 - 1/ℛ0. The main innovation of this paper is to use a system of ODEs to describe the infection status of the AIDS population.
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Shuyuan Chen "Analysis of a multi-state HIV transmission model based on differential dynamical system", Proc. SPIE 12610, Third International Conference on Artificial Intelligence and Computer Engineering (ICAICE 2022), 126104M (28 April 2023); https://doi.org/10.1117/12.2671263
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KEYWORDS
Diseases and disorders
Matrices
Dynamical systems
Differential equations
Complex systems
Data modeling
Data transmission
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