Dynamics of simplicial SEIRS epidemic model: global asymptotic stability and neural Lyapunov functions.
J Math Biol
; 89(1): 12, 2024 Jun 16.
Article
em En
| MEDLINE
| ID: mdl-38879853
ABSTRACT
The transmission of infectious diseases on a particular network is ubiquitous in the physical world. Here, we investigate the transmission mechanism of infectious diseases with an incubation period using a networked compartment model that contains simplicial interactions, a typical high-order structure. We establish a simplicial SEIRS model and find that the proportion of infected individuals in equilibrium increases due to the many-body connections, regardless of the type of connections used. We analyze the dynamics of the established model, including existence and local asymptotic stability, and highlight differences from existing models. Significantly, we demonstrate global asymptotic stability using the neural Lyapunov function, a machine learning technique, with both numerical simulations and rigorous analytical arguments. We believe that our model owns the potential to provide valuable insights into transmission mechanisms of infectious diseases on high-order network structures, and that our approach and theory of using neural Lyapunov functions to validate model asymptotic stability can significantly advance investigations on complex dynamics of infectious disease.
Palavras-chave
Texto completo:
1
Base de dados:
MEDLINE
Assunto principal:
Simulação por Computador
/
Doenças Transmissíveis
/
Conceitos Matemáticos
/
Epidemias
/
Modelos Biológicos
Limite:
Humans
Idioma:
En
Ano de publicação:
2024
Tipo de documento:
Article