Key result
An age-structured mathematical model of hand-foot-mouth disease demonstrated that the disease-free equilibrium is globally stable when R0<1, whereas an endemic equilibrium exists and is stable when R0>1.
The study provides a mathematical framework demonstrating that the basic reproduction number R0 determines the global stability of hand-foot-mouth disease in an age-structured model with time delay.
May inform HFMD modeling for outbreak thresholds; leaves open clinical translation without empirical validation.
The global dynamic behavior of an age-structured hand-foot-mouth disease (HFMD) model with saturation incidence and time delay is investigated in the work. The time delay occurs during the transition from latent to infectious individuals. Firstly, the model is expressed as an abstract Cauchy problem. The presence of equilibria is then pointed; meanwhile, we define the model’s basic reproduction number R0 . The conclusions show that a threshold of R0=1 can be used to evaluate whether the disease is on the verge of extinction or is still present. When R0<1 , the disease-free equilibrium is globally stable. While R0>1 , there exists an endemic equilibrium, and the global stability of the endemic equilibrium is also demonstrated. Finally, some numerical examples are given to demonstrate the obtained conclusions.
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Yan et al. (2023) studied Hand-foot-mouth disease (HFMD). Age-structured mathematical model with saturation incidence and time delay was evaluated on Basic reproduction number (R0) threshold and equilibrium stability. An age-structured mathematical model of hand-foot-mouth disease demonstrated that the disease-free equilibrium is globally stable when R0<1, whereas an endemic equilibrium exists and is stable when R0>1.
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